MARCH I
P T I M A
MATHEMATICAL PROGRAMMING SOCIETY NEWSLETTER
lHIM ~III I~ III IIPIE 'lk'l
L
III I'ii fMi 111111 iLll h1I
F
E
A HE MAIN ACTIVITY of the
1T Features Department is to
U provide highquality feature ar
R ematical programming. Our goal is to
E publish at least one article in every issue
S of OPTIMA. Feature articles have always
beenwelcome and several have appeared.
They have, however, appeared less frequently dur
ing the last few years. Given the very rapid devel
opment in many areas of mathematical program
ming, the increased interaction with other areas,
and the vast number of new successful applica
tions, it is felt strongly among members that fea
ture articles should again constitute a prominent
part of OPTIMA. In order to stimulate this ac
tivity, I have solicited articles by leading experts
in various fields of mathematical ...., i 1.1..1 i" !
In ,. .. ,,l, year articles on combinatorial op
timization used in railway planning, Grabner
bases;,,,l ',r .'1 I ,;. ii,,ii:... random ized al
gorithms, and structural optimization are ex
pected to appear. It is our hope that many people
will be inspired by these contributions and sub
mit articles for forthcoming issues.
AS A GUIDELINE TO AUTHORS, I want to
point out that a feature article should be written
in away that is understandable to the general MPS
member. It could typically present a new tech
nique, the stateoftheart ofan area, provide his
torical perspective, or describe an application.
Formulae are allowed but should be used spar
i,,i ill r ,r..,, most welcome. Belowis a
complete list of feature articles that have appeared
so far in OPTIMA. Prospective authors can re
quest any of those from me. The recommended
way ofsubmitting an article is by email using the
address given below. The format should be a plain
text file with TeX commands wherever needed.
I ,o.. or photos can be sent by ordinary mail.
Articleswillbesubjectto 1;I _., ..l; i. 1 1..r 11
not be refereed.
PAGE TWO
t a t :i ,
Interviews 26
MORE ON PAGE NINE more feature articles 79
conference notes
book reviews
gallimaufry
1013
1418
19
I II II II I 10 IFJ9111hl III, 11r, oil
  ~s
The SOFTWARE & COMPUTATION I
Department of OPTIMA is the new home T
for readers interested in computational ac W
A
...I ..' ,I I ., I. I, 1 . y . l, R
t . .. , ,l ,t .. , ,  ,. I .
II , .., ,
,,, I. ,, r,, ,, , ,11, 1 ,
i., 1 ,
tain information on test problems and problem gen
erators (including evaluating same), compile and
maintain a list of recent technical reports related to
computation, and compile and maintain a list ofavail
able commercial quality software (including evaluat
ing same). Obviously, some of the more n ,".. in
formation is best transmitted through a directory
accessible via anonymous ftp, with OPTIMA guiding
readers to what is available on the Internet.
In order for this column to be successful and respon
sive to reader views, I herein announce a general call
for contributions to this Department. This is to include
n o, ,, I... .. q l [I .. I , .. ,,u rl ,I .... . II
as related news items about conferences, workshops,
appointments, awards, and personal achievements that
you would like to communicate to your peers.
I
16011211111MACH1199
A SECOND RESPONSIBILITY ofthe
Features Department is to collect and
compile news. I am currently building
a network of news reporters to assist me
in this task. We welcome news about
conferences, workshops and other ac
tivities as well as personal news, such as
appointments, awards and other
achievements. News regarding software
should be sent to the Software and Com
putation editor, Faiz AlKhayyal. Any
.r ,ll. F ,, .. p .q r._r ,
encouraged to contact me as quickly as
possible. News should preferably be sub
mitted to me by email using the same
format as the feature articles.
OPTIMA exists to provide service to the
members. Any ideas on topics for feature
articles or any other activities are, of
course, most welcome!
CLAUDE LEMARiCHAL
Karen Aardal
Features Editor
Department of Econometrics
Tilburg University
P.O. Box 90153
5000 LE ,il..,, ,
The Netherlands
email: aardal@kub.nl
Tel.: +31 13663254
FAX: +31 13 663280
Feature articles published in
earlier issues ofOPTIMA:
* The ellipsoid algorithm
(P. Wolfe, Number 1, June 1980)
* Algorithms: The influence offinite precision arithmetic
(W. Murray, Number 2, Oct. 1980)
* Mathematicalprogramming at Oberwolfach
(A. Bachem, Number 3, March 1980)
* Some roads hardly taken
(R. G. Jeroslow, Number 4, July 1981)
* Mathematicalprogramming activities in the USSR
(B. Korte, Number 6, March 1982)
* Atplay in thefields of scheduling theory
(E.L. Lawler et al., Number 7, June 1982)
* Testing the theory of evolution
(L.R. Foulds, Number 10, Aug. 1983)
* Theprogramming of(some) intelligence: opportunities
at the OR/AI interface
(R.G. Jeroslow, Number 14, Jan. 1985)
* Are you all salesmen here?
(E.L. Lawler et al., Number 19, Sept. 1986)
* Highlights ofMike Todd's research
(L.E. Trotter, Jr., Number 26, April 1989)
* Some comments on notation for quasiNewton methods
(W.C. Davidon et al., Number 32, March 1991).
laudk Lemarifch(l r Ic ii'L I
Ill, 19 4PDaii : i. I' :I I malillill tll
.,1 s L',' I l ,i ; /I'/,l l a d a ,lll ll i
lyzing numerical methods in
nonsmooth optimization. The
prize was jointly awarded to
RogerJ.B. Wets, who will be inter
viewed in the next issue of OP
TIMA. The Dantzig Prize is
awarded once every three years by
the Mathematical Programming
Society and the Society for Indus
trial and Applied Mathematics to
recognize original, broad and deep
research making a major impact
on the field. Among Lemarechal's
many important contributions to
nonsmooth optimization is the so
called bundle method. Next to his
theoretical work, he has been in
volved in numerous collaborative
projects on applied optimization
problems. He recently published,
with J.B. HiriartUrruty, the two
volume book, Convex Analysis
and Minimization Algorithms
(Springer Verlag, 1993).
Lemarechal graduated from the
engineering school in Toulouse
(part of the French "GrandeEcole"
system) and received his Ph.D.
degree from Universite de Paris IX,
Dauphine. In 1971 he received an
appointment at INRIA (Institut
National de Recherche en
Informatique et Automatique) le
Chesnay, France, where he is still
working.
I 1' f11.1. ,_ l .;Iu 1hit ii n I I t i
liI I "r ii l 1 il0 110 1 Ihlllth
I/ (l lllll11: h 'll )
CL: I went to INRIA just as I had
graduated. It was an institute created
in 1967 for work in applied math
ematics, and more specifically, on
problems coming from industry. At
the start it was a very small institute.
We were about 10 people, including
the housekeepers and the concierge!
I first worked on partial differential
equations and ordinary differential
equations. Then I moved to optimi
zation, and I was lucky.enough to get
an application from the glass com
pany, Saint Gobain. It concerned the
management of a glass oven and
could be interpreted as a multiprod
uct, multimachine lotsizing prob
lem. It was very well formulated. All
the equations of the model were
present, so for me it was "only" a
matter of finding an appropriate al
gorithm. However, it was a nonlin
I. 1 r , i'. ] i ,. .bhIn. fr hiI.,
classical methods were not really
suitable. It took me awhile to analyze
it since Iwas quite fresh in optimiza
tion. The problem was decompos
able, so Lagrangian relaxation was,
in principle, suitable, but it was not
convex, so the Lagrangian dual was
nondifferentiable. At that time I
didn't know that nonsmooth optimi
zationexisted. Iwas,however, lucky
to find Lasdon's book, Optimization
Theory for Large Systems,
1.i..'.1l!., ll 1970), which has got a
very good introduction to elemen
tary convex analysis in an appendix.
This appendix contained all the
material necessary to understand
what can be done in this subject.
    I
N? 45
MARCH 1995
PAGE 2
I'AGL 3 N~45 MARCH 199
The glass company project was the
origin of the development of bundle
methods. It took me about one year
to find the appropriate solution
scheme, and when I had finished, I
went back to Saint Gobain and told
them very proudly "OK, I have got
the solution," but they told me,
"What? We don't care about this
p ,.,l 1 .1 ` !. 1, ,. I i t i r i. t ...... J
and second, there was a mistake in
the formulation anyway." If the mis
take had not been present, the prob
lem would have become perfectly
convex with a nice dual, so all this
research would not have been car
ried out. So, it was a "happy mis
take!"
OPTIMA: One of your most
important contributions to
nonsmooth optimization is
the bundle method. Could you
describe the principle behind
this technique?
CL: There are two ways of describ
ing bundle methods. The way to
explain it that appeared at that time,
i.e., about 20 years ago, is as follows.
If you minimize a smooth function,
you first need to find a descent direc
tion. If the function is smooth, i.e., if
the gradient exists, it suffices to move
in the direction opposite to the gra
dient, or even anywhere in the half
space opposite to the gradient. If,
however, the function is nonsmooth,
instead of having one gradient, you
have a bunch of generalized gradi
entsor subgradientswhich form
the socalled subdifferential. If you
generate a subgradient (by an
oracle), you are not sure that the
direction opposite to this
subgradient is a descent direction.
Whatyou need to do to find a descent
direction is to consider the set that
forms an obtuse angle to all
subgradients, which is a set much
smaller than the halfspace opposite
to the subgradient. In the bundle
method you start by computing one
subgradient. If the opposite direction
is a descent direction, it is all right,
but if it is not, there is a way of forc
ing the oracle to compute a new, dif
ferent subgradient that forms an
acute angle with your direction. You
then pivot your direction so as to
have an obtuse angle with both
subgradients, and so forth. You can
prove that either your starting point
is optimal, or eventually, after
enough such pivots, you really get a
descent direction.
One more comment: this approach
was "invented" simultaneously by
Phil Wolfe and myself, but Phil be
haved wonderfully towards me.
While I was very young and totally
unknown, he immediately moved
aside, and then he started to put my
own work continuously to advan
tage, advertising it at every occasion.
I am also very grateful to Michel
Balinski, who had a decisive influ
ence on my career, helping me and
encouraging me from the very begin
ning. Then Bob Mifflin was the
"worker of the first hour." Later on,
K.C. Kiwiel, J.J. Strodiot, J. Zowe
joined us (in alphabetical order!), as
well as several others. It is my plea
sure to acknowledge the important
role they all played in the develop
ment of the field.
OPTIMA: In which direction
did your work proceed after the
Saint Gobain application?
CL: What happened then, in the mid
'70s, was that we quite rapidly found
appropriate algorithms which were
rather satisfactory for optimization
of convex functions. We were also
able to generalize these algorithms to
nonconvex functions. On the other
hand, my point was, and this I feel
very strongly about, that work in
nonsmooth optimization should
keep close to smooth optimization.
You should not become an expert in
a difficult subject before you are an
expert in the easy subject in which the
difficult one is contained. Therefore,
I did work on smooth optimization.
Furthermore, I considered the re
search in nonsmooth optimization to
have reached a kind of equilibrium,
by the development of appropriate
software that can solve significant
problems, and on top of this, appli
cations were coming that involved
"ordinary" optimization. However,
I did not totally abandon my spe
cialty; I kept an eye on the
nonsmooth world.
OPTIMA: Which are currently
the main issues in nonsmooth
optimization?
CL: On the purely theoretical side, a
S i , l ,I l ,.t..i, i' L ,1 l 1' .lw to
properly generalize the concept of
second derivative to the case of func
tions which are convex but which
have no first derivative. The motiva
tion is to design algorithms that are
really extremely fast (those existing
at present may be slow; there is a
reason for that). I have been asking
myself this question for about 20
years, and I must confess that no
substantial progress has been made.
On the application side there are
several issues. It would, for instance,
be a good thing to develop compu
tational codes especially tailored to
Lagrangian relaxation, enabling the
resolution of largescale reallife
problems (Lagrangian relaxation is
one of the main applications of
nonsmooth optimization). This is,
however, fairly difficult since large
scale problems involve broad exper
tise, almost by definition. Develop
ing such codes involves joint work,
not only between applied mathema
ticians but also with people from the
application world as well. This is
why there has been very little devel
opment of software for decompos
able systems so far. For instance, I
have for several years been in contact
with EDF (the French Electricity
Board), and progress is very slow.
OPTIMA: If you look at the
realworld problems that you
have studied, would you say
that there are tools available
for solving them?
CL: I would say that the tools are not
too bad. What I would like to have is
excellent tools, which is much more
demanding.
OPTIMA: What is the major
deficiency of the present tools?
CL: Speed of convergence. From the
theoretical point of view it is very
difficult to develop excellent tools. It
has actually been proved that it is im
possible! The complexity theory of
Nemirovskii (Nemirovskii and
Yudin, Problem Complexity and
Method Efficiency in Optimization,
W iley,19 ,,. ...J i l! ... . .. ,
not exist any fast algorithm to mini
mize a general convex function.
Therefore, if we really want "excel
lent tools," we are forced to use heu
ristic methods. This negative theo
retical result is extremely important
as a safeguard to prevent people
from trying to prove theorems that
have got to be wrong. Unlike the tra
ditional theory of computational
complexity where it is still not
known whether P is equal to NP,
Nemirovskii's result tells you thatfor
sure such algorithms do not exist!
The same theory tells you also that
one particular variant of a bundle
method is optimal in a certain sense:
its rate of convergence cannot be
made faster independently of the
number of variables. These results
are true only if you consider the gen
eral class of convex functions; for
some particular subclasses, the situ
ation may change.
OPTIMA: Does the community
aim at developing a general
purpose code for solving generic
nonsmooth problems?
CL: As far as solving generic
nonsmooth problems, the existing
codes are all right, at least theoreti
cally. On the other hand, it is ex
tremely difficult to develop codes for
specific problems. The reason is sim
ply that we do not know how to clas
sify convex functions. Let's consider
the generic problem of minimizing
convex functions given the oracle
I
N? 45
MARCH 1995
PAGE 3
000
that computes the subgradient. We
don't know right now which sub
classes of convex functions are easy
in the sense that they can be mini
mized quickly with the help of this
oracle. Maybe some day we will
know what kind of functions are
easy, but right now it is impossible to
say.
OPTIMA: In this way it is hard
to know exactly what you are
developing for.
CL: Right! We have got to develop
general codes, but we have no idea
what particular problem will be
more amenable to a specific method.
Therefore, we cannot develop the
specific method.
The big open question is the one that
I mentioned earlier.
OPTIMA: You mentioned
earlier that a very important
open question is how to general
ize the secondorder concepts
from classical calculus. If you
had such a generalization, what
would the consequences be?
CL: The aim would be to have
algorithms that, due to Nemirov
skii's result, would not be
superlinear, but at least, based on
some serious grounds, likely to be
very fast. Alternatively, this generali
zation might help us to say which
problems are easy, i.e., amenable to
fast convergence.
OPTIMA: Which areas provide
input to, or interact with,
nonsmooth optimization?
CL: The introduction of convex
analysis into the field, more deeply
than has been the case before, is one
of the new inputs that can be useful.
Here I think more of the introduction
of convex analysis in numerical op
timization, rather than on the theo
retical side. Convex analysis is, of
course, wellknown on the theoreti
cal side for optimality and stability
conditions, but for algorithmic de
velopment it is relatively new. I also
feel strongly about the harmony be
tween smooth and nonsmooth opti
mization.
OPTIMA: What is your feeling
about possible future develop
ments in nonsmooth
optimization?
CL: For the future, there is another
field of application of nonsmooth
optimization, which has just been
born but is growing very fast,
namely, eigenvalue optimization.
You have a symmetric matrix that
depends on certain parameters and
you want to adjust these parameters
such that the maximal eigenvalue
becomes as small as possible. This is
a nonsmooth problem occurring in
both socalled robust control, which
is an extremely expanding subject in
optimal control, as well as in combi
natorial optimization (see, e.g., C.
Delorme and S. Poljak, "Laplacian
Eigenvalues and the Maximum Cut
Problem," Mathematical Program
ming62 (1993) 557574, or L. LovAsz,
"On the Shannon capacity of a
graph," IEEE Trans. Information
Theory 25, (1979) 17). There are al
ready some approaches available for
this problem, such as a very recent
one by Nemirovskii based on interior
point methods; see also the work by
the team of S. Boyd at Stanford (In
formation Systems Laboratory). This
technique is extremely powerful but
rather heavy. Convex optimization
would, hopefully, result in a more
flexible and versatile method even
though the speed of convergence
would be more modest.
I also think that there will be an ex
treme need for development of algo
rithm s for q1i .i I ., [. .ti rtn, i ,
and this leads me to a second way of
describing bundle methods. Think of
the DantzigWolfe algorithm where
you solve a sequence of linear pro
gramming problems. The bundle
principle can be viewed along the
lines of just adding a quadratic term
to the DantzigWolfe master pro
grams. This has the beneficial effect
of stabilizing the DantzigWolfe
mechanism, which is highly un
stable. Each master program will
now be a quadratic problem instead
of a linear one. So, the more we want
to have software for large problems,
the more we will need efficient soft
ware for solving quadratic problems.
OPTIMA: What is, in your
opinion, the situation in the
field of general nonlinear
pI 11,o1n' in..1?
CL: I feel that nonlinear program
ming in general needs fresh blood.
One proof to me that this is the case
was, for instance, that when the ellip
soid method was developed, it cre
ated a lotofnoise. Next, it was the de
velopment of interior point methods,
which now very much dominate the
literature in the field. This was to me
a sign that the community was in
need of a new idea and that new fresh
blood is needed which, in a sense, is
a bad sign for the nonlinear commu
nity.
Moreover, I think that the general
work that has been done in nonlin
ear programming the last 4050 years
has basically come to an end. There
are few important theoretical devel
opments to foresee. I feel that the
only really important developments
are going to be at the computational
side, like the improvement of the
simplex method for linear program
ming over the last decades. I also
believe that for the field to revive,
new ideas are needed; one is the use
of convex analysis, which is why I am
so excited about it.
I agree with John Dennis who says
that we should work closer to the
applications because research in this
field has to be motivated by applica
tions. I am extremely proud that my
own research has started with a spe
cific application. I consider myself
very lucky for this reason. In general,
it L, ..1 !ui t u Ii becausetheseapplica
tions, of course, come from people
who are totally outside our world,
and we have no common language.
They express themselves in a way
that is extremely hard for us to un
derstand and conversely, of course.
Therefore, it requires a lot of gener
osity from both sidesand, in par
ticular, from our side!
I~~
N 45
MARCH 1995
PAGE 4
'AGE 5 N~45 MARCH 1995
ick den Hertog and
Jiming Liu were two of
the three finalists for the
A.W. Tucker Prize which
is awarded by the Math
ematical Programming Society
for an outstanding paper by a
student. The third finalist, and
winner, was David P. William
son who was interviewed in the
previous issue of OPTIMA.
Dick den Hertog received both
his undergraduate and his Ph.D.
in computer science and applied
mathematics from Delft Univer
sity of Technology, Delft, The
Netherlands. His thesis "Interior
point approach to linear, qua
dratic and convex programming
OPTIMA: How did you choose
your Ph.D. topics?
DDH: I also worked on interior point
methods for my Engineering degree,
and I really liked it, so Icontinued the
work for my Ph.D.
JL: After I got my bachelor's degree,
I went to another institute for three
years as a computer programmer.
After a while I got tired of comput
ers, so when I decided to take a
master's degree, I wanted to choose
a topic between computer science
and applied mathematics. That is
why I chose computational math
ematics. In 1990 I tried to apply to
some schools in the U.S., and even
tually I got financial support from
George Washington University. I
DICK DEN HERTOG & JIMING LIU
Algorithms and complexity"
was supervised by Kees Roos.
He currently has an appoint
ment with the consultancy firm
Center for Quantitative Meth
ods (CQM), Eindhoven, The
Netherlands.
Jiming Liu received his under
graduate degree in combinato
rial optimization from Beijing
Institute of Technology. He is
completing his Ph.D. thesis at
George Washington University,
Washington D.C., supervised by
Anthony Fiacco. His submission
to the Tucker Prize competition
consisted of five papers on sta
bility and sensitivity analysis of
generalized equations and varia
tional inequalities.
already knew of Anthony Fiacco
since I had studied his book with
McCormick (A.V. Fiacco and G.P.
McCormick, Nonlinear Program
ming, Sequential Unconstrained
Minimization Techniques, Wiley,
1968) already in China. When I came
to V .I l..i hin. in ProfessorFiaccowas
interested in stability and sensitivity,
so he asked me to write some papers
with him. So I started very early, just
after beginning my Ph.D., to write
papers. Later on, I started to write on
my own. Some of this work is follow
ing new directions and some is ex
tending my work with Fiacco.
OPTIMA: Within your field of
research, what is the most cen
tral result?
DDH: Of course, Karmarkar's work
is the most important one. It was the
root of all developments in the field
of interior point methods. Besides
that, I think the book of Fiacco and
McCormick was very stimulating for
me. My research mainly concen
trates on the pathfollowing meth
ods, which forms a subclass of the
interior point methods, and the path
following techniques go back to the
book of Fiacco and McCormick.
Also, the book of Nesterov and
Nemirovskii (Y.E. Nesterov and A.S.
Nemirovskii, SelfconcordantFunc
tions andPolynomialTimeMethods
in Convex Programming, Central
Economical and Mathematical Insti
tute, USSR Academy of Science,
Moscow, USSR, 1989), published
later,i. :a .m im l ..It n I I l. .,1, I,. r
me. Here I also want to mention that
the work by, for instance,
Anstreicher, Gonzaga, Ye and, last
but not least, my supervisor Kees
Roos has all been very important to
me. When I started to work on inte
rior point methods, Kees Roos gave
me his articles, and they stimulated
me to start working in this field. For
me, Karmarkar is the "father" of the
interior point methods, but I should
be careful here! Some of the interior
point methods go back to the'60s, but
at least he gave the impetus that
started an important development.
JL: Can I saysomethinghere?As I see
this whole development, I think a
main contribution of Karmarkar is
that he in some sense pointed out that
the simplex method is not the only
way.
DDH: But Khachian had already
pointed that out, so I don't think it is
as simple as that.
JL: But Karmarkar was the first one
to really challenge the simplex
method.
DDH: If you look at the implemen
tation of interior point methods to
day, they are very different from
Karmarkar's. So, it' ., 1 difficult to
check if the claim that Karmarkar
made at the time is really true, at least
for the variant that he proposed.
OPTIMA: So, let me ask you,
Jiming, what the central results
are in your area.
JL: I think that Fiacco and Steve
Robinson pioneered this field. At the
beginning they made very important
contributions. Fiacco proved some
very basic sensitivity results, but
these results do not take care of the
nonsmooth case. I believe that Steve
Robinson was the first one to come
up with a very nice idea about how
to deal with the nonsmooth charac
teristics of the KarushKuhnTucker
conditions.
OPTIMA: What would you con
sider to be your own biggest
contribution?
DDH: I developed a machinery to
prove complexity results for path
following methods, also for long
step methods, which could easily be
extended to the nonlinear convex
case. To obtain these results I used
many results of others.
JL: I think I wrote a couple of papers.
In three years there were about 20,
and these papers cover a lot of areas,
but most concern stability and sensi
tivity analysis.
OPTIMA: Can you give an
example of such a result?
JL: Actually, it's kind of technical!
For instance, Steve Robinson proved
a very beautiful result which says
that if we have the MFCQ and gen
eral secondorder sufficient condi
tions, then the perturbed solution is
upLipschitz continuous, which is
the basic property we want. Since my
background is half computer science
and half applied mathematics, I al
N? 45
PAGE 5
MARCH 1995
PAG 6h N045MRC 19
Sr
ways want to deal with something
we can compute, so I developed a
theory trying to estimate the
Lipschitz coefficient. I believe this
work is important in practical situa
tions. Another important contribu
tion is that I proved a very nice result
for variational inequalities. I provide
a necessary and sufficient condition
for strong stability and I think that
result is very cute.
OPTIMA: Which are the re
search questions that you would
like to study next?
DDH: Concerning interior point
methods, I would like to try to get
some further complexity results. For
linear programming problems, the
most efficient methods are the
U
O
Cu
primaldual ones. If you look at the
nonlinear programming problems,
then we can get good complexity re
sults only for the pathfollowing
methods. So, I think it is a nice area
here to prove some complexity re
sults for the primaldual methods for
nonlinear problems. In practice these
methods have proved to be very ef
ficient, but the theory is not yet there.
JL: I am trying to integrate different
algorithms in optimization. My gen
eral point of view on optimization is
that here, I talk about nonlinear pro
gramming problems since I wrote
most of my papers on nonlinear pro
gramming; this subject has reached
maturity. But one development
would be the following: Suppose we
Associate Professor
(Research)
Department of Operations Research
STANFORD UNIVERSITY
are dealing with some kind of gen
eral nonlinear programming prob
lembecause my feeling is that users
usually don't want to provide special
structure. Then assume that for a
given algorithm this problem has got
a good complexity result. Maybe for
another class of problems this
.Il...rir I ..i:..m n .' i ,'is veryhigh.
For a second algorithm we probably
have another distribution of com
plexity results, and so on. So, the
point here is first of all: How can we
identify which type of algorithms are
suitable for which class of problems?
Of course, this is difficult. I have been
doing a lot of programming, and I
studied a lot of algorithms, so I have
coded many algorithms to see which
algorithm works best for a given
problem.
The Department of Operations Research, Stanford Uni
versity, is seeking applications for the position of Associate
Professor (Research) in connection with modeling and algo
rithm development work in the Systems Optimization
Laboratory. The successful candidate will collaborate with a
. ,11, l group conducting research on planning under uncer
tainty. The appointment may be held for a period of up to
six years, depending on performance and the i iil I1 .h of
research funding. This is a nontenure track, externally
funded position, which is not renewable. Initial external
funding to support this position is in place at the moment.
Applicants should display excellence in research through
publications in the stochastic mathematical programming
area. In addition, they should possess extensive experience
in modeling and the implementation of largescale algo
rithms.
Letters of application and resumes should be addressed to:
Chairman
SOL Search Committee
Department of Operations Research
Stanford University
Stanford, CA 943054022
The deadline for receipt of applications is May 1, 1995.
Stanford University is an affirmative action/equal oppor
tunity employer and especially welcomes applications
from women and minorities.
DDH: Best for your implementation
then?
JL: Right... it's not mature yet, but my
current results are very promising,
especially for unconstrained optimi
zation.
OPTIMA: Is there some particu
lar event from your time as a
Ph.D. student that you remem
ber particularly well?
DDH: I remember several occasions
when the whole interior point
method group at Delft was very ex
cited about new results which we
obtained. I also remember many
phone calls with my supervisor,
Kees Roos, late in the evenings, when
one of us suddenly discovered some
thing!
JL: It's a happy occasion to obtain a
new result. I also remember once I
wrote a paper, and I discovered later
that the basic assumption was
wrong! It was very embarrassing.
But mostly I remember the happy
moments.
OPTIMA: What are your plans
for the near future?
DDH: I like it very much to work in
the consultancy firm. It is very enjoy
able to talk to people about their
problems and to solve them by OR
techniques. I am actually very aston
ished that these techniques can be so
useful in practice, because I heard so
many negative stories. I don't think
they are true. But I still want to stay
in touch with the academic world
and to publish papers, mainly on
practical work. I was also surprised
that these two years at CQM gave me
a lot of very good ideas on what I
would like to work on in the future.
What I would like to do is to work
about four years at CQM, then two or
three years at a university, four years
CQM and so on. That would be ideal!
JL: I prefer to get an academic job, but
the market now is very tough, and I
don't think it will improve in the next
two or three years. I just have to see
what happens!
I 

N 45
MARCH 1995
PAGE 6
PAGM7 E 4 MACHf99
In their paper [1], the group mod
estly describes the technique as fol
lows: "In 1954 Dantzig, ,,II ..I..
and Johnson [2] showed a way to
solve large instances of the TSP; all
that came afterward is just icing on
the cake. The purpose of the present
paper is to describe some of the icing
we have added on top of the previous
layers. Our icing comes in five fla
vors:
a. l \ppkpiic, Bob Bixby,
\ .L ( .l u .1 Hill Cook have
...I i, ... i 97 in the
i l'i ii h. .... i .r instance is
. t, l,.. I . r .... .. .r w which an
. .I i"." I,! .h .. .. I .... 'n. T he pre
. 1 4 I . .. (instance
tn!, ,. I ,.'. i, ,r I I B)was held
[. i ... ,. ,. ,.
. pl.b .. ' ,. ~r .. I.. Igues started
their first runs on a 3,038city in
stance in January 1992, using about
sixty workstations and a computer
program based on known techniques.
After monitoring the growth of the
branchandcut tree, they realized
that new tricks were needed. By April
1992, they had come up with suffi
ciently good tools to solve the 3,038
city instance. Since then they have
improved their techniques further
and solved several previously un
solved instances from the TSPLIB.
The 7,397city instance was actually
solved twice. The first time was on a
network of Sun Sparcations at
Bellcore, taking the idle cycles from
machines at night and weekends. The
second time, to write a certificate of
the optimal solution, was with the ar
ray of Silicon Graphics machines at
Silicon Graphics' Center in Houston.
The array consisted of 10 Challenge
XL machines, each having 20 proces
sors and 2 gigabytes of memory.
(i) new ways of finding cuts,
(ii) new ways of handling the
LP relaxations,
(iii) new ways of selecting an
edge on which to branch,
(iv) new ways of finding an
incumbent tour,
(v) solving the problem in
parallel on a network of
UNIX workstations."
Along with a comprehensive descrip
trc.n .f rh "Lirer lI r h nFr ing trhe"
present a nice historical account ot
the computational development since
Dantzig, Fulkerson and Johnson.
The paper is available by anonymous
ftp from netlib.att.com in the direc
tory netlib/att/math/applegate/TSP.
The certificate of optimality of in
stance pla7397 can be found in the
same directory.
TRAVELING
SALESMAN
INSTANCE
SO I /
The "LaserLogic"
process was de
vised at the
AT&T Bell
Laboratories fa
cility in Cedar
ANOTHER
LAYR.O
I
UlL, : .' J J 1
sey, in 1986. At
the time, it seemed as if it might well
be competitive with other methods
for producing custom chips. For the
technique to work, it was necessary to
be able to get good solutions to the
TSP in under 20 minutes on their
workstations. Given the speed and
memory capacity of the workstations
at the time and the size of the largest
instances, it was not possible to use
very sophisticated TSP heuristics.
However, Jon Bentley (of AT&T Bell
Labs' Computing Science Research
Center) and David Johnson did pro
vide a fast implementation of the
simple nearest neighbor heuristic,
which easily met the time bounds
and produced solutions that were two
to four times shorter than the ones
initially used, which were simply to
cut the interconnections in the order
in which they occurred in the listings
produced by the CAD tools used to
design the circuits. The LaserLogic
process eventually proved
NEXT PAGE )
MARCH 1995
N? 45
PAGE 7
ON THE INSTANCE PLA7397
The instance arose in an AT&T Bell
Laboratories application involving
programmable logic arrays (PLA's),
and was contributed, together with a
33,810 and an 85,900city instance,
by David Johnson. Programmable
logic arrays are VLSI chips that are
:., i,, I; ,I.i r ..! as a regular array
of interconnected components which
can be converted to custom inte
grated circuits by using a laser to
vaporize specified interconnections.
( 'I" i i. the order in which the in
terconnections are to be vaporized is
a moreorless canonical traveling
salesman problem.
TIM""U"N"09mali"m m
uncompetitive but, as David Johnson puts it,
"Nevertheless, it is nice to know, even after the
fact, precisely how much room for improvement
there was. For larger instances, we must settle for
slightly weaker estimates, such as those deter
mined by the HeldKarp lower bound on optimal
tour length, which is typically between 0.5 and
1% below the optimal length. Had the
LaserLogic application arisen today, we probably
could have provided much better solutions within
the specified 20 minute time bound, although
,il not optimal ones. On a modern workstation,
nearest neighbor takes just 3 seconds to handle
the 85,900city instance. Thus we might try
something like the ( I ''. Wright savings heuris
tic, which gets within 10.1% of the HeldKarp
lower bound for this instance in about 17 sec
onds, or a fast implementation of 3opt, which
gets within 3.7% in about 90 seconds, or even the
famous LinKernighan algorithm, which gets
within 1.6% in about 7 minutes." For further de
tails see [3].
COMPILED BY KAREN AARDAL, USING INFORMATION
PROVIDED BY WILLIAM J. COOK, BELLCORE, AND DAVID S .
JOHNSON, AT&T BELL LABORATORIES.
References
[11 D. Applegate, R.E. Bixby, V. ChvAtal and
W.J. Cook, "Finding cuts in the TSP," Prelimi
nary report, August, 1994.
[2] G.B. Dantzig, R. Fulkerson and S.M.
Johnson, Solution of a largescale traveling
salesman problem," Operations Research 2
(1954), 393410.
[3] J. Bentley, L. McGeoch, D.S. Johnson a d E.
Rothberg Nearoptimal Solutions to Veryarge
Traveling Salesman Problems (forthco ng).
0/
(I,
The Committee
on Stochastic
Programming
(COSP)
A
x
COSP is an official committee of MPS, currently with 12 members:
Aharon BenTal (Israel), John R. Birge (U.S.A.), Michael Dempster
(England), Jitka Dupaovi (Czech Republic), Yuri Ermoliev (Austria/
Ukraine), Kurt Marti (Germany), John Mulvey (U.S.A.), Andris
Prekopa (Hungary), Secretary Andrzej Ruszczyiski (Austria/Poland),
Tamas Szintai (Hungary), Chair: Stein W. Wallace (Norway), Will
iam Ziemba (Canada).
The major activity of COSP is to organize an International Confer
ence in Stochastic Programming every three years. So far, there have
been six such conferences: Oxford, England (Dempster, 1974),
Koszeg, Hungary (Prikopa, 1981), Laxenburg, Austria (Wets, 1983),
Prague, Czechoslovakia (Dupacovi, 1986), Ann Arbor, U.S.A. 'P.;...:
1989), Udine, Italy (Andreatta and Salinetti, 1992). The next meet
ing will be in Israel in 1995. It is described separately in this issue of
OPTIMA. During its history, COSP has had two previous chairs,
namely Andris Prekopa and Roger J.B. Wets. Until 1992, the
secretary was Jitka Dupacovi.
About one year before a conference takes place, the chair of COSP
appoints two committees, one to suggest the site of the next meeting,
the other to nominate a new chair and secretary of COSP. This com
mittee may also nominate new ordinary members. During the confer
ence a business meeting is held, and those present vote on the choice
of the next site and on new members. The list of names is sent by the
chair to the Council .I Ii' t.., approval. The current committees
are chaired by Sen (committee members) and King (site).
COSP operates an email list of scientists interested in stochastic pro
gramming. Anything sent to cosp@iiasa.ac.at will be forwarded to
all addresses on the list. To be included in this list, please contact
Ruszczy'nski at rusz@iiasa.ac.at. This rather extensive list has been
used to communicate new results, report on computational experi
ments, and gives news about positions, conferences, workshops, etc.
Another concern of COSP is the establishment of a database for sto
chastic programming problems and the design (modification) of
standard input formats.
Karl Frauendorfer (frauendorfer@sgcll.unisg.ch) and David Gay
(dmg@research.att.com) are working on these issues. Frauendorfer
takes the main responsibility for the contents of the database, whereas
G i; '!1 run it; Gay already administers netlib's Ip/data and I .',.
erators collections (linear programming test problems).
Together they also consider the possibility of adding features to the
standard input format. Anyone with ideas on the input format or
with problems they think fit for the problem base, should contact
Frauendorfer or Gay. There will be a special session on these issues at
the next International Conference on Stochastic i',... I ,..'i'' in
Haifa, Israel.
Stein W. Wallace, Department of Managerial Economics and Opera
tions Research, The Norwegian Institute of Technology, University
of Trondheim, N7034, Trondheim.
Eithan Schweitzer, Faculty of Industrial Engineering and Manage
ment TechnionIsrael Institute of Technology, Haifa 32000, Israel.
 
PAGE 8
N? 45
MARCH 1995
PAGE 9 N0 45 MARCH 1995s
CHINESE
MATHEMRTICRL
PROGRAMMING
SOCIETY FOUNDED
The Third National Conference on Optimiza
tion, with about 100 participants, was held in
Xi'an October 510, 1994. At the conference it
was unanimously decided that a permanent
organization for mathematical programming
shouldbe created, which ledto the establishment
of the Chinese Mathematical Programming
Society. The councilwasformedwith YueMinyi
as president, Yu Wenci andZhang Xiansun as
vice presidents, and Han Jiye as secretary.
The purpose of the society is to promote the de
velopment of the theory and application of
mathematicalprogrammingin China. To coor
dinate with the activities ofMPS, it was decided
to hold triennialnationalsymposium thesame
years as the international symposia. Hence, the
next Chinese symposium willbeheldin 1997in
Wuhan, which is the capital ofthe Hubeiprov
ince. In addition to the triennialsymposia, con
ferences on special topics in mathematicalpro
gramming will occasionally be organized. A
biannual newsletter will be issued in Chinese.
S Now for a few words about
COAL and the decision to
dissolve it: The Committee on
I Algorithms (COAL) was formed in
1973 by a handful of members of
Sthe Mathematical Programming
Society to develop guidelines for
the reporting of computational re
sults and for the comparison of
optimization software. The guide
lines were subsequently published
and adopted by Mathematical Pro
gramming and Operations Research,
as well as other journals.
In order to keep the growing com
munity of researchers informed of
new developments in computa
tional mathematical programming
and to promote the goals of COAL,
a newsletter (later called the COAL
Bulletin) was started with the first
issue appearing in September 1978.
Initially, the newsletter was only
distributed to a mall croup of r 
searcher ii naed in so tn, are Jd 
velopm'ent bt %at n e entuail l enCr
to all mctr.,cL ei %i lien the !oci>t\
Agreed to i. C r thie pubbiaLatin n. i.
mailing co.t.
In addition Io th. nei letter,
COAL acil el\ prrnimoted increa ed
research on compuitatioial iiue~,
and world to open more
channel tr the publiic.
tion of ikch researh. (. O
This wai a.ionimliihed
by sponoring as.e.oln at MIl'S
SORSA/TIMS, and SIAM meetings,
organizing small focused meetings,
Sand maintaining a library of test
problems and problem generators.
As the quality and significance of
Sthe contributions improved, the
Beale/OrchardHayes Prize was
created to recognize outstanding
developments in computational
Immmo
optimization. As computational
issues became more and more an
integral part of the optimization
community and the optimization
literature, the members of COAL
reduced their activities as a group.
Then, at the MPS meeting in Ann
Arbor last August, COAL voted
unanimously to dissolve itself,
having succeeded in accomplishing
all of its goals. There will be a final
farewell issue of the Bulletin to
include contributions that were
inhand at the time, an article on
the history of COAL and the news
letter, and a master in
S dex of all issues.
O Simultaneously, the
MPS Council suggested
F that an expanded
S OPTIMA can serve as
the focal point for com
W municating with inter
A ested members. There
are still many issues that
R need to be addressed
E and certainly the speed
of progress in comput
inlg. both hardware and
ort% ire., call for a forum to keep
abrieat ol dei. elopments. The Soft
i\.ire ind Computation Department
%ili till lhi. \ oid.
mpt tat ion
Fa. I khayyal, Software and
Computation Editor
School of Industrial and Systems
Engineering
Georgia Institute of Technology
Atlanta, Georgia 303320205 USA
email: faiz@isye.gatech.edu
phone: +1 404 8943037
fax: +1404 8942301
I
PAGE 9
N? 45
MARCH 1995
PAC 10 N"l45 MARCH 1995~
c F. FF r[ I r
E ; : ,
Forthcoming
Conferences
"
PACE 10
N? 45
MARCH 1995
OPTIMIZATION DAYS 1995
Montr6al, May 1012
Seventeenth Symposium on
Mathematical Programming
with Data Perturbations
Washington, D.C.,
May 2526, 1995
Ettre Majorana Centre for
Scientific Culture International
School of Mathematics "G.
Stampacchia", Erice, Sicily,
Italy, June 1321, 1995
) 6th Stockholm
Optimization Days,
Stockholm, Sweden,
June 2627, 1995
VII International Confer
ence on Stochastic Program
ming, Nahariya, Israel,
June 2629, 1995
SConference on Optimization
'95, Braga, Portugal,
July 1719
International Symposium
on Operations Research with
Applications in Engineering,
Technology, and Management
(ISORA), Beijing, Aug. 1922,
1995
International Workshop on
Parallel Algorithms for Irregu
larly Structured Problems,
Lyon, France, Sept. 46, 1995
Symposium on Operations
Research 1995, University of
Passau, Germany, Sept. 1315
AIRO '95 Annual Confer
ence, Operational Research
Society of Italy, Ancona, Italy
Sept. 2022, 1995
ICCP95lnternational Con
ference on Complementarity
Problems: Engineering &
Economic Applications, and
Computational Methods,
Baltimore, Maryland, U.S.A.
Nov. 14, 1995
) Conference on Network
Optimization, Feb. 1214,
1996, Center for Applied Opti
mization, Gainesville, Florida
1 XVI International
Symposium on Mathematical
Programming, Lausanne,
Switzerland, Aug. 1997
AGE 11 No45 MARCH 1995
OPTIMIZATION DAYS 1995
Montr6al, May 1012
GERAD (Groupe d'itudes et de Recherche en Analyse des Decisions)
5255, avenue Decelles, Montreal, CANADA, H3T 1V6
Tel: (514) 3406043; email: jopt95@crt.umontreal.ca
FAX: (514) 3405665
Seventeenth Symposium on
Mathematical Programming
with Data Perturbations
Washington, D.C.
May 2526, 1995
This symposium is designed to
bring together practitioners who use
mathematical programming optimi
zation models and deal with ques
tions of sensitivity analysis with re
searchers who are developing tech
niques applicable to these problems.
Contributed papers in mathemati
cal programming are solicited in
the following areas:
(1) Sensitivity and stability analysis
results and their applications. (2)
Solution methods for problems in
volving implicitly defined problem
functions. (3) Solution methods for
problems involving deterministic or
stochastic parameter changes. (4)
Solution approximation techniques
and error analysis.
Clinical presentations that describe
problems in sensitivity or stability
analysis encountered in applica
tions are also invited.
Abstracts of papers for presentation
should be sent in triplicate to Pro
fessor Anthony V. Fiacco. Ab
stracts should provide a good tech
nical summary of key results, avoid
the use of mathematical symbols
and references, not exceed 500
words, and include a title and the
name and .,II mailing address of
each author. The deadline for sub
mitting abstracts is 17 March
1995.
Approximately 30 minutes will be
allocated for presenting each paper.
Anthony V. Fiacco, Organizer
Sponsored by the Department of
Operations Research and the Insti
tute for Management Science and
Engineering, School of Engineer
ing and Applied Science, The
George Washington University,
I,.1 l ..i. D.C. 20052. Tel.
(202) 9947511.
Ettre Majorana Centre for
Scientific Culture
International School of Math
ematics "G. Stampacchia"
Erice, Sicily, Italy
June 1321, 1995
FIRST ANNOUNCEMENT
This workshop aims to review and dis
cuss recent advances and promising re
search trends in the field of Nonlinear
Optimization concerning theory, algo
rithms and innovative applications.
Both the finite and the infinite dimen
sional cases will be of interest.
As usual, the course ,il be structured to
include invited lectures and i.... I r... I
lectures. Proceedings including the in
vited lectures and a selection of contrib
uted lectures will be published.
Invited lecturers are:
J. Abadie, V. Demyanov, Y.G.
Evtushenko, M. Fukushima, L. Grippo,
J.J. Judice, O.L. Mangasarian, J.J.
More, J. Nocedal, J.S. Pang, P.M.
Pardalos, E. Polak, L. Qi, S.M.
Robinson, R.T. Rockafellar, R.
Schnabel, E. Spedicato, Ph. Toint
For details contact:
Prof. Gianni Di Pillo, Dipartimento di
Informatica e Sistemistica, Universith di
Roma "La Sapienza", via Buonarroti 12,
00185 Roma, Italy.
email: erice@peano.dis.uniromal .it
FAX: +39648299218
_____ ____ ____ I ____ ____ ____ ____ ___
VII International Conference
on Stochastic Programming
Nahariya, Israel, June 2629,
1995
The VII Conference on Stochastic
. be hosted by the
TechnionIsrael Institute of Tech
nology, and held in Nahariya, Israel
(near Haifa) on June 2629, 1995.
The conference is I. .II. 1... by the
EURO XIV14th European Confer
ence on Operational Research, which
will be held at the Hebrew Univer
sity, Jerusalem, July 36, 1995.
The Conference will take place at the
Carlton Hotel, Nahariya, Israel.
Nahariya is a lovely small resort town
on the Mediterrenean Sea, located 30
kilometers north of Haifa and about
140 kilometers from BenGurion Air
port. The weather in JuneJuly in
Nahariya is about 2830C by day and
about 2022C by night. The hotel is
located at the center of the town with
shops and restaurants nearby. It pro
vides :,ll service, airconditioned
rooms with telephone, radio, T.V.
and video service, outdoor swimming
pool, sauna, nightclub, bar, cafeteria
and a restaurant. The beach is within
walking distance.
NEXT PAGE )
6th Stockholm
Optimization Days
Stockholm, Sweden,
June 2627, 1995
Theoretical, computational
and applied papers are wel
come for the 6th Stockholm
Optimization Days, a two
day conference on optimiza
tion, to be held at KTH
(Royal Institute of Technol
ogy) in Stockholm, Sweden,
June 2627, 1995.
Sessions are planned
on various aspects of
optimization, includ
ing nonsmooth F
optimization, linear
and nonlinear pro
gramming.
I
Invited speakers include:
A. BenTal, Technion, Haifa, Israel
R.E. Bixby, Rice University, Houston, TX, USA
J. Desrosiers, GERAD, Montreal, Canada
P.E. Gill, UC San Diego, CA, USA
C.C. Gonzaga, Federal Univ. of Rio de Janeiro, RJ, Brazil
A. Griewank, Technische Universitat Dresden, Germany
D.W. Hearn, U. Florida, Gainesville, FL, USA
C. Lemarechal, INRIA, Rocquencourt, France
R. Mifflin, Washington State University, Pullman, WA, USA
W. Murray, Stanford University, CA, USA
A. Nemirovskii, Technion, Haifa, Israel
Yu. Nesterov, CORE, Belgium
M.L. Overton, Courant Institute, NY, USA
C. Sagastiztbal, INRIA,
SRocquencourt, France
A. Sartenaer, FUNDP,
Namur, Belgium
T. Steihaug, University
0 R of Bergen, Norway
Ph. Toint, FUNDP,
S Namur, Belgium
R. Vanderbei, Princeton
University, NJ, USA
Abstracts (maximum 200 words) should be sent
by May 1, 1995, (preferably by email) to:
email: optdays@math.kth.se
address:
Optimization Days
Division of Optimization and Systems Theory
KTH
S100 44 Stockholm Sweden
Fax: +46 8 22 53 20.
Further information may be obtained from the
addresses listed above.
The conference is financially supported by the
Goran Gustafsson Foundation and the Swedish
National Board for Industrial and Technical Devel
opment (NUTEK). Organizers are Ulf Brannlund
(head), Anders Forsgren, Per Olov Lindberg and
Krister Svanberg from the Division of Optimization
and Systems Theory, Department of Mathematics,
Royal Institute of Technology (KTH).

N? 45
MARCH 1995
'AGE 11
PAG 12 ~ ~ ~ IR I No45 MACH 199
The main topics of the conference are:
*Stochastic programming, theory
and application
.Stability and sensitivity analysis
*Stochastic combinatorial
optimization
*Statistical approach to stochastic
programming
*Stochastic approximation techniques
*Optimization of discrete event
(simulation) models
Application of stochastic program
ming to artificial r,. !,Io . finance,
production, reliability, etc.
One hour, stateoftheart tutorial
and review lectures will be presented
by invited speakers: J.R. Birge, A.
Gaivoronsky, G. Pflug, B. Polyak,
A. Shapiro and S. Zenios. The tuto
rial and review lectures will be held
in special (non parallel) sessions.
Contributed sessions and presenta
tions are welcome. The contributed
presentations are expected to be 30
minutes (including about 5 minutes
for questions and/or discussion).
Presentations will be grouped into
sessions of 90 minutes each, by topic.
S11... will be two or three simulta
neous parallel sessions.
The social part of the conference will
consist of a reception, sponsored by
the Mathematical Programming Soci
ety, a dinner at RoshHaniqra after
visiting the famous caverns formed
by the powerful waves of the
Mediterrenean, and a banquet on the
last evening of the conference. An ex
cursion to Galilee on Friday, June 30,
1995, will be organized for partici
pants who stay over the weekend.
The members of the international
scientific committee are: Z. Artstein
(Israel), M. Avriel (Israel), H. Ben
Haim (Israel), A. BenTal (Israel),
J.R. Birge (U.S.A.), M.A.H.
Dempster (Canada), J. Dupaeovd
(Czech Rep.), D. Elmakis (Israel),
Y. Ermoliev (Russia), A. Gaivoronsky
(Italy), G. Infanger (U.S.A.), A.J.
King (U.S.A.), P. L'Ecuyer (Canada),
T.M. Liebling (Switzerland), K.
Marti (Germany), A.S. Nemirovskii
(Israel), G. Pflug (Austria), A.
Prekopa (U.S.A.), B. Polyak
(Russia), S.M. Robinson (U.S.A.),
R.T. .... I ir. I r (U.S.A.), U.G.
Rothblum (Israel), A. Ruszczyhski
ii'..1 ,,, I, S. Sen (U.S.A.), A. Shapiro
(U.S.A.), M. Teboulle (Israel), S.
Uryasev (U.S.A.), and S.W. .II .
(Norway).
The members of the organizing
committee are: Arkadi Nemirovskii,
Reuven Y. Rubinstein (Chair),
I ,l r..i Schweitzer of the Faculty of
Industrial r '. i. ; i.. L and Manage
ment at the Technion, and Marc
T i .. il.: of the Department of
Statistics and Operations Research
at TelAviv University.
The last date for submitting abstracts
was March 1, 1995, but for more in
formation and for registration please
contact the conference secretariat:
Mrs. Nilly Schnapp, Faculty of In
dustrial Engineering and Manage
ment, Technion, Haifa 32000, Israel.
Fax: 9724235194 Email:
iernsO 1 @technion.technion.ac.il
The email address of the organizing,
committee is: gosp@ie.technion.ac.il
Conference on
Optimization '95
Braga, Portugal, July 1719
The main aim of the meeting is to
gather experienced researchers in
Optimization and to invite them to
describe their latest results, experi
ences or applications in a t ,. ..11I,
atmosphere for an audience with an
expected large number of students.
The conference is organized by the
Optimization Group ofAPDIO 
The Operations Research Society of
Portugal. It will take place at the
University of Minho, in Braga, a city
50 km north of Oporto. The pro
gram includes contributed communi
cations and invited lectures in six
different themes by the following
experts:
(1) Linear Programming, D.
Shanno, Rutgers University, USA (2)
Nonlinear Programming, J. Dennis,
Rice University, USA (3) Global
Optimization, R. Horst, University
of Trier, Germany (4) Integer
Programming, L. Wolsey, CORE,
Belgium (5) Network i i..1.. ,
T. Magnanti, MIT, USA (6)
Complementarity and Variational
Inequalities, K. Murty, University of
Michigan, USA.
There is a limit of 60 contributed
talks. The conference language is
English.
Prospective authors are requested to
submit an extended abstract (1 page,
1.5 space), by March 30, 1995, with
a cover page including the name of
the author, affiliation and address,
and key words. All the submitted
abstracts will be refereed by the Pro
gram Committee. Authors will be
notified of acceptance by May 1, 1995.
Submit abstracts to:
(, I' i 'i C I \CE SECRETARIAT
Departamento de Produgao e
Sistemas
Escola de Engenharia Universidade
do Minho
4700 I .., 1 ... .
Tel.: +35153604455
FAX: +35153604456 email:
copt95@ci.uminho.pt
CALL
F O
International Symposium on
Operations Research with
Applications in Engineering,
Technology, and Management
(ISORA)
Beijing, Aug. 1922, 1995
The symposium is intended to pro
vide a forum for researchers working
in Operations Research who deal
with theoretical, computational and
applications aspects of optimization.
Optimization is understood in the
widest sense to include linear, non
linear, stochastic, combinatorial, and
multiobjective systems. Papers pre
sending original research in these ar
eas are sought. Typical, but not ex
clusive, topics of interest include:
Linear and nonlinear .. .......;
Combinatorial and global optimi
zation Multiobjective optimization
SStochastic ... i,.....i .. Sched
uling and network flow Queuing
systems Quality technology and re
liability Simulation Optimiza
tions in VLSI Neural network Fi
nancial modeling and analysis *
Manpower planning Production/
Inventory control Flexible manu
facturing systems Decision analysis
Decision support systems Micro
computer software of OR methods.
Papers on realworld applications
will be *. il appreciated.
Authors are requested to submit 5
copies (in F,! ; I!i of an extended
abstract of not more than 10 pages
by April 1, 1995, to one of the fol
lowing addresses:
Professor Kan ( Il, n Institute of
A .l ,.,t I ,,.! .,..... u r 1 . ,
Academy of Sciences, Beijing
100080, P.R. China; or Dr. Ding
Zhu Du, Computer Science Depart
ment, University of Minnesota,
Minneapolis, MN 55455, U.S.A.
The extended abstract should in
clude the email address of the con
tact person. Authors will be notified
of acceptance or rejection by April
25, 1995. A cameraready copy of
each accepted paper is required by
May 30, 1995. The conference wel
comes any special session on the
above topics. The proposal for a spe
cial session should also be sent to
one of the above addresses before
April 1, 1995. A formal proceedings
will be published and selected papers
will be put in a special issue of The
Journal of Global Optimization.
One author of each accepted paper
should attend the conference and
present the paper.
The symposium will be held at the
West Suburb Hotel, a threestar ho
tel in the university area, 15 kilome
ters from the center of Beijing. The
room rate is about US$35 per day.
~ ~ _L
N 45
MARCH 1995
PAGE 12
S I
One day of : l. ....... to the Great
S II11 is included in the 7. _: I ,,;...
fee (US$300).
For information about the program,
registration and local arrangements,
please contact Kan Cheng at FAX
8612541689 or email
ISORA@amath3.amt.ac.cn or
D.Z. Du at FAX 16126250572
or email dzd@cs.umn.edu.
Conference sponsor: The Asian
Pacific Operations Research Center
within APORS and CAS.
Cosponsors: The Institute of Ap
plied Mathematics, Chinese Acad
emy of Sciences; The Operations
Research Society of ( !,,c The Na
tional Natural Science Foundation
of China; The State Science and
Technology Commission of China
ICCP95
International Conference on
Complementarity Problems:
Engineering & Economic Appli
cations, and Computational
Methods
The Johns Hopkins University
(Homewood Campus) Balti
more, Maryland, U.S.A.
Nov. 14, 1995
The conference will bring together
for the first time engineers, econo
mists, industrialists, and academicians
from the U.S. and abroad who are in
volved in pure, applied, and/or com
putational research of
complementarity problems, to
present and discuss the latest results
in this subject and to offer sugges
Symposium on Operations Research 1995
University of Passau, Germany, Sept. 1315
Sections at this conference include: Linear Programming; Nonlinear Pro
gramming; Combinatorial and Discrete Optimization; Stochastic Models
and Optimization; Realtime Optimization; Scheduling; Control Theory;
Statistics, Econometrics; Macroeconomics; Mathematical Economics and
Game Theory; Neural Networks and Fuzzy Control; Simulation; Decision
Support and Information Systems; Banking, Finance, Insurance; Produc
tion; Logistics; Transportation and Traffic; Inventory; Practical OR
(Application Reports); Decision Theory and Experimental Economics;
and Environmental Aspects.
Conference languages are English and German. The scientific program in
cludes invited plenary and semiplenary lectures as well as contributed pa
pers. Presentation of the latter is limited to 30 minutes including discussion.
The I. ,, i for submission of abstracts is April 1, 1995.
Software i', i.. ,.. Participants are encouraged to present software solu
tions for their contributions or software systems.
Mailing address for abstracts and further information:
Prof. Dr. P. :.l. I .r i.... Universitdt Passau, Wirtschaftswissenschaftliche
Fakultat D94030, Passau
Tel. +49951509339 email: sor95@winf.unipassau.de
tions for collaborative research and
further development of the field.
The conference will last four days
and will consist almost entirely of in
vited presentations. There will be a
small number of selected contributed
talks, and the conference is limited to
100 participants (including the
speakers). A refereed volume of pro
ceedings of the conference will be
published.
There are three major themes of the
conference: engineering applications,
economic equilibria, and computa
tional methods. Each theme will be
represented by experts in the area.
Topics to be covered in the confer
ence are listed below.
AIRO '95 Annual Conference,
Operational Research Society
of Italy
Ancona, Italy, Sept. 2022,
CALL 1995
1995
AIRO '95 Prof. Ferdinando
F 0 R Pezzella Istituto di Informatica 
S Facolth di Ingegneria Universith
S: degli Studi di Ancona Via Brecce
Bianche 60131 Ancona, Italy
Tel: +39712204826
FAX: +39712204474
email: airo@anvaxl.unian.it
Engineering applications: Contact
mechanics problems, structural me
chanics problems, nonlinear obstacle
problems, elastohydrodynamic lubri
cation problems, traffic equilibrium
problems.
Economic applications: Applied gen
eral economic equilibrium, game
theoretic models, NEMS.
Computational methods: Pivotal and
path f.;.1.. methods, smoothing
techniques, quadratic programming
based methods, interior point meth
ods, and projection/proximal based
methods; software development,
modeling language interfaces.
Contact one of the organizers for fur
ther details if you are interested in
participating in the conference or in
contributing a paper for possible pre
sentation.
Organizers:
Michael C. Ferris, (on leave at) De
partment of Economics, University of
Colorado Campus, Box 256, Boul
der, CO 80309
Tel.: (303) 4922651
Email: ferris@cs.wisc.edu
JongShi Pang, Department of Math
ematical Sciences, The Johns
Hopkins University, Baltimore, MD
21218 Tel.: (410) 5167216
Email: jsp@vicpl.mts.jhu.edu
Conference on
Network Optimization
Feb. 1214, 1996, Center
for Applied Optimization
University of Florida
Organized by Bill Hager, Don
Hearn and Panos Pardalos
hager@math.ufl.edu
hearn@ise.ufl.edu
pardalos@ufl.edu
The conference will bring together
researchers working on many differ
ent aspects of network optimization:
algorithms, applications, and soft
ware. The conference topics include
diverse applications in fields such as
engineering, computer science, op
erations research, transportation,
telecommunications, manufacturing,
and airline scheduling.
Since researchers in network optimi
zation come from many different
areas, the conference will provide
a unique opportunity for cross
disciplinary exchange of recent
research advances as ..11 as a foun
dation for joint research cooperation
and a stimulation for future research.
Advances in data structures, com
puter technology, and development
of new algorithms have made it pos
sible to solve classes of network
optimization problems that were
recently intractable. For example,
recent advances have been made in
techniques for solving problems re
lated to airline scheduling, ir..lIr..
communication and transportation,
and VLSI chip design. Computa
tional algorithms for the solution of
network optimization problems are
of great practical .l, ....
The conference will be held at the
Center for Applied Optimization,
University of Florida, Gainesville,
FL.
All presentations are invited. A col
lection of refereed papers will be
published in book form by Kluwer
Academic Publishers. For further
details, please contact one of the
conference organizers.
 II ~" ~
PAGE 13
N? 45
MARCH 1995
PAGE 14
R E V I E W S
The Linear Complementarity Problem
by R.W. Cottle, J.S. Pang, and R.E. Stone
Academic Press, Boston, USA, 1992
ISBN 01121923509
The linear complementarity problem (LCP) originated in the works of Cottle and others
as a unifying model for the study of linear and quadratic programming problems and
bimatrix games. Given an n x n real matrix Mand a real nvector q, the problem seeks
a nonnegative vector x such that Mx+q is nonnegative and orthogonal to x. LCP and
its various generalizations, namely, the nonlinear complementarity problem, the gen
eralized complementarity problem (over closed convex cones), the variational inequal
ity problem, generalized equations, and the recent vertical (horizontal, mixed) linear
complementarity problem, have found many applications in optimization, economic
, I rr i',...i'i .i .,,_,,, nn ... .. ,. ,, .i. ThestudyofLCPhasledto new ideas
and techniques for analyzing complex systems. For example, Scarfs computational
scheme for finding fixed points ofcontinuous mappings, Robinson's inverse and implicit
function theorems for nonsmooth functions, and (the somewhat recent) univalence
results forpiecewise affine functions have had their origins in the LCP theory. Although
basic existence, uniqueness, and stability questions have been answered and various
computational schemes have been proposed, there are still many interesting open
problems.
The book under reviewcontains an exhaustive account of the LCP. Of the seven chapters
in the book, the first two deal with introduction and background material. Chapter
3 deals with the existence and uniqueness aspects. In this chapter, various matrix classes
associated with the LCP are introduced and studied. Chapter 4 deals with the pivotal
algorithms for solving LCPs. Here, the algorithms due to Lemke, Cottle,
Chandrasekaran, and Van der Hayden are fully discussed. In Chapter 5, splitting and
L TJ ..... pr, ; .. . r; ... II. j, ,, .. .. I I. 1 1 1, ... I ,. I J... .I. I, I, I, I .., .... I .
to the interior point methods. This chapter also deals with residues and error bounds.
Intricate geometric and degreetheoretic analysis ofLCP is covered in Chapter 6. The
final chapter deals with the stability and sensitivity aspects of the LCP.
"This extremely
wellwritten book
can be used either
as a textbook (at
the senior under
graduate or at the
graduate level) or
as reference book."
~  ~

N 45
MARCH 1995
_... ...... .
MARCH 1995
_________ ________
The notes and references given at the end of each chapter outline the historical devel
opment of the subject. The exercises vary from routine to .1, 1.. ;'.:. There is an
extensive bibliography. This extremely wellwritten book can be used either as a text
book (at the senior undergraduate or at the graduate level) or as reference book.
This book is highly recommended to anyone interested in the LCP, linear and qua
dratic programming, optimization, variational inequalities, and other related topics.
M. SEETHARAMA GOWDA
InteriorPoint PolynomialAlgorithms in
Convex Programming
by Y. Nesterov and A. Nemirovskii
SIAM, Philadelphia 1994
ISBN 0898713196
Theappearance, !....... I .. r..i.. I. l' . r ... t ...'..i chapterinthestudy
ofcomplexity in mathematical programming, which has since resulted in the production
of over 1000 papers according to the bibliography [3]. Karmarkar's method had a slight
I .. , I ,.j ,,, .. ... I I ,. ,L ,,, 1 ~ ., l r .. 1... I ,,,r .. . r! ....,,l .. .,1, 1
polynomialtime algorithm for linear programming at the timeKI ,. I,; ... ... 11.
,. 1 I ,.l ..... I, .. I fY u d in andN r. ,.. I .1 c,.1 i . ...... . ... !
convex optimization. The computational developments since Karmarkar's paper, both
for interiorpoint and simplex methods, have l'.. ,,, ., nr ..I *. II .11 1
in the lead article by Lustig, Marsten, and Shanno with commentaries on it appearing
in [5]. These developments, however, are not the subject of the present book, which
provides a truly comprehensive study of the foundations of interiorpoint methods for
convex programming.
Karmarkar used projective transformations and an auxiliary potential function in his
algorithm which was pi .. ... T' .. 1 I .... .....i : ... 1 .. .. in a rather restrictive
form. A large amount of effort went into .J..'. i.., .TL i .J extending these ideas and
removing the restrictive assumptions over the next few years. Also, connections with
classical barrier methods and methods of centers were established, and the first path
following methods, with a superior theoretical complexity bound, were developed by
Renegar and soon thereafter Gonzaga. These led to primaldual algorithms and the
explosion of research referred to above.
At the same time as these developments, mainly concerned with complexity issues and
practical computation for linear programming, Nesterov and Nemirovsldi began their
pathbreaking (as opposed to; ,rI .. 1,. I research into what the key elements of
interiorpoint methods were, what allowed polynomial complexity bounds to be estab
lished, and to what general classes ofproblems such analyses could be extended. This book
is the result of five years of their investigations.
The key idea is that of a selfconcordant barrier for the constraint set, a closed convex
set or cone in a finitedimensional space. The notion of selfconcordance requires that
the convex barrier function satisfy certain inequalities between its various derivatives;
of its second derivative, which defines a seminorm at every point of the interior of the
convex set or cone. These conditions ensure, for instance, that Newton's method behaves
N? 45
PAGE 16
Na 45
"This is a book that every
mathematical program
mer should look at, and
every serious student of
complexity issues in opti
mization should own."
nicely in a reasonably global sense. From such a barrier one ... ' r'. I..I .. :
methods, of either barrier or methodofcenters type; if the barrier satisfies an additional
propertynaturalfor a convexcone, oneobtainspotentialr. r, .....I I .I in,. I i1 .
the number of iterations necessary to obtain an eoptimal solution depends polynomially
on In (1/i) and 0, a parameter associated with the barrier.
Chapter 1 of the book provides a very useful overview of the ideas underlying the work
and the contents of each chapter. Then Chapter 2 contains the basic definitions and
properties of selfconcordant functions and barriers, including the beautiful result that
every convex set in R" admits a selfconcordant barrier with parameter 0 of order n.
C hapters3 and4areconcerned nl, 0 .1 ,I.t .. II .. n .. .. 111. i ..l, ,. .. i ... ,, ...
respectively and demonstrate that the r ,. I "'. '". ..... I ..,, I .1 .. L convex
programmingproblem' :rl, ..,r1. .... .. ,;r withalinearobjective function) is the
knowledge of a selfconcordant barrier together with its first two derivatives for the
constraint set, with a reasonably small value for its parameter. (The authors also show
concern for the practical efficiency of variants of their methods.)
Chapter 5 provides tools for constructing such barriers and several examples. While the
result quoted above assures the existence of a barrier with parameter of the order of the
dimension, such a barrier may not be easily computable. For example, the usual barrier
for a polyhedral set in R" defined by m inequalities is the standard logarithmic barrier,
with parameter m not n. On the other hand, the cone of positive semidefinite matrices
of order n, a set of dimension n(n+1)12, admits a barrier of parameter n. (This cone arises
frequently in important optimization problems.) ( hi .... I .. ,. I..... ... fthe
toolsdevelopedpreviouslyto .i. .,,,,,,. .. .. 1, ,l.I ... ..... .I,. .... ii ,
methods for their solution. Chapters 7 and 8 address extensions to variational inequali
ties and various acceleration techniques respectively.
This is a book that every mathematical programmer should look at, and every serious
student ofcomplexity issues in optimization shouldown. I.. ,..I.!.. .... .. 'II.....' ,
thefirstchapter, theintroductorym ar .1 .I i.. I.' ,I .ir ,. l.i.l.I.._.,.,,.
cal notes at the end of the book can be read. For a more detailed study, a serious com
mitment is necessary; this is a technically demanding tourdeforce. The authors provide
m motivation an d e .., i .... . i,..i.. ,,,, ,i,. i. ir.i .. .. r.. i .. I, .
The reader is advised to skim forwards and backwards to help understand some of the
definitions and results. For example, the standard logarithmic barrier function S In x
for the nonegative orthant is introduced on page 40 (with related barriers on pages 33
t..! .. r I ., r r Ip, I ri n,..r ,, ...,n ,, .! ll, .. I ,., I c concordantfunctions
are first defined on page 12. Likewise, a hint of the barriergenerated family on page 66
would assisting understandingthedefinitionofaself ..,.....i, i, I .,, ,I ..,. I ,.l.' 58. The
authors' overview in Chapter 1 is also very helpful in showing the direction the argument
will take.
There seem to be very few misprints. One possibly confusing one appears in (2.2.16):
w2 should be wo in the numerator. And the excellent bibliographical notes were prepared
for an earlierversion of the book; the chapterbychapter remarks need the chapter numbers
increm ented byone.T . l.I,..: .i. ,r It. ... l, ,r l, in. I . ..i.t r, r..i.. .r.
that have since appeared in print. Forc .nq ..1. :, ... ... il .i, .i n .i,. .,
unfortunately, this has not been ,r... ri, ...1 ,r.. I ...... the summer of 1993.
Before concluding, let me mention two subsequent reports. Giiler [1] has found a lovely
connection between selfconcordant barriers for convex cones and their characteristic
functions, whichwereintroducedby .. ... i... i r.i b. f....rr .r ...l.. n, i, ..r..,. In
homogeneous cones. And Nesterov and the reviewer [4], by further restricting the class
S__ I
MARCH 1995
PAGE 17
of cones and their barriers II. I 11 1 ....... important examples), have developed
longstep and symmetric primaldual interiorpoint methods for certain convex prob
lems, extending those for linear programming.
In summary, this is an outstanding book, a landmark in the study of complexity in
mathematical programming. It will be cited frequently for several years and is likely to
become a classic in the field.
References
1. O. Gdiler, "Barrier functions in inte
riorpoint methods," Department of
Mathematics and Statistics, University of
Maryland, Baltimore County, Baltimore,
MD, 1994.
2. N.K. Karmarkar, "A new polyno
mialtime algorithm for linear program
ming," Combinatorica 4 (1984), 373
395.
3. E. Kranich, "Interior point methods
for mathematical programming: a bibli
ography," available from NETLIB: send
email to netlib@research.att.com
containing the message "send intbib.tex
from bib" and/or "send intbib.bbl from
bib."
4. Yu.E. Nesterov and M.J. Todd, "Self
scaled cones and interiorpoint methods
in nonlinear programming," School of
Operations Research and Industrial En
gineering, Cornell University, Ithaca,
NY, 1994.
5. ORSA Journal on Computing, 6
I ''I 1ff.
M.J. TODD
Constructive Approximation
by R. A. De Vore and G. G. Lorentz
SpringerVerlag, Berlin, 1993
ISBN 3540506276
As stated in the preface, the book under review is to be seen as a modern version of G.
G. Lorentz: Approximation ofFunctions, NewYork, 19(.' i .., ..if, i ri, rhI 
same classical questions in approximation theory, a field also known as constructive
theory of functions. Of course, the authors have added many new results obtained since
the publication of that book, and the presentation is in a more general frame; never
theless the choice of the topics considered has almost been unchanged, and some modern
aspects of approximation theory are only sketched or missing. New are, for example,
the theory of Kfunctionals and interpolation spaces, and the DitzianTotik approach
to algebraic approximation. Furthermore, there are three chapters (5, 12, 13) on splines,
approximation by splines and interpolation bysplines, altogether more than 100 pages
which is about a quarter of the book.
Another major part of about 100 pages is devoted to best approximation, in particular,
best approximation by algebraic and trigonometric polynomials as well as by splines.
Chapter 3 is concerned with the standard material, e.g., the general theory of existence
and uniqueness ofelements of bestapproximation, the Chebyshev theory, and the theory
of Haar systems. The "Central Theorems ofApproximation" .. ,I1.J 1./1 the authors,
namely JacksonBernsteintype theorems for best approximation, are given in Chap
ters 7 and 8. The latter deals in detail with the influence of the endpoints in case of
algebraic approximation. Here the reader can find the classical results ofA.F. Timan
and V.K. Dzjadik as well as the more recent ones of Z. Ditzian and V. Totik.
__ _ _ ___ .1 _____ ___ ___ ___ ____ ___ ___ __
N? 45
MARCH 1995
PAGE 18
N 45
"...we can recommend
this book to everyone
who is interested in the
topics dealt with and
who wishes to have a
presentation in modern
language of approxima
tion theory."
Apart from this there are some minor chapters ,1;,,:.. with Lagrange, Hermite and
I.,, I. I, .," .... ..I ...' i ,, i.'. ,withapproximationbylinearoperators, inparticular
with the norms of projection operators and the ButzerScherer theory of commuting
operators (Chapter 9), I. ... ... ..... i i ... .. ..., ..... ...1 (Chapter 10), and
with saturation and Miintz approximation (Chapter 11).
Chapters 2 and 6 provide the necessary material on the function spaces used through
out and on the moduli of smoothness and Kfunctionals. In particular, the equivalence
between moduli of smoothness and Kfunctionals in certain instances, Marchaudtype
inequalities and the extension theorems ofWhitney are given here. There is also a short
exposition of the so,. .:1. i 0,qinterpolation spaces.
Let us also mention Chapter 1 which may serve as an introduction presenting, among
others, the celebrated theorems of K. Weierstrass (1885), L. Fej&r (1900) and S. Bernstein
(1912) on the approximation of continuous functions by polynomials.
All in all, the book is exactly what the authors state in the preface or, in other words,
"a modern presentation of selected topics in classical approximation theory." Most of
the material is covered by at least one of the textbooks on approximation theory which
were published up to .... d... ri, ....il .I.Achieser(1956), P.J. Davis(1961),
A.F. Timan (1963), I.P. Natanson (1964/65), E.W. Cheney (1966), G.G. Lorentz
(1966), or the book on splines by L.L. Schumaker (1981).
Of course, one cannot give an absolute answer to the question whether the choice of
topics is optimal or whether there was a need to write this book at all. This answer has
to be left to the reader, but we can recommend this book to everyone who is interested
in the topics dealt with and who wishes to have a .... .... ......1. ... I 1,........ : of
approximation theory.
Let us finally mention that the book contains an extensive bibliography, even if some
of the abovementioned ,I.... 1 .... ;.. On the other hand, there is only a very
poor index, e.g., no entries mentioning the theorems of Bernstein, Weierstrass, Fejer
or Timan can be found, and the entries 'Fej&r operator' or 'Fourier series' only give a
hint to Page 3, although these topics are dealt with in detail in Chapter 11.
R. L. STENS
MARCH 1995
I I
PAGE 19
MARCH 1995
... ... ... .. . ... .... 1
MARCH 1995
The Faculty ofManagement, McGill University,
announces a tenure track position in Operations
Management beginning Sept. 1995. Apply in
writing to: ProfessorAlbertTeitlebaum, Faculty
of Management, McGill University, 1001
Sherbrooke St. West, Montreal, Quebec, Canada
H3A 1G5.iScholars interested in conducting
research in Germany may contact the Alexander
von Humboldt Foundation, Suite 903, 1350
ConnecticutAve. NW, Washington, DC 20036,
Phone: 2022962990, Fax: 2028338514.
#Deadline for the next OPTIMA is June 1, 1995.
I Don.Ild l i \ h e 'ni I 1 1 i
I d earn, i\ ull Edu
.lll L i l ,1 1.
The Netherlands
email: aardal@kub.nl
Faiz AlKhayyal, SOFTWARE & COMPUTATION EDITOR
Georgia Tech
Industrial and Systems Engineering
Atlanta, GA 303320205
email: faiz@isye.gatech.edu
Dolf Talman, BOOK REVIEW EDITOR
Department of Econometrics
Tilburg University
P.O. Box 90153
5000 LE Tilburg
The Netherlands
email: talman@kub.nl
Elsa Drake, DESIGNER
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