Title: Optima
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Permanent Link: http://ufdc.ufl.edu/UF00090046/00055
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Title: Optima
Series Title: Optima
Physical Description: Serial
Language: English
Creator: Mathematical Programming Society, University of Florida
Publisher: Mathematical Programming Society, University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: October 1997
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Volume ID: VID00055
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Mathematical Programming Society Newsletter

A a n ta s t i c


Left to right:
Dominique de Werra,
George B. Dantzig and
Tom Liebling at the
opening session in
the concert hall.

The Sixteenth International Symposium on Mathematical
Programming, August 24-29, 1997, was hosted by Ecole
Polytechnique Feddrale de Lausanne (EPFL). Tom Liebling,
Dominique de Werra and their team made a great effort to
organize a symposium of supreme quality that was also the
biggest one ever. Despite the size of the meeting, the organization
ran as smoothly as for a small workshop. We thank them all!

council news 12 conference notes 14

The opening session was held on
Monday, August 25 in the Metropole
Concert Hall downtown Lausanne.
Tom Liebling called the meeting to or-
der. Welcome addresses were also given
by A. Bidaud, President of the City
Council of Lausanne, J.-C. Badoux,
President of the EPFL, and Dominique
de Werra, Vice-President of the EPFL
and International Advisory Committee
Chair. Plenary talks were given by
George B. Dantzig: "How Linear
Programming First Began," and John
Dennis, Chairman of the Mathematical
Programming Society: "An Essential
Tool for Decision Support."
During the opening session the Beale-
Orchard-Hays, Dantzig, Fulkerson
and Tucker prizes were awarded or
announced. The jury reports and the
names of the prize winners can be
found on the following pages.
reviews 17 gallimaufry 19


A In



The scientific program consisted of 446 parallel sessions divided over 25
different topics. Twenty-five semiplenary lectures were presented. The number
of participants was the biggest ever: 2268 people from 63 countries. The
following special sessions were organized:

Anthony V. Fiacco's 70th Birthday
Philip Wolfe's 70th Birthday
The Pivot Choice Challenge, with Love to George
Tucker Prize Session
Steven Vajda Memorial Session
The Mystical Power ofTwoness: In Memoriam Eugene L. Lawler.

Equally well taken care of was the social program. On Tuesday evening, August
26, a Simplex Birthday Party was organized. The Master of Ceremonies was Dick
Cottle, and speeches were given by Bob Bixby, Hans Kuenzi, Tom Magnanti, and
Phil Wolfe. All these addresses are included in OPTIMA, beginning on Page 4.
Wednesday evening featured a cruise and banquet on Lac Leman. The Collkge de
Cuivres de Suisse Romande provided beautiful musical intermezzi.

Clyde Monma (L) and Les
Trotter, previous and cur-
rent Society treasurers.

ww ttciS


The 1997 Beale-Orchard-Hays Prize
The Beale-Orchard-Hays Prize is dedicated to the memory of
Martin Beale and William Orchard-Hays, two pioneers in com-
putational mathematical programming.
The Beale-Orchard-Hays Prize honors a paper or book on com-
putational mathematical programming. There are three criteria
that are important in selecting the winning nomination:
1. The magnitude of the contribution to the advancement of
computational and experimental mathematical programming.
2. The originality of the ideas and methods.
3. The clarity and excellence of the exposition.
For the 1997 award, the work must have appeared in the open
literature within the years 1993 through 1996.
After reviewing many excellent nominations, the prize commit-
tee decided to award the 1997 prize to Steven Dirkse (pictured,
left) and Michael Ferris (right) for their paper: "The PATH
Solver: A Nonmonotone Stabilization Scheme for Mixed
Complementarity Problems" which appeared in the journal
"Optimization Methods and Software" in 1995.
In their paper the authors propose a pivoting-based Newton's
method for the mixed complementarity problem, a problem
which is important since it includes several problems such as
solving the KKT conditions for nonconvex nonlinear program-
ming, finding equilibria of games both with linear and nonlin-
ear structure, and solving variational inequalities. In extensive
computational testing, the solver described in the paper domi-
nates every other recent code in efficiency. It is also very robust.
Furthermore, the authors have been instrumental in collecting
the first comprehensive test set for this important class of prob-
lems. They have made this test set, called MCPLIB, as well as
various algorithms, available for comparative testing at the Uni-
versity of Wisconsin.




10 PT I M A 5i


The 1997 Dantzig Prize
The George B. Dantzig Prize is
jointly administered by the Math-
ematical Programming Society and
the Society for Industrial and Ap-
plied Mathematics. This prize is
awarded to one or more individuals
for original research which, by virtue
of its originality, breadth and depth,
is having a major impact on the field
of mathematical programming. The
contributions eligible for consider-
ation must be publicly available and

may address any aspect of mathemati-
cal programming in its broadest
The 1997 George B. Dantzig Prize
was jointly awarded to Roger
Fletcher and Stephen M. Robinson
"for sustained, fundamental, and illu-
minating contributions to the area of
mathematical programming ranging
from stability theory and sensitivity
analysis to broad algorithmic develop-
ments in nonlinear programming."

Justification: It is the committee's
unanimous judgment that the broad,
sustained, and fundamental works of
Roger Fletcher and Steve Robinson
deserve the Dantzig Prize. One can-
not consider the nonlinear part of
mathematical programming without
wondering why they have not already
been recognized.
Roger Fletcher has made fundamental
algorithmic contributions to almost
all areas of nonlinear optimization.
He is well-known for his contribu-
tions to the development of nonlinear
conjugate gradient and variable-met-
ric methods for unconstrained opti-
mization, but his contributions have
also had a profound impact on non-
linear least squares and nonlinearly
constrained optimization. His influ-
ence on the development of optimiza-
tion and its impact on applications is
deep and far-reaching.

Steve Robinson's work has funda-
mentally affected the analysis of the
solution, stability, and sensitivity of
nonlinear optimization problems. In
particular, he introduced generalized
equations and the strong-regularity
condition into optimization. His
work has had a major impact in the
analysis and development of algo-
rithms for systems of nonlinear equa-
tions, nonlinear complementarity,
variational inequalities, and
nonlinearly constrained optimiza-
Not only is their contribution im-
portant, but its sustained nature con-
tinues to impress us.

Roger Fletcher and Stephen M. Robinson are congratulated by Ellis Johnson (R).

The D. Ray Fulkerson Prize
The D. Ray Fulkerson Prize in Dis-
crete Mathematics was awarded at
the opening session of the XVI In-
ternational Symposium on Math-
ematical Programming held in
Lausanne, Switzerland.
The committee for the 1997 prize
consisted of Ron Graham, Ravi
Kannan, and Eva Tardos (chair).
To be eligible, papers had to be
published in a recognized journal
during the six calendar years pre-
ceding the year of the Symposium.
The term discrete mathematics is in-
tended to include graph theory, net-
works, mathematical programming,
applied combinatorics, and related
subjects. While research in these ar-
eas is usually not far removed from
practical applications, the judging
of papers is based on their math-
ematical quality and significance.

The 1997 Fulkerson prize was awarded to Jeong
Han Kim, for the paper The Ramsey Number
R(3,t) Has Order, .1 which ap-
peared in Random Structures and Algorithms vol 7
issue 3, 1995, pages 173-207.

The Ramsey number R(s,t) is the minimum n such
that every red-blue coloring of the edges of the
complete graph K includes either a red complete
graph on s nodes or a blue complete graph on t
nodes. The Ramsey number was introduced by
Erd6s and Szekeres in a paper in 1935. The 1947
paper by Erd6s on the symmetric Ramsey number
R(t,t) is generally viewed as the start of the proba-
bilistic method in combinatorics. Since then de-
velopments in bounds on the Ramsey number
have been intertwined with developments of the
probabilistic method.

After the symmetric case, the Ramsey number
R(3,t) is the most studied. Erd6s and Szekeres
proved that R(3,t) is O(t), this upper bound was
improved by Graver and Yackel in 1968 to
0 (t2 LE), and then in 1990 by Ajtai, Koml6s,
and Szemeridi to 0 l-). The best known lower
bound for R(3,t) was W Ic due to a 1961 pa-
per by Erd6s.

Jeong Han Kim's paper solves this 60-year-old
problem by improving the Erd6s lower bound to
match the upper bound ofAjtai,
Koml6s, and Szemeredi. The
paper is a veritable cornucopia
of modern techniques in the

probabilistic method; it uses mar-
tingales in a sophisticated wa, r..
obtain strong large deviation
bounds. J f

0 P T I M A -5 51


David Karger

The 1997 Tucker Prize
The jury examined 21 sub-
mitted papers. The '97 vin-
tage is abundant, diversified
and of high quality. It covers
many fields of Mathematical
Programming and gives en-
couraging evidence of the vi-
tality of the Society.
The choice of three finalists
was difficult. The jury solic-
ited the advice of some re-
nowned specialists. We would
like to thank them for their
anonymous but highly appre-
ciated contributions. As one
of them put it, "Phew, it was
The three finalists are David
Karger, James Geelen, and
Luis Vicente.
The winner is David Karger.
His thesis on "Random sam-
pling in graph optimization
problems" is at the crossroads
of computer science and opti-
mization. Karger showed that
applying random sampling to
traditional network optimiza-
tion leads to surprisingly
simple algorithms whose run-
ning times are asymptotically
faster than previously known
algorithms for these problems.
In particular, he gives a linear
time algorithm for computing
a minimum cost spanning tree
and an O(n2) algorithm for
computing a global minimum
cut. The jury found the con-
tribution deep, original and
The second laureate is James
Geelen for his work on
"Matchings, matroids and
unimodular matrices." In his
thesis James Geelen general-
izes the idea of unimodular
matrices to square matrices,
focusing on the principal mi-
nors. Just as matrices and
their minors link with
matroids, square matrices and
their principal minors link

Jallc (acI


with objects known as "Delta-
matroids." Geelen obtained a
nice generalization of results of
Camion on unique
representability and of Tutte
on excluded minors. Some of
his proof techniques have al-
ready been applied with success
to solve other difficult prob-
Our third laureate is Luis
Vicente. His work entitled
"Trust-region interior-point
algorithms for a class of nonlin-
ear programming problems"
pertains to the domain of con-
tinuous optimization. By
drawing on the most efficient
known techniques such as
sequential quadratic program-
ming, trust regions and interior
point algorithm, Luis Vicente
proposes and analyzes new
efficient methods to solve
difficult nonlinear program-
ming problems, in particular,
those arising in the area of
optimal control.


Master of Ceremonies
Richard W Cottle's Speech
"As you know, tonight we are here to celebrate
the 50th birthday of the Simplex Method. It's the
type of thing that some people call The Big Five-
Oh. Sometimes it is an occasion to take stock and
think about the half century that's passed and
perhaps the half that might be coming. In any
event, these have been fifty incredibly productive
and happy years despite the appearance of certain
upstarts [interior point methods] now in their
One might ask what the future holds in store for
the Simplex Method will there be a mid-life cri-
sis? Who knows? Here is a somewhat pessimistic
thought from the English poet, T.S.
S Eliot. He said 'The years between fifty
and seventy are the hardest. You
are always being asked to do
Things and are not yet decrepit
enough to turn them
down.' Well, being in that
age bracket, I can attest to
rli.. truth of that state-
ment. However, I
think there is a
much more optimis-
tic way of looking at
Things, and that is
what we are here to do
Ss' 'me twenty-one years ago at
Srl-.. symposium in Budapest,
Jack Edmonds gave me this little
pin. It's a likeness of a polytope,
and with a little generosity, you
could think of it as a simplex I'm
sure Jack did. On this simplex is written
NON STOP MAGIC. I think we've got a
magical method that we've been benefiting
from for a long time, and I prefer to think
that this magic will continue to be here
: in a non-stop way. Certainly the inspir-
0 \<



10 P T I M~ A 5 5



v ing example set by its inventor, George
Dantzig, gives a lot of support to this

O point of view.
Now I'd like to tell you what we have in
store for the presentations this evening.
We'll have four speakers, the first of
whom I'll introduce in a moment. Once these
talks are over, I think we should all participate in
a nice singing of a certain
song, and you may feel
free to use the Simplex
Method's first name in
this. T
So let me call forward the
first of our speakers this
evening. This is H.P.
Kuenzi. I'd like to say just
a word or two about him.
For those of you who are
not so acquainted with the
scene here in Switzerland, he is a very important
figure due in part to his early involvement in
mathematical programming and operations re-
search generally. He is a coauthor of a very well-
known book on nonlinear programming. It was,
for example as I understand it the first Ger-
man language book on the subject ever pub-
lished. He was a founder and a driving force in
the formation of the Swiss OR Society, and you
are probably aware of the fact that he subse-
quently had a career in politics and affairs of
state. It is a great pleasure for me to introduce to
you H.P. Kuenzi."

Hans Kuenzi's Speech
"It is a great honor for our country that the im-
portant and high-level International Symposium
on Mathematical Programming is held in Swit-
zerland at the EPFL. We are very happy that we
have the unique opportunity to discuss with more
than 1400 scientists from 62 different countries
the large field of mathematical programming,
which developed immensely during the past

years. As president of the Support Committee of
our Symposium I have also the honor to welcome
you to Lausanne in the French-speaking part of
Ladies and gentlemen, before I turned to politics
(as a member of the government of the Canton
Zurich), I was professor of Mathematics of Op-
erations Research at the University of Zirich. In
this double function as politician and
mathematician I am very glad about
two important events: As a Swiss politi-
cian I am glad that the constitution of
our state can celebrate its 150th birth-
day. As a mathematician I
am also glad that we can
celebrate the 50th Simplex
Birthday Party at this ex-
clusive Symposium.
At this occasion I remem-
ber the times when we in
Switzerland began to study new
methods for linear programming. I
myself received a grant in 1958 from
the Swiss national science founda-
tion, which gave me the opportu-
nity, as a young professor, to study
the new field of operations research
in the USA. There I had the grand
opportunity to meet you, George
Dantzig, at the Rand Corporation in .
Santa Monica, and I recall the inter-
esting discussions with you about the
theory and applications of linear programming in
several domains, especially in economics. At the
same time I became acquainted with Philip
Wolfe whose works, especially on the theory of
nonlinear programming, I appreciated very
When I returned to Switzerland, I gave my first
courses in linear programming in Zurich and
started writing my first book in German, also on
Linear Programming, together with Professor
Willhelm Krelle from the University of St Gallen.
It was the first book on this topic that appeared

in Switzerland. The reason this book was so
popular among the students was surely the sym-
pathetic 'Introductory Remarks of George B.
Dantzig,' which he began with the words, 'In the
briefspan of one decade from its conception in
1947, in connection with the planning activities of
the military, linearprogramming has come into
wide use in industry. In academic circles, mathema-
ticians and economists have written books on the
subject. Interestingly enough, in spite of its wide ap-
plicability to everyday problems, linearprogram-
ming was unknown except for isolated examples
without influence before 1947.. 'I am sure that
this first book stimulated many students in Swit-

zerland to study this interesting algorithm.
In the beginning of the sixties several chairs in
operation research and computer science were
created where, within the field of applied math-
ematics, the theory and practice of mathematical
programming and the simplex algorithm were
treated more and more.
Dear George Dantzig, with these short greetings I
hope to have convinced you that, thanks to you,
linear programming and the simplex method
came to Switzerland. I thank you forty years later
for this, and I am happy to be able to celebrate




0 P T I M A -5 51





the 50th birthday of the Simplex Algorithm,
whose father you are, together with you here.
As a little birthday gift I again give you the little
book, written 40 years ago, entitled Linear Pro-
gramming, with introductory remarks from
George B. Dantzig, where you finally wrote, 'This
paper is an introduction for German speaking read-
ers to the basic ideas of linear programming and in
particular to the simplex method. It is with great
pleasure that I recommend this book to those inter-
ested in the subject.
September 11, 1958 George B. Dantzig, The Rand
Corporation, Santa Monica, California"

"It's been suggested by a number of people that I
have some jokes ready for this occasion, but as
you see, there is no audio-visual equipment here,
and I wouldn't be able to identify those jokes
with slides that would tell you they're jokes; so
I'm going to skip that and move along to the next
speaker, who will be Phil Wolfe.
Phil Wolfe began his career at Princeton after
graduating from Berkeley. He was there for a
while and then joined the RAND Corporation
where he worked in the field of mathematical
programming for many years, developing an
enormous number of ideas from which we all
have derived great benefit. I'm happy to say that
I've known him since 1961 and regard him as a
good friend. It's a pleasure to introduce him to
you now.

Phil Wolfe's Speech
(The editor has kindly allowed me to expand on
the remarks I made at the banquet. What follows
is what I would have said were it not that ban-
quet diners, unlike readers, cannot skip para-
"I was delighted at being invited to speak in cel-
ebration of the simplex method, since I owe the
major part of my career to it. I hope that it will
be heard as tribute to the simplex method and,
even more, to George Dantzig and others who
contributed so much to it.
In yesterday's plenary session George spoke of the
excitement he and his colleagues felt about their
work in the Air Force's Project SCOOP in the
forties. While Washington was the best place to
be, you didn't have to be there to share in that
excitement, as I found.

The birth year of the simplex method was also
that of the second edition of Theory of Games and
Economic Behavior by von Neumann and
Morgenstern. As a second-year graduate student
in mathematics at Berkeley in the Fall of 1949,
planning to work in the foundations of math-
ematics, I was unaware of both. My reading then
included not only Hilbert and Ackerman's
Mathematische Logik but Astounding Science Fic-
tion Magazine. The October 1949 issue of the
latter (price $0.25) changed my career. A short
story, 'The Finan-Seer' by E.L. Locke, told how a
group of university professors rescued their
school's failing finances by using something
called Game Theory to beat the stock market.
Entranced, I got the book the story cited and
started trying to understand this new kind of ap-
plication of mathematics. Converted, I found a
Berkeley professor, Edward Barankin, willing to
guide work in that area.
While not a fan of game theory, Ed was serious
about the application of mathematics to indus-
trial problems and had personal connections with
Princeton University, with the Rand Corpora-
tion, with the Management Science Research
Project at U.C.L.A., and with former Berkeley
student George Dantzig. He had me read dozens
of reports from those friends. I learned something
of the simplex method and of the broad range of
important problems that it and related techniques
might address.
When I was looking for a job for the summer of
1951, Ed turned to George, and I was invited to
work with Project SCOOP in Washington! His
people were full of the excitement he spoke of.
On arriving I visited each to learn about the
work. One, after shaking my hand, said, 'My job
is to make a detailed model of the American
economy. You'll have to excuse me now, I'm ter-
ribly busy.' Others George and Alex Orden es-
pecially had time for me; and so have they in all
the years afterward.
The work of SCOOP had attracted so much at-
tention that the Air Force and the Bureau of
Standards held the 'Symposium on Linear In-
equalities and Programming' that June (which
much later we designated the First Symposium
on Mathematical Programming). There, at my
first scientific meeting, I was thrilled to see people
I had known only through their writings: George
Forsythe, Theodore Motzkin, Albert Tucker.
At that time the possibility that degeneracy might
make the simplex method fail was of concern.

Alan Hoffman, at the Bu-
reau of Standards, had
just created the celebrated
problem on which the
method did indeed fail. George asked me to
study the issue, although he had really resolved it
already; a report by his student, Edmonston,
showed that sufficiently small perturbations in
the data of a problem would let the simplex
method work. I found that the perturbations
could be recast as a lexicographicc" ordering of
the data. That, or perhaps just that word, taken
from my German reading, was the contribution
of my first technical paper.
Returning to Berkeley I split my time between
the management science studies Barankin en-
couraged and my self-chosen thesis topic, a
theory of games with no stop rule, in which each
player would make an infinite sequence of moves.
Barankin didn't like my subject much and judged
it adequate only when a paper by David Gale and
F.M. Stewart appeared on the same subject but
with fewer results than I already had. Still, he
wanted it to be only part of my dissertation and
had me include the lexicography work as the
other. Actually, neither games nor programs got a
lot of respect at Berkeley then. A fellow graduate
student wanted me to explain linear program-
ming. 'You mean you are trying to find a certain
vertex of a polyhedron,' he asked, 'and there are
only finitely many vertices?' I answered, 'That's
right.' 'But that's trivial!' he declared. That re-
mark was easier to ignore than one by Griffith
Evans, Chairman of the department, normally
kindly, whose distinction awed us all. Toward the
end of my thesis defense he said, 'This is all very
well, Mr. Wolfe, but where is the mathematics?'
With Barankin's aid the defense succeeded. He
performed one more invaluable service, helping
me get an instructorship at Princeton University,
where I arrived in the Fall of 1954. That was just
when Albert Tucker, department chairman,
needed an eager young man to run errands, teach
calculus, and participate in his ONR Logistics
Research Project, which had supported such lu-
minaries as Shapley, Gale, and Kuhn. (Neither Al
nor I could have guessed that a life-long friend-
ship would begin there. Forty years later I told Al
how a story in Astounding Science Fiction got
me into game theory, and he told me that the au-
thor learned about it from a popular lecture of
Al's. I find that wonderful.)



10 P I M A 5i



Marguerite Frank was another member of the Lo-
gistics Project. Together we developed the basic
idea of the 'Frank-Wolfe' algorithm, tying it
closely (and probably unnecessarily) to the find-
ing of Barankin and Robert Dorfman at Berkeley,
that the solution of a convex quadratic program-
ming problem is a 'complementary' extreme
point solution in an appropriate simplex tableau.
We submitted this work, naturally, to the Naval
Research Logistics Quarterly. At the same time
Harry Markowitz, at The Rand Corporation, had
written his seminal paper modeling the portfolio
problem and solving it as a parametric quadratic
programming problem and sent it to the Quar-
terly. Our buddy Alan Hoffman was the editor,
and economically sent our paper to Harry for ref-
ereeing, and his to me. Years later Harry and I
confessed to each other that we had not really un-
derstood what we read, but felt it important, and
approved it. They appeared back to back in the
March-June, 1956 issue. I then determined to
understand Harry's algebra. I didn't, but found
that it could be modelled as basis changes in the
simplex method. That suggested an algorithm
that actually used the simplex method in the
Barankin-Dorfman tableau with a special device
to ensure complementarity. I wrote that up as 'A
simplex method for quadratic programming'
early in 1957 and rushed a copy to George, who
had joined the Rand Corporation. His letter of
January, 1957, said, 'Assuming validity of your
proof, I am very much impressed...' It was valid,
and I joined Rand in June, 1957.
It was hoped that I could replace Bill Orchard-
Hays, who had just left Rand after writing a pro-
duction simplex method routine for the IBM
704. Leola Cutler was able to adapt that code to
quadratic programming, and the observation that
only six instructions needed changing was great
advertising-if you ignored the fact that you had
to massively rearrange the punched-card input
data. I became quite skilled at wiring the card re-
producing machine. However, I found Bill's as-
sembly language routine impenetrable and pio-
neered the use of FORTRAN at Rand, to the
amusement of its professional programmers.
With Leola's help the resulting simplex method
package proved more effective than some in as-
sembly language and, owing to the modular de-
sign the higher level language facilitated, highly
flexible. It served as a vehicle for testing many
computational variants of the simplex method
and as a subroutine in other procedures. The lat-
ter aspect brought to Rand two visitors of great

importance in my later life: Michel Balinski, for
whom we programmed his new procedure for
finding all the vertices of a polyhedron, and
Ralph Gomory, who wanted it for his work in
integer programming.
I could go on for hours about the excitement of
working at Rand at that time amidst its stellar
cast (and not even mention the sun-drenched
beach a block away). Most important for me
were Ray Fulkerson and, of course, George. I've
been called a student of George's. I never was in
the formal sense, but as a colleague I certainly
studied his work and his methods. One result of
careful attention to his attacks on several differ-
ent large-scale linear programming problems was
the realization that they had a common idea that
could be formalized as what we called 'the de-
composition principle.' That concept turned out
to have great appeal it made sense in specialties
ranging from computer science to economics. I
have been gratified ever since in the linkage of
my name to George's in that work (and only
mildly vexed at seeing a recent translation from
Russian refer to 'Dantzig-Hulf).
Most of my work at Rand, until Gomory lured
me to the IBM Research Center in 1966, was
spent in testing and trying to improve variants of
the simplex method; teaching the simplex
method (UCLA and USC); extending the sim-
plex method (the reduced gradient method); and
using the simplex method practically (for ex-
ample, to prescribe a minimum-cost diet every
week for some California dairy herds). I even
used some of the simplex method in a procedure
I proposed for the solution of a system of nonlin-
ear equations, a generalization of the secant
method. It seemed good in practice and I tried
hard to establish its convergence in general, and
couldn't; indeed, a colleague showed later that it
could blow up on nice-looking problems. Un-
known to me, a distinguished predecessor pro-
posed the method a long time ago. He wrote,
'The study of its convergence presents some diffi-
culties.' I learned this from Ortega's book on
nonlinear equations, where he writes of 'the
method of Gauss and Wolfe.'
I must stop here, although I never stopped cel-
ebrating the simplex method: using it, teaching
it, even defending it against the hilariously mis-
understood threat of the ellipsoid algorithm (OP-
TIMA No. 1, June, 1980). I think I've said
enough to justify declaring gratefully, Happy
Birthday, Simplex Method!"

"The next speaker will be Tom Magnanti from
MIT. It's difficult to summarize all the accom-
plishments that Tom has racked up over the
years. He's been president of this and that, editor
of this and that Operations Research, for ex-
ample. At MIT he is a professor at the Sloan
School as well as the Department of Computer
Science. He is member of the National Academy
of Engineering. I'm delighted to say he is a
graduate of my department at Stanford. In addi-
tion to that, he was of course a prize student of
George Dantzig. It's a pleasure to welcome him
to address you this evening."

Thomas L. Magnanti's Speech
"Thank you Dick. As I was sitting at the dinner
table, I had an idea. I don't know if George
Dantzig is up to this or not; I didn't ask him
about it. But, it strikes me that in keeping with
the celebration this evening, each of us should
have a personal toast with George, and as we do
this we could contribute $10 to the Dantzig Prize
so we cannot only all jointly celebrate with
George but also collect money for this important
prize. We'll see if George is up to 1,400 toasts
this evening! I think he's still pretty robust and
probably can do it. (At this point, George
Dantzig interrupts.) George just said he'd prefer
to just contribute the money himself and forget
about the toasts.
It is difficult to follow
our previous speakers
who have so much
history of working
with George Dantzig.
Let me share one brief
story with you, and
then I'd like to do
something a little bit
different for this evening. The story goes back
about 20 years, when George was visiting MIT
and I had a few less gray hairs. On that occasion
we were traveling in my car, which had very poor
shocks, through some terrible roads, lined with
one pothole after another, in Cambridge, Massa-
chusetts. Sitting in the back seat of the car were
George Dantzig, Bob Dorfman, and Saul Gass.
As we would drive down the street, about every
ten feet we'd hit a bump, jolting them all in-
deed, it would seem that at each pothole one of
them would rise and hit his head on the top of



0 P T I M A -5 51



the car. We finally arrived safely at our destina-
tion. Later my wife Beverly said, 'You could have
set back the history of linear programming com-
pletely by driving around Cambridge with these
gentlemen; you could have killed them all off in
this one evening.'
Some of you may think that the Simplex Method
originated with George Dantzig, project
SCOOP, and the Rand Corporation. But actu-
ally the Simplex Method started in New England.
It originated late in the last century. There's a
corporation in New England called the Simplex
Wire and Cable Company. I don't know if you
ever heard of this company. It used to have a fa-
cility right next to MIT. They're the company
that installed the first transatlantic underground
telephone cable. They developed the Simplex
Method for putting cable underground. So I
think that we must address a priority issue here as
we undertake our celebration.
In graduate school, all of us develop keen friend-
ships with our fellow students, who generally are
the same age as us. In many cases, we develop
life-long relationships with these individuals.
Now I had the occasion of meeting a certain indi-
vidual, about my age, a year before I enrolled in
graduate school and this individual and I actually
had one of these rare occurrences when we trav-
eled from undergraduate to graduate school to-
gether. Occasionally, we get to meet the parents
of the students who we study with and we de-
velop lifelong relationships with them as well.
Now my newfound friend was called Simplex. I
had encountered this friend through a book that
Saul Gass had written. My friend and I traveled
to Stanford University to study. And what I'd
like to do this evening is in honor of my friend
Simplex's birthday, and as we sometimes do at
birthday parties, to recall some of the events of
the day when my friend was born. Hopefully, this
recollection will put this 50th birthday celebra-
tion in some perspective: by reflecting on some of
the events of 1947, we might be able to attain
some sense of how historic it is to have a friend
(method) who's reached such a ripe old age.

Some Events in 1947
Monumental Events
* India and Pakistan become independent.
* Hungary becomes a Soviet satellite. Romania
becomes a Communist state.
* At the Harvard commencement exercises June
5, U.S. Secretary of State George C. Marshall

proposes the Marshall Plan to give financial aid
to European countries 'willing to assist in the
task of recovery.' Congress authorized some
$12 billion in the next 4 years.
* President Truman asked Congress to aid
Greece and Turkey to combat Communist ter-
rorism March 12. Congress approves the
Truman Doctrine on May 15.
* United Nations Security Council voted unani-
mously April 2 to place under U.S. trusteeship
the Pacific islands formerly mandated to Japan.
Social and Economic Events
* The U.S. Congress passes Taft-Hartley Act,
over President Truman's veto, to curb strikes.
* The major world powers sign the General
Agreement on Tariffs and Trade (GATT) to
significantly lower tariff barriers, end some tar-
iff discrimination, and help revitalize world
* On April 11, Jackie Robinson and the Brook-
lyn Dodgers break the color barrier in major
league baseball.
* Levittown, nearly identical prefab housing,
goes up on Long Island to meet the booming
post World War II housing demand.
* Ronald Reagan becomes President-yes he does!
Of the Screen Actors Guild.
* Minute Maid Corporation has its beginnings
as the Vacuum Foods Company (more on or-
ange juice later!).
* Sony Corporation begins as the Tokyo Tele-
communications Company.
* Hollywood black list of alleged communist
sympathizers compiled.
* Paris couturier Christian Dior introduces the
'New Look' design.
Scientific Inventions/Products
* Transistor.
* Long Playing Records.
* B.F. Goodrich introduces the first tubeless au-
tomobile tires.
* Reddi-Wip, Inc., introduces Reddi-Wip, the
first major U.S. aerosol food product. Founder
Marcus Lipsky advertises aerated 'real'
whipped cream inpressurized cans.
* Colgate-Palmolive-Peet introduces Ajax
* The Raytheon Company introduces the first
commercial microwave oven.
* MSG (monosodium glutamate) is produced
commercially for the first time.
* Almond Joy was introduced to augment the
popular Mounds bar.

* Variable pitch i
* The Polaroid
Land Camera
develops its own
films within its
body in 60 seconds.
* Subatomic particle pion.
* Willard Frank Libby discovers the atomic time
clock (carbon 14 dating).
* Joshua Lederberg and Edward Lawrie Tatum
find that sexual reproduction occurs in bacteria
leads to the field, bacterial genetics.
* OR pioneer and British physics Nobel Laure-
ate Patrick Maynard Stuart Blackett advances
the theory that 'all massive rotating bodies are
magnetic.' (He has previously worked on cos-
mic rays and especially on the electrical par-
ticles known as 'mesons.')
* Flying a U.S. Bell X-1 rocket plane, U.S. Air
Force captain Chuck Yeager breaks the sound
The Arts
* Tennessee Williams' A Streetcar NamedDesire
wins the Pulitzer Prize as does W.H. Auden's,
The Age of Anxiety.
* Albert Camus publishes The P.I':
* Thomas Mann publishes Doctor Faustus.
* Tom Clancy
* Stephen King
* David Mamet
* Salman Rushdie
* Kareem-Abdul Jabbar
* Johnny Bench
* Dick Fosbury (of the Fosbury Flop)
* Nolan Ryan
* Elton John
* Farrah Fawcett
* Arnold Schwarzenegger (counterpoint to
Farrah Fawcett?)
* Steven Spielberg
* Hillary Rodham Clinton
* Dan Quayle (Republican offset to Hillary
Rodham Clinton?)
* O. J. Simpson
And, one other very important thing happened in
1947: A young fellow by the name of George
Dantzig develops a mathematical model called
linear programming. He discovers a clever
method of solution, my friend Simplex.
I hope that looking back upon the events of the
day in 1947 gives all of us some sense of the his-
toric nature of your birthday, Simplex. As we
look back upon these scientific discoveries, the




important economic events of the day, and the
important artistic achievements of the day, I
think that the Simplex Method stands shoulder
to shoulder against any of those accomplishments
- in terms of its intellectual and scientific contri-
bution, its economic contribution, and perhaps,
most importantly for all of us, its artistry. Thank
you very much."

"To round out this quartet of speakers we have
Bob Bixby, professor at Rice University, also
known as Mr. CPLEX, the man who gave us the
bag or we could say the bag man, I'm not
sure. He's going to reflect on the past and, I be-
lieve, also on the future of linear programming
and the simplex method. Ladies and gentlemen,
here is Bob Bixby."

Bob Bixby's Speech
"I thank the organizers very much for this invita-
tion. It's a great honor.
It was trying to think how
r start. One of my
Friends suggested
something, and I de-
.ided it was not a
SI-ad idea. He sug-
Sested I start out by
S..' ing, 'The Simplex
Method: she has
been veery, veery
good to me.'
Indeed, it's true.
All of us here owe a
great deal to the Simplex Method. I among all of
us probably owe the most. I'm simply thankful
that George hasn't asked me to pay up!
I decided that I would say just a few short words
about the development of computation in the
Simplex Method. I will try to keep it short. I have
a stack of about 200 slides over there in case any-
body wants to hear more.
So, as I was preparing this talk of course, I want
to emphasize that I was not around when the
early codes on linear programming were being
written, so I had to ask people!
If you go back to about 1952, '53, the very first
codes were being written at The Rand Corpora-
tion by Orchard-Hays in collaboration with
George Dantzig. In those days they could solve,

after a couple of years of work, problems on card
programmable computers, problems with about
twenty-six constraints. And 'solve' you have to
take with a grain of salt. It took them eight hours
to solve one such problem, and somebody had to
be standing there feeding the cards through the
machine. That was 1953.
You get into the sixties, '62 through the mid six-
ties, and the first commercially successful codes
were being developed. That is what John Tomlin
told me: LP90 and LP94, which ran on IBM
7090, 7094 computers. These codes could solve
problems with up to one thousand rows. Of
course, there was a small problem as I understand
it. These machines had ten tape drives on them.
Now, as I say, I wasn't around, so I don't really
know what a tape drive is, but I can imagine. Ap-
parently a problem took eleven tape drives to ac-
tually run, so somebody had to stand there.
I also talked to Milt Gutterman who, many of
you may know, was an important figure in the
development of computer codes for linear pro-
gramming in the late sixties, early seventies, and
beyond. He related to me a story from when he
started his first real job in about 1960. He
walked in the door, as a freshly trained OR ana-
lyst, and there was somebody standing with
stacks of cards, picking them up, walking a few
steps and putting them down, waiting, picking
them up, walking a few steps, putting them
down, ... And he asked this young man what he
was doing. He said 'solving a linear program.'
So it was a big step from there to the early 1970s
and the first real codes, ones that could be used
on a wide variety of problems. It was actually
quite a remarkable collection of codes that were
developed in the late sixties and early seventies,
culminating with the development of a code
called MPS3 with Whizard, which originally was
written by Dennis Rarick, John Tomlin, Jim
Welsh, with a number of other people making
important contributions. That code, which was
based upon super sparsity, an idea that emerged
around 1971, is still, to this day in my opinion,
quite a good code. The problem is that it was
written in the tradition of the day. It was written
for a specific machine. It was written in machine
language. It was not flexible.
Those codes: MPS3, MPS3 with Whizard,
MPSX, MPSX/370 and a number of other codes
brought us into the eighties. The early eighties is
when I started to get into the subject. Up to that
point, I had been working on something called

matroids which are not related to hemorrhoids!
How many of you know what matroids are?
(Comment a show of a few hands.)
When I first learned about linear programming in
1965, of course, we worked with those things
called tableaus, and I liked them so much that be-
tween 1965 and 1982, I couldn't face a linear
program. But right about then, in the early eight-
ies, personal computers came out and I was lucky
enough to be at Northwestern University, to-
gether with a fellow named Bob Fourer, who had
been at Stanford where all this activity in linear
programming was going on. The pilot models
had been developed there, and Bob just knew a
lot about the practice of linear programming. I
knew nothing about it.
Fourer showed up at Northwestern and pro-
ceeded to painstakingly inform me about how
one should really write a linear programming
code. And then Tom Baker, a good friend of
mine who started Chesapeake Decision Sciences,
proceeded to prod me for two years to take this
code that I had started writing and develop it fur-
So I got started in linear programming in the
early eighties, and it was a perfect time to get
started. Integer programming was flowering. Ma-
chines were becoming available in which memory
was essentially unlimited. Really, if you look back
at the codes that were available before, if they had
had unlimited memory, they could have been
written to be as good as those we have today.
That brings me to 1984, a very exciting time.
That was when Karmarkar published his work. It
seemed like competition was in the air, with new
and larger problems constantly being solved. I re-
member working on a problem together with Irv
Lustig, John Gregory, Dave Shanno, and Roy
Marsten. The problem arose from airline crew
scheduling and had 837 rows and some 13 mil-
lion columns. It would have been unimaginable
just a few years before to solve, even the LP made
up of the first 30,000 columns of that model, and
we solved the full LP in about 6 minutes using a
special-purpose simplex method. Today we can
solve that model on a workstation in about two
and a half minutes using standard LP tools.
I am very much involved in research on the Trav-
eling Salesman Problem, a problem that serves as
a good indication of what is being done in integer
programming these days. And integer program-
ming, in my opinion, is the place where the sim-

0 P I A 5 5


plex method has found its home. We a
problems in which we solve sequences
sands of linear programming problems
them having on the order of fifteen th
straints, thirty thousand variables, and
four hundred thousand nonzeros, and
think even a minute about it. We just
By the way, something we have Don C
thank for is the Dual Steepest Edge Al
which has really carried the Simplex M
ward into this generation.
There are numerous new applications
programming that lie ahead of us. We'
the explosion in the airline industry. T
ing compared to what we're about to s
ply-chain optimization, and in other, a
covered, areas of application.
Finally, I would just like to close with
that I am going to attribute to John Fo
made it at the end of a talk a few years
which, after putting up a bunch of tab
'So, we see that the Simplex Method is
faster than the Simplex Method.'"




re solving
of thou-
, each of
ousand con-
three or
we don't
let it run.
oldfarb to
[ethod for-

of linear
ve all seen
hat's noth-
ee in sup-
s yet undis-

a remark
rrest. He
ago, in
les, he said,
ten times

Mathematical Programming's Cover

Several colleagues asked me about the origin of the now familiar cover
design of MathematicalProgramming at the 16th Symposium in
Lausanne. The story is simple though.

There were a number of technical points to negotiate with our pub-
lisher when the journal was launched in 1971 on the basis of the pool
of papers presented at the 7th Symposium held in the Hague in 1970.
Among these were the cover, the density (or number of words per
page), and others. I dealt with these, the Society having only come into
existence some time after the journal.

North-Holland's dictum was clear: simple, one color, though two tones
of the one color would be acceptable. I felt two features needed to be
pictured: extreme point and separation. Indeed, the attractive logo of
the Lausanne Symposium elicits similar ideas. I toyed with drawings
myself but soon realized that angles aesthetic to the eyes are not triviali-
ties, so a professional hand was needed. I posed the problem to an out-
standing architect (and an old and dear friend) Philetus Holt of
Princeton, NJ. He solved it and graciously gave it to me for the cover.



John Dennis

T he Mathematical Programming Society is
in fine fettle. Our treasury is plush, the
journal continues in the forefront and the
backlogs are manageable. We have just
elected an outstanding slate of officers.
The meeting in Lausanne was the largest
ever, the organization was superb, the talks were great, the
lake cruise was beautiful, the weather was nice, and the hotel
prices were not as high as some of our members feared they
might be. Tom Liebling and his committee did a wonderful
job. I think special thanks are in order for the polite and
helpful young people in the information T-shirts. The chal-
lenge is there for Georgia Tech, host of the 2000 meeting,
to meet.
By MPS tradition, the 2000 meeting will be in North
America. As you know, our society does not have a confer-
ence staff, and our meetings are organized and held at the
university that submits the most compelling proposal. This
means that we count on the local organizers to make our
meeting work. This is one reason why I am very excited
about having a meeting at GaTech. This major international
center for mathematical programming, operations research,
and systems engineering is one of the premier US engineer-
ing schools. GaTech has some fine new facilities as a result
of the recent Olympic Games held in Atlanta, and Atlanta is
a beautiful city with interesting restaurants in every price
You know by now that the Councils of both organizations
have approved a contract for SIAM to provide the MPS
membership services we were previously paying ISI (Interna-
tional Statistical Institute) to provide. In choosing a pro-
vider, we were limited for practical reasons to other profes-
sional organizations large enough to have a permanent staff.
The only serious candidates were INFORMS and SIAM.
The bids were similar, and both were more attractive than
our existing arrangement. Our choice of SIAM was influ-
enced by their outstanding use of the Internet in delivering
member services and by the consideration that there would
be less of a perception that MPS was being "taken over" by a
larger society-INFORMS with which it has so many
common interests.
Some of you have told me that fear of "takeover" makes you
uneasy about this change, but all agree that a change from
the current arrangement was needed and that the concern
about a takeover would have been greater had we hired IN-
FORMS instead of SIAM. I appreciate your expressions of
concern since it demonstrates the loyalty that we all feel for
MPS, with its informal (but committed) volunteer gover-
nance, its single-minded emphasis on research, and its
strong international flavor. We have no intention of becom-
ing a SIAM "Activity Group" for Math Programming; nor
does SIAM have any interest in blurring the distinction be-
tween our two societies. We on the Council and Executive
Committee simply feel that the professional staff of SIAM
can handle our member services more ably than the available

alternatives. Our firm intention is that you will see a differ-
ence only in better service. Some noticeable changes that we
expect to see include an up-to-date address list, accessible
and updateable through the Web.
There is more change afoot; we are now seeking bids for a
new journal publisher. Our goals are to make an agreement
that will halve our library subscription price, to keep the
journal free to our members, to increase the Society's share
of subscription revenues, and to keep abreast of develop-
ments in electronic publishing as an alternate or additional
distribution system. Several members have told us of rescu-
ing our journal from their library "cut" list where it was
placed because of the high library subscription price. There
is no reason why we should tolerate being out of line in our
subscription price. I have named an ad hoc committee of
Steve Wright, Jan Karel Lenstra, and Bob Bixby to study the
issues and recommend a new publisher. SIAM, INFORMS,
Wiley, and Springer have all submitted preliminary bids.
The current publisher also submitted a bid but, unlike the
other bidders, they have expressed reluctance to lower the
subscription price.
The MPS owns the tite and MPS logo/cover art and the
copyright of all but the first volume, so though the format
will certainly change to have less of that expensive white
empty space, Math Programming A&B will still be recog-
nizable to its loyal readers, and we will keep the same edito-
rial systems in place. As an aside, you will enjoy Michel
Balinski's article in this issue on how the cover art came to
be. Also, I really enjoyed Richard Cottle's talk in the Phil
Wolfe birthday session in which he solved the "MPS Prob-
lem" he derived from the MPS logo.
I felt at this symposium that we have been around long
enough now to have a proud history. Tony Fiacco, Alan
Hoffman, Phil Wolfe, and, of course, George Dantzig, were
active at the symposium. I only wish, as I am sure many of
you do, that Garth McCormick had been there and that
Martin Beale could have been there. I want my students to
have the experience that I had as a young researcher; I was
inspired by the presence at meetings of the "legends."
Finally, I want to end this column with a tribute to Jan
Karel Lenstra and Don Hearn. Don is Mr. OPTIMA. He
has given years of valuable service to making OPTIMA a
fine newsletter. Karen Aardal will become editor and Don,
who is taking on administrative duties at the University of
Florida, will continue as publisher. Jan Karel is Mr. MPS.
He embodies all the values that make ours such a fine soci-
ety, and he is the repository of a vital store of knowledge of
the Society. He is unselfish in his devotion to MPS, and he
gives great advice. I owe him more than I can possibly say
here. Jan Karel, Clyde Monma, and Steve Wright were cru-
cial in the big decisions we have made, and they and Chair-
Elect Jean Phillipe Vial will be counted on for the big ones
we will make. Thanks, Jan Karel, and do not think we are
going to stop trying to take advantage of all you have to of-
fer just because your term has ended.



0u-- -- P T


At the business meeting in Lausanne, John
Dennis (Chairman), Jan Karel Lenstra (Vice-
Chairman), and Steve Wright (Chairman,
Executive Committee) reported on the
following items:
Lausanne Symposium
Election results
Editors, Mathematical Programming
Series A and B, and OPTIMA
Change of membership administration
from ISI to SIAM
Location of next international symposium
Location of IPCO meetings in '98 and '99
Suggested revision of the constitution.
The Chairman-Elect Jean-Philippe Vial also
had the opportunity to address the members at
the business meeting.

The Lausanne Symposium was a huge success!
The Chairman of the Local Organizing Com-
mittee, Thomas Liebling, reported on the
number of sessions and participants and some
financial aspects of the meeting. Tom and the
whole Lausanne team received an enthusiastic
applause for their fantastic effort.
The 1997 election results, as announced on July
3, 1997, are as follows:
Chairman-Elect: Jean-Philippe Vial (Switzer-
Treasurer: Clyde Monma (USA)
Council Members-at-Large: Karen Aardal (The
Netherlands), Kurt Anstreicher (USA), David
Shmoys (USA), Uwe Zimmermann (Germany)
Jean-Philippe Vial will act as Vice-Chairman
until August 1998 when he will become Chair-
man. In August 1998 our current Chairman
John Dennis will become Vice-Chairman, a po-
sition that he will keep until the Symposium in
year 2000.

Don Goldfarb and John Birge will continue as
editors of Mathematical Programming A and B
respectively. Don Hearn will end his term as
editor of OPTIMA and will act as "publisher."
Karen Aardal will replace Don as editor. Don
Hearn is the founding editor of OPTIMA and
has acted as editor since the start in 1980. His
work has been very much appreciated by the
members, and he was thanked with warm ap-
plause by everyone at the meeting.

Membership services for the Mathematical Pro-
gramming Society will be handled by the Soci-
ety for Industrial and Applied Mathematics
(SIAM), effective January 1, 1998, upon termi-
nation of the current contract with the Interna-
tional Statistical Institute (ISI). The agreement
with SIAM was approved by MPS Council in
December, 1996.
Under the terms of the agreement, SIAM will
handle traditional membership services such as
maintenance of the membership address list,
provision of the address list to the publishers of
Mathematical Programming and OPTIMA, an-
nual distribution of the list to MPS members,
and annual membership renewal. SIAM person-
nel will also handle routine queries about mem-
bership, address changes, and missed copies of
the journal.
The agreement also enhances the services cur-
rently provided by ISI in a number of ways. The
online, searchable membership list (currently
maintained on an informal basis by Steve
Wright) will be integrated with the official MPS
membership list and maintained professionally
by SIAM. MPS members will appear in the
Combined Membership Listing for the Math-
ematical Sciences, alongside members of SIAM,
MAA, and other societies. (MPS members can
purchase the Listing by checking a box on their

annual renewal.) Reminder notices for member-
ship renewal will now be sent up to five times,
in contrast to the current single notice. Mem-
bership can be renewed quickly and conve-
niently through the World-Wide Web.
In approving the new agreement with SIAM,
the MPS Council took into account the excel-
lent level of service provided by SIAM to its
own members, the quality of the SIAM Web
site, and the attractive financial terms of the
agreement. The many MPS members who are
also members of SIAM are familiar with the
high standards of this organization and the
many shared interests of the two societies. We
look forward to a productive relationship in the
years ahead.

The International Symposium on Mathematical
Programming in year 2000 will be hosted by
Georgia Institute of Technology. George
Nemhauser and Martin Savelsbergh will share
the responsibility of the organization. We wish
them the best of luck and look forward to At-
lanta 2000!

The 1998 IPCO meeting will be held in Hous-
ton. Andy Boyd will be chairing the Local Orga-
nizing Committee, and Bob Bixby will be the
Chairman of the Program Committee. The
1999 meeting will be held in Graz with Reiner
Burkard as Local Chair and Gerard Cornudjols
as Program Chair.

A few revisions to the Constitution of the Math-
ematical Programming Society were suggested.
The suggestions were approved at the business
meeting. The current Constitution is printed in
full on the following page.



10 P T I M~ A 5 5


Constitution of the Mathematical Programming Society

Adopted 27 July 1978 Adopted in revised form 29 August 1997

I. Name
The society is an international
organization to be called
'Mathematical Programming
Society'. It will henceforth, in
these statutes, be referred to as
the Society.
II. Objectives
Its objectives are the
communication of knowledge of
the theory, applications, and
computational aspects of
mathematical programming and
related areas and the stimulation
of their development. In order to
realize these objectives, the
Society publishes a journal, holds
International Symposia and
sponsors such other activities
consistent with the objectives as
may be directed by the Council.
III. Membership
The membership of the Society
consists of individual members
and of corporate members.
Individual members as well as
corporate members join the
Society by application in a form
prescribed by the Council.
IV. Council
1. The elected members of the
Council of the Society are the
Chairman, the Vice-Chairman,
the Treasurer, and four at-large
members. The Editors-in-chief of
the journal and the Chairman of
the Executive Committee shall be
invited to all Council meetings
and shall be included on all
Council correspondence. All must
be members of the Society.
2. The Chairman chairs the
meetings of the Council. The
Council votes by majority of the
elected members present, with
the Chairman having a casting
3. The Chairman will submit a
report on the activities of the
Society when he relinquishes his
office, and his report will be
published in the journal or in a
newsletter of the Society. He will
chair a business meeting on the
occasion of any International
Symposium held during his term
of office.
4. The Vice-Chairman replaces
the Chairman whenever the
necessity arises.
5. The Treasurer is responsible
for the administration of the funds
of the Society, as directed by the
Council. The Treasurer shall
make a financial report to the
Society at the International
Symposium held within his term
of office.

6. The Editors-in-chief of the
journal are appointed by the
Council subject to the terms of
the contract in force with
publishers of the journal. They
are responsible for implementing
the directives of the Council, in
the organization of the journal,
and for carrying out its policy.
7. At each International
Symposium there will be a
meeting of the outgoing Council
and of the incoming Council.
These meetings may be
combined at the discretion of the
Chairman. An additional
meeting must be held at the
request of at least three
members of the Council. The
place of such a meeting is
decided by the Chairman. The
Chairman makes arrangements
for the taking of minutes at
meetings of the Council and
business meetings of the Society.
8. The policies of the Council are
carried out by the Executive
Committee. The Chairman of the
Executive Committee is
nominated by the Chairman of
the Society and is appointed by
the Council. He is responsible for
executing the executive
directives of the Council, for
advising the Council, and for
organizing the Executive
Committee. The Chairman of the
Society and the Treasurer are ex
officio members of the Executive
Committee. The Chairman of the
Executive Committee may
appoint additional members with
the concurrence of the Chairman
of the Society.
9. The Council appoints such
other committees as it finds
necessary to carry out the
business of the Society or to
further its objectives. The
Chairman of the Society and the
Chairman of the Executive
Committee are ex officio
members of all such committees.
V. International Symposia
1. International Symposia are
sponsored by the Society at
intervals of between 24 and 48
months. The Chairman of the
Society nominates and the
Council elects the Chairman for
the organization of the next
International Symposium.
2. Fees for the International
Symposium are fixed by the
local organizing committee, in
consultation with the Chairman
of the Society. The Council shall
adopt guidelines regarding the

financial obligations between
the Society and the organizing
3. In the following section on
elections the word 'term' is
defined to be the period from
the end of the business meeting
held during the International
Symposium to the end of the
business meeting of the
following International
VI. Elections
1. Elections for the Offices of
Chairman, Treasurer and the
four at-large members of Council
are held four months prior to
each International Symposium.
The elected Chairman serves on
Council for the two terms
following his election. He is the
Chairman from one year after
the beginning of his first term
until one year after the
beginning of his second term. He
takes the office of Vice-Chairman
during the remainder of his
period of service. The Treasurer
takes office one year after the
beginning of the term following
his election and he serves until
one year after the beginning of
the next term. At-large members
of Council serve for the term
following their election. If the
office of Chairman becomes
vacant, it is filled automatically
by the Vice-Chairman. The
Chairman, after consultation
with Council, may appoint a
member of the Society to fill any
other office that becomes vacant
until the next election. No one
may serve for more than two
consecutive terms as an elected
at-large member of Council.
2. The Chairman invites
nominations for all elections,
giving at least two months notice
through the journal of the
Society of the closing date for
the receipt of nominations.
Candidates must be members of
the Society. They may be
proposed either by Council or
by any six members of the
Society. No nomination that is in
accordance with the constitution
may be refused, provided that
the candidate agrees to stand.
The Chairman decides the form
of the ballot.
VII. Secretariat
1. The Council is assisted by a
Secretariat, which is supervised
by the Chairman of the
Executive Committee and

2. The Secretariat will keep an
up-to-date list of members of the
Society, and a list of past and
present members of the Council,
with an indication of their
VIII. Fees
The membership fee is fixed by
Council, and may differ for
individual and for corporate
members. A member who has
not paid his dues before the end
of the current year will be
deemed to have left the Society.
IX. Journal
The Journal is distributed free of
any charge addition to the
membership fee to all members
of the Society, to their last
known address.
X. Agents
Council may approve the
payments of membership fees,
or of subscription fees for the
journal, in national currency, to
local agents in countries where it
is difficult for individual members
to obtain convertible currency.
XI. Other activities
In addition to International
Symposia, the Society may
sponsor conferences and
seminars. The organization of
such sponsored meetings is
subject to directives by the
Chairman of the Society.
XII. Amendment of the Con-
If proposed by at least ten of the
membership of the Society, or by
vote of the Council the
constitution may be amended by
a majority of voters, either at a
business meeting of the society
on the occasion of an
International Symposium, or by
a written ballot. Proposals must
reach the Vice-Chairman at least
two months before the voting
takes place.
XIII. Bylaws
1. In order to carry out the
obligation as set forth in this
constitution and to conduct the
business of the Society, the
Council shall adopt bylaws. The
bylaws may be adopted,
annulled, or amended by an
affirmative vote of at least four
members of the Council. The
Council shall have the authority
to interpret the bylaws.
2. Council shall pass bylaws
governing elections designed to
promote and maintain
international representation of
the Council and Executive



0 P T I M A -5 51

) Algorithms and Experiments
(ALEX98) Building Bridges
Between Theory and Applications
Trento, Italy
Feb. 9-11, 1998
) ICM98
Berlin, Germany
Aug. 18-27, 1998
) International Conference on
Nonlinear Programming and
Variational Inequalities
Hong Kong
Dec. 15-18, 1998

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George Nicholson

Student Paper


The INFORMS Student Affairs
Committee announces the 1998
George Nicholson Competition for
this year's best OR/MS papers writ-
ten by a student. There are four con-
ditions for eligibility:

1) The entrant must have been a
student on or after January 1, 1997;
2) The paper must present original
research results;
3) The research must have been con-
ducted while the entrant was a stu-
dent; and

4) The paper must be written by the
entrant with only minor outside
editorial assistance. One or more
advisors may appear as co-authors of
a paper, but the student must be the
'first author'.
Prizes will be awarded at the
INFORMS Montreal Meeting,
April 26-29, 1998. Winners will be
invited to present their papers at the

Entrants should submit six (6) cop-
ies of one paper comprised of no
more than 25 double-spaced pages.
The entries must be accompanied by
a letter signed by both a faculty ad-
visor and the entrant attesting that
the four eligibility conditions have
been satisfied. These entries should
be delivered no later than January
15, 1998, to the chair of the prize

GarrettJ. van Ryzin
Graduate School of Business
412 Uris Hall
Columbia University
New York, NY 10027
gjvl @columbia.edu

0 T M 5

International Congress of
Berlin, Germany
August 18-27, 1998
The Organizing Committee is
pleased to announce that the next
International Congress of Mathema-
ticians will take place in Berlin, Ger-
many, from Tuesday, August 18,
through Thursday, August 27,
It will be held under the auspices of
the International Mathematical
Union (IMU) and sponsored by
many other institutions.
Mathematical Program
Responsibility for the scientific pro-
gram lies with the Program Com-
mittee appointed by IMU. There
will be about 20 one-hour Plenary
Lectures covering recent develop-
ments in the major areas of math-
ematics and about 170 45-minute
Invited Lectures in 19 sections. The
sections are as follows:
1. Logic
2. Algebra
3. Number Theory and Arithmetic
Algebraic Geometry
4. Algebraic Geometry
5. Differential Geometry and Global
6. Topology
7. Lie Groups and Lie Algebras
8. Analysis
9. Ordinary Differential Equations
and Dynamical Systems
10. Partial Differential Equations
11. Mathematical Physics
12. Probability and Statistics
13. Combinatorics
14. Mathematical Aspects of Com-
puter Science
15. Numerical Analysis and Scien-
tific Computing
16. Applications
17. Control Theory and Optimiza-
18. Teaching and Popularization of
19. History of Mathematics
Every registered participant (tradi-
tionally called Ordinary Member) of
the Congress will have the opportu-
nity to give a short presentation, ei-
ther during a poster session or in the
form of a 15-minute lecture. A for-
mal call for such presentations will
be issued in the Second Announce-
ment. Informal mathematical semi-


nars may be organized at the initia-
tive of groups of participants. En-
glish, French, German, and Russian
are the official languages of the
All Plenary and Invited Lectures will
be published in the Proceedings of
ICM'98; after the Congress, a com-
plimentary copy of these Proceed-
ings will be sent to each Ordinary
Member. Abstracts of all lectures
and of all short presentations will be
distributed free of charge to Ordi-
nary Members at Congress check-in.
The Fields Medals and the
Nevanlinna Prize will be awarded
during the Opening Ceremony on
the first day of the Congress. This
will take place in the International
Congress Center Berlin (ICC); all
other scientific events will be held at
Technische Universitaet Berlin. No
scientific activities are scheduled for
Sunday, August 23.
In an effort to reach out to a wider
audience, the ICM'98 organizers
have initiated several cultural activi-
ties related to mathematics that are
attractive to the general public. In
particular, there will be a
VideoMath Festival, software dem-
onstrations, talks about mathematics
and its relations to other subjects,
several exhibitions (Mathematics in
the Arts, etc.), and other events
(Mathematics and Music, etc.).
Special consideration will be given
to the impact of the Nazi regime on
mathematics in Berlin and Ger-
Social Events: On August 18 there
will be a buffet-banquet for all regis-
tered participants of ICC. During
the Congress, a number of guided
tours of Berlin, visits to museums,
and walking tours will be offered.
On Sunday, August 23, it will be
possible to choose from several ex-
cursions. For that evening tickets
have been reserved for the opera,
The Magic Flute, at the Deutsche
Opera. Registered participants may
purchase tickets in advance for these
events as well as for many day trips
and pre- or post-congress tours to
places of interest in the vicinity of
Organization: Up-to-date informa-
tion about all aspects of ICM'98 is
available on the following website:
http://elib.zib.de/ICM98. This in-

eludes information about registra-
tion, abstract submission, etc. Cor-
respondence should be directed to:
icm98@zib.de. It will be forwarded
to an appropriate member of the
Organizing Committee. If electronic
communication is not available, you
may also write to the ICM'98 Secre-
tary Prof.Dr. J. Winkler at the ad-
dress below.
Registration and Accommodation:
DER-CONGRESS, a professional
congress and tour organizer, has
been appointed by the Organizing
Committee to handle all non-scien-
tific matters for individual partici-
pants: registration to the Congress
and the social events, hotel reserva-
tions, tourist program, collection of
registration fees, etc. The formal
registration procedure for the Con-
gress will be described in the Second
Announcement (below).
Participants will be housed in several
hotels in Berlin; the necessary reser-
vations have already been made by
DER-CONGRESS. In addition,
DER-CONGRESS will make stu-
dent residences available and will
provide a certain number of private
accommodations at an inexpensive
rate for participants willing to accept
less comfort. Detailed information
on locations and rates will be pro-
vided in the Second Announcement.
Forms for registration and accom-
modation requests will be made
available on the ICM'98 server in
January 1998.
The Second Announcement of
ICM'98 will describe the activities
of the Congress in more detail and
give instructions on how to com-
plete the registration process and
obtain accommodations. It will pro-
vide more, although not complete,
information on the scientific pro-
gram, contain a call for contributed


short presentations, and give in-
structions regarding the submission
of abstracts.
The Second Announcement will
also include advice on how to pro-
ceed upon arrival at airports and
train stations, and it will be accom-
panied by a brochure describing the
day trips and tours organized by
Several conferences of a more spe-
cialized nature are scheduled imme-
diately before and after ICM'98.
The Second Announcement will
also contain a list of such "satellite
To receive the Second Announcement,
fill out the form on the ICM'98 server
Alternatively, send an empty e-mail to
icm98@zib.de with 'Second
Announcement' in the 'SUBJECT' line to
receive an e-mail form or contact the
ICM'98 Secretary Prof. Winkler at the
address below.
The Second Announcement will be
mailed from Berlin at the beginning of
1998. Electronic Information on
ICM'98 at URL: http://elib.zib.de/
ICM98 (with request form for Second
ICM'98 General E-mail Address:
Address for general correspon-
c/o Prof. Dr. J. Winkler
TU Berlin, MA 8-2
Str. des 17. Juni 135
D-10623 Berlin, Germany
Phone: +49/30/314-24105
Fax: +49/30/314-21604
E-mail: winkler@math.tu-berlin.de
Organizing Committee President:
Prof. Dr. M. Groetschel
Konrad-Zuse-Zentrum fuer
Informationstechnik (ZIB)
Takustrasse 7
D-14195 Berlin-Dahlem
E-mail: groetschel@zib.de
Phone: +49/30/84185-210
FAX: +49/30/84185-269
Secretary: Sybille Mattrisch
Phone: +49/30/84185-208
ZIB-URL: http://www.zib.de


1 OCTBE I 1 P 165

International Conference on Nonlinear Programming
and Variational Inequalities
Hong Kong
December 15-18, 1998
First Announcement
The conference aims to review and discuss recent advances and promising
research trends in some areas of Nonlinear Programming and Variational
Topics Include:
Nonlinear Complementarity Problems
Variational Inequality Problems
Nonsmooth Optimization Problems
Minimax Problems
Multi-level Optimization Problems
Structured Optimization Problems
Quadratic and Nonquadratic Methods
Invited Speakers Include:
O. Burdakov (CERFACS, France)
S. Dempe (Freiberg Univ. of Mining and Tech., Germany)
F. Facchinei (University of Roma, Italy)
S.C. Fang (North Carolina State University, USA)
M. Fukushima (Kyoto University, Japan)
L. Lasdon (University of Texas at Austin, USA)
Z.Q. Luo (McMaster University, Canada)
J.M. Martinez (University of Campinas, Brazil)
J.J. More (Argonne National Laboratory, USA)
S. Nash (George Mason University, USA)
J.S. Pang (Johns Hopkins University, USA)
P.P. Pardalos (University of Florida, USA)
E. Polak (University of California at Berkeley, USA)
D. Ralph (University of Melbourne, Australia)
R.T. Rockafellar (University of Washington, USA)
E. Spedicato (University of Bergamo, Italy)
K.L. Teo (Curtin University of Technology, Australia)
P. Tseng (University of Washington, USA)
R.J.B. Wets, (University of California at Davis, USA)
H. Yabe (Science University of Tokyo, Japan)
Y. Yuan (Chinese Academy of Sciences, China)

Conference Chairs:
L. Qi (University of New South Wales, Sydney, Australia), Email:
J. Zhang (City University of Hong Kong, Hong Kong), Email:
Organizing Committee:
A. Fischer (Technical University of Dresden, Germany)
M. Fukushima (Kyoto University, Japan)
C. Kanzow (University of Hamburg, Germany)
J. Han (Chinese Academy of Sciences, China)
J. Sun (National University of Singapore, Singapore)
R.J.B. Wets (University of California at Davis, USA)
R. Womersley (University of New South Wales, Australia)
C. Xu (Xi'an Jiao Tong University, China)
X. Zhang (Chinese Academy of Sciences, China)

Call for Papers
Titles and abstracts of contributed papers must be received by July 31,
1998. The abstracts should be typed in Latex, not exceed one page, and
be sent to maopt@cityu.edu.hk by email.
Special Arrangements
Conference proceedings, special issues of some journals, tours and eco-
nomical hotel accommodations will be indicated in the Second An-
Further Information:
Email: maopt@cityu.edu.hk
Home page: http://www.cityu.edu.hk/ma/
or contact Conference Chairs.



rLb -Em ---

& *VSIL ___A

^ "^*Trjf ^?i i40=""1!

Visualization and
by Christopher V. Jones
Kluwer Academic Publishers
Dordrecht, 1996
ISBN 0-7923-9672-3
Have you ever looked at a contour plot of a nonlinear
function? Have you ever looked at the feasible region
of a 2-variable linear program? Have you ever looked
at a Gantt chart to analyze the solution to a scheduling
problem? Have you ever looked at a plot of the non-
zero entries in a matrix? Have you ever seen the farthest
inserting algorithm in action? Have you ever seen the
Lin-Kernighan edge-exchange algorithm in action?
Have you ever seen Edmond's matching algorithm in
Visualization is, and rightfully so, an important tool
in the toolkit of an optimizer. It helps to gain insight
into a problem, an algorithm, or solution. The above
examples and many more are discussed in the new book
Visualization and Optimization by Chris Jones.
The book is not the prototypical example of a text in
operations research or mathematical programming. It
does not discuss a specific problem or a specific meth-

odology; instead, it focuses solely on howvisualization
can be used to support building and understanding
optimization models, algorithms and their solutions.
The book takes the point of view that techniques from
visualization, when applied appropriately, can improve
our ability to solve people's problems. The purpose of
visualization is much the same as the purpose of op-
timization: to provide insight into complex problems.
Optimization uses sophisticated algorithms to uncover
optimal solutions to complex problems. Visualization
uses carefully designed representations to help people
understand complex problems. The book also issues
a warning: visualization, like optimization, can easily
be misused.
The book covers a lot of material. It presents basic
background material from cognitive psychology and
other fields relevant to visualization; it provides guid-
ance for those seeking to visualize their problems,
models, and algorithms; it discusses existing research
and practice on using visualization to support optimi-
zation analysis; it surveys research that has applied
optimization to creating visualizations; and it suggests
research directions for those interested in pursuing
research on visualization applied to optimization.

The books divided into three parts. Part I: "AFrame-
work for Visualization and Optimization." It presents
relevant background material from cognitive psychol-
ogy, computer graphics, visual design, and other areas.
Part II: "Visualization and the Modeling Life-Cycle."
It discusses how visualization has been or might pro-
ductively be used to support distinct phases of the
modeling life cycle. Part III: "Visualization for Opti-
mization." It focuses on how different representation
formats have been or could be used to support opti-
The book is a pleasure to read and contains a wealth
of information, including many informative illustra-
tions. Even so, it becomes clear that the area of visu-
alization and optimization is still in its infancy. It has
not yet lived up to its potential. Visualization offers an
opportunity to make optimization even more enjoy-
able, understandable, and accessible. It can enhance our
ability to deliver optimization to students as well as

~ 1..




1 OCTBE I 1 P 185

Primal-Dual Interior-Point

by Stephen J. Wright
SIAM, Philadelphia, 1996
ISBN 0-89871-382-X
Since Karmarkar's method for linear programs ap-
pearedin 1984, numerous interior-point methods have
been proposed and studied for various problems.
Among others, primal-dual interior-point methods
have been harmoniously developed both in theory and
in practice. Now they are known to be very efficient
and powerful numerical methods for solving large scale
linear programs. This book covers both theory and
practice of primal-dual interior-point methods for
linear programs and briefly mentions their extensions
to other mathematical programs. The book is well-
organized, comprehensive, and easy to read for experts,
graduate students and even good undergraduate stu-
dents who want to study this subject for the first time.
Chapter 1 gives an overview of this book introducing
fundamental ideas and various important issues on
primal-dual interior-point methods. This chapter it-
self is a nice self-contained survey on the subject.
Chapters 2 and 3 serve as preliminaries and back-
ground. They are devoted to the standard form linear
program, the duality theory, the fundamental ideas of
primal-dual interior point methods, the complexity
theory of algorithms, etc. Chapters 4, 5 and 6 are the
major theoretical part of this book. These three chap-
ters present full theoretical complexity analyses of the
most important primal-dual interior-point methods,
i.e., potential-reduction methods, path-following
methods and infeasible-interior-point algorithms,
respectively. Chapters 7 and 9 discuss some further
theoretical issues on primal-dual interior-point meth-
ods; superlinear convergence and finite termination in
Chapter 7, and a homogeneous self-dual formulation
of primal-dual interior-point algorithms which incor-
porates a mechanism of getting infeasibility informa-
tion in Chapter 9. Chapter 8 describes extensions of
primal-dual interior-point methods from linear pro-
grams to some other types of problems such as convex
quadratic programs, convex programs, linear and
nonlinear monotone complementarity problems, and
semidefinite programs. The last two chapters place
much emphasis on practical aspects of primal-dual in-
terior-point methods. Chapter 10 presents Mehrotra's
predictor-corrector algorithm on which many current
software packages are based, and in Chapter 11 there
are some computational issues involved in efficiently
and stably solving large sparse systems of linear equa-
tions for primal-dual search directions. Finally, several
software packages, some of which are free and avail-
able through the Internet, are listed in the appendix.

Stochastic Models

by H.C. Tijms
John Wiley, Chichester, 1994
ISBN 0-471095123-4
StochasticModels is a modernized version of the author's
previous book that also appeared with Wiley, under the
title Stochastic Modeling and Analysis.
It contains four chapters:
1. Renewal Theory with Applications
2. Markov Chains: Theory and Applications
3. Markov Decision Processes and their Applications
4. Algorithmic Analysis of Queueing Models
Each chapter is concludedwith section, Bibliographic
Notes, and a well-sized section of References.
Chapter 1 provides the basics of renewal theory, the
Poisson process and renewal reward processes. Further,
it contains two larger sections on Reliability and In-
ventory in which the theoretical results are applied.
Chapter 2 gives a very complete presentation of dis-
crete and continuous time Markov chains and uses the
applications to illustrate the modeling aspects. It is
concludedwith sections on TransientAnalysis and the
Phase Method.
Chapter 3 is devoted to the average reward Markov
decision processes. It treats Policy Iteration, Linear
Programming and Value Iteration. We also find an
interesting section on tailor-made policy iteration
algorithms that exploit the specific structure of the
application of interest.
Chapter 4 starts with the more advanced queuing
models as the ordinary M/G/1 queue, the M/G/1
queue with batch arrivals and the G/G/1 queue. After
that it continues with a thorough and extensive algo-
rithmic analysis ofmulti-server queues including finite
capacity models. As for most of the models treated in
this chapter, analytical results are very limited; the
emphasis is on approximations, particularly for the
distribution of the waiting time.

As the titles of the chapters clearly indicate (applica-
tions, algorithmic), the book is an attempt to help the
reader to become an engineer in stochastic modeling.
Although, as the author remarks, we all know that the
only way to become a modeler in this difficult area is
by doing. This bookwith the many examples in the text
and over a hundred interesting exercises, is an excel-
lent way to start.
Each of these chapters can verywell be used as the basis
for a course. The chapters are to a large extent inde-
pendent. Chapter 2 can be studiedwithout almost any
knowledge of the renewal theory in Chapter 1, and
Chapters 3 and 4 require only a very basic knowledge
of Markov chains. Each chapter starts with the basic
material which requires little background and only a
limited amount of intuition but then continues with
more advanced topics which ask for a higher level of
understanding. Particularly, Chapter 4 is very inter-
esting but not so simple.
In the preface we read that this book is more directed
to students than to researchers, in contrast to the pre-
vious version. I agree with that; it is definitely one of
the best books for students who want to get acquainted
with stochastic modeling, but it is a lot more than
another set of lecture notes.
In all four chapters we discover special topics in which
we recognize the author's research. We find many
important and useful approximations which take us
one step further than analysis could. The emphasis is
on applications and approximations which are useful
for the engineer. But at the same time, these sections
are important for researchers who are treating prob-
lems for which no standard models exist.
For me that is just what makes Stochastic Models so
much more attractive than most of the books in this
area. Therefore, I can recommend it to anyone who is
interested in Stochastic Operations Research.



At the Symposium, OPTIMA changed editorial staff. Don Hearn, who founded
OPTIMA in 1980, has been the editor since the start. He will now help the new edi-
tor, Karen Aardal, with several publication aspects. The editorial structure will be
slightly different from previous years. Karen will as editor continue with her previ-
ous task as "Features Editor." To get news on developments in our field, including
software, and also to assist Karen in suggesting and attracting Feature articles,
OPTIMAwill have two "Area Editors"; Mary Beth Hribar, Rice University, for Con-
tinuous Optimization, and Sebastian Ceria, Columbia University, for Discrete
Optimization. Book reviews will, of course, continue to form an important section
of OPTIMA. The new Book Review Editor is Robert Weismantel, ZIB-Berlin. You
will find the addresses of all editors on the last page of OPTIMA. In the next issue
of OPTIMA there will be a short presentation of all of them. The new staff hopes
that the members of MPS will continue to provide OPTIMA with Feature articles,
software information, conference notes, and all possible ideas and suggestions!

,As the new editor of OPTIMA,
I would like to extend a warm
STHANK YOU to my predeces-
sor Don Hearn for his fantastic
D job with producing OPTIMA
since 1980. I also would like to
Thank the secretarial staff at the
O Center for Applied Optimiza-
Stion at the University of Florida
in Gainesville for all their assis-
tance through the years. Elsa
Drake at Gator Engineering
SPublication Services has given
OPTIMA its distinguished pro-
fessional style. Fortunately they
Swill all continue to help with

preparing and publishing OP-
TIMA! Thanks as well to Don's
wife Joyce who has spent numer-
ous hours on editing and proof-
reading OPTIMA. Also, many
thanks to the previous associate
editors Faiz Al-Khayyal, Soft-
ware and Computation Editor,
and Dolf Talman, Book Review
Editor, for all their efforts.
In the next issue of OPTIMA
there will be an interview with
Don, where he tells us about
both his work with OPTIMA
and his scientific activities.


I wish to enroll as a member ofthe Society.

My subscription is for my personal use and not for the benefit of any library or institution.

O I willpay my membership dues on receipt ofyour invoice.

E I wish to pay by creditcard (Master/Euro or Visa).





Mail to:
The Mathematical Programming Society, Inc.
c/o International Statistical Institute
428 Prinses Beatrixlaan
2270 AZ Voorburg
The Netherlands

Cheques or money orders should be made pay-
able to The Mathematical Programming Soci-
ety, Inc., in one of the currencies listed below.
Dues for 1997, including subscription to the
journal Mathematical Programming, are
Dfl.110.00 (or $65.00 or DM100.00 or 40.00
or FF330.00 or Sw.Fr.80.00).
Student applications: Dues are one-half the
above rates. Have a faculty member verify your
student status and send application with dues to
above address.
Faculty verifying status









Center for Applied Optimization
371 Well Hall
PO Box 116595
Gainesville FL 32611-6595 USA


Karen Aardal
Department of Computer Science
Utrecht University
P.O. Box 80089
3508 TB Utrecht
The Netherlands
e-mail: aardal@cs.ruu.nl
URL: http://www.cs.ruu.nl/staff/aardal.html
Mary Elizabeth Hribar
Center for Research on Parallel Computation
Rice University
6100 Main Street MS 134
Houston, TX 77005-1892
e-mail: marybeth@caam.rice.edu
URL: http://www.caam.rice.edu/~marybeth/

Sebastian Ceria
417 Uris Hall
Graduate School of Business
Columbia University
New York, NY 10027-7004
e-mail: sebas@cumparsita.gsb.columbia.edu
URL: http://www.columbia.edu/~sc244/
Robert Weismantel
Konrad-Zuse-Zentrum fir Informationstechnik (ZIB)
Takustrasse 7
D-14195 Berlin-Dahlem
e-mail: weismantel@zib.de

Elsa Drake, DESIGNER
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