Nov.1994
i
International
Symposium on
Mathematical
Programming
conference notes 1112
book reviews
1418
gallimaufry 19
Ia
MATHEMATICAL PROGA MMING SOCIETY NEWSLETT
MATHEMATICAL PROGRAMMING SOCIETY NEWSLETTER
B
.
P~ct 2 N0 44 NOV 1994
KA TA MURTY (I.)
WITI I DICK cOliLE
*4
r ..n .\i.:
',,, ""' ...... Mathematical Program
ming, Aug. 1419, 1994. The meeting began on
Sunday night with opening remarks from Dean I'.. .r
Banks of the Michigan College of Engineering,
Mayor Ingrid Sheldon of Ann Arbor, and Jan Ka .I
Lenstra, Chair of the Society. Katta Murty, progi ..
chair, and Pulitzer Prizewinning composer Willi id mn
Bolcom then described the background of Bolcol,,
original composition, "Haunted Labyrinth," bas. I
on the solution of a linear complementarity problem. .ENSTRA
Noted pianist Robert Conway performed the piece
exquisitely to an enchanted audience, who intently followed the musical path
through a haunted house to the complementary solution (see accompanying
article).
JOHN BIRGE, general chair of the symposium, .II .1 the meeting to order
for the Monday morning session, which included the Society's prize presenta
tions. The names of the winners and reports of the prize committees are car
ried in this issue of('! I '
In celebration of George Dantzig's 80th birthday in
1994 and his vast contributions to the field, Lenstra
S. ...... .1 Dantzig with a special award from the So
S ..I.ger Wets delivered an address on what
Sr ,.. has called "the real problem" of optimizing
1... .. editions of uncertainty. Professor Wets
.. .I ....1 the broad tree of student descendents that
( ,.. I )antzig has had in this area and gave in
ilI ...o the origin of stochastic programs and the
S '! t abilitiess for practical computation with
today's technology.
Bill Cook then took the stage, giving a colorful ple
BIRGE nary lecture on "Large Scale Combinatorial Opti
mization," which referred significantly to his work with David Applegate,
Robert Bixby and Vasek Chvital in solving the largest traveling salesman
problem ever.
Parallel sessions, including more than 1,000 talks, began after the opening
session and lasted throughout the week. The parallel sessions were broken up
with 20 tutorial lectures on topics across the realm of mathematical program
ming. Among the many sessions were particularly fascinating talks on Eco
nomics and Mathematical Programming, featuring Ralph Gomory of the
Sloan Foundation and Herb Scarf of Yale University; a special session for
Richard Cottle, in honor of his 60th birthday; and a special session on the
TSP with Applegate and Chvital.
M any sessions attracted record
numbers of observers and great inter
est. Of particular note were the ses
sions on semidefinite programming
and talk of the variety of new prob
lem areas opened by this research: the
stochastic programming sessions
spurred by new computational expe
rience, the nonsmooth optimization
sessions featuring links across areas of
mathematics, and the variety of prac
tical combinatorial optimization and
integer programming sessions.
Wednesday afternoon featured the
Society Business Meeting and the an
nouncement of the next symposium
site at Lausanne, Switzerland, in
1997 under the direction of Thomas
Liebling. More than 300 participants
then attended a banquet picnic at the
historic Greenfield Village in
Dearborn, Michigan, featuring visits
to the laboratories of Thomas Edison
and the Wright brothers.
Overall, the meeting attracted more
people than any previous symposium,
with more than 1,070 registered at
tendees from 53 different countries.
Of that number, fewer than half
came from the United States, with
more than 80 participants each from
Canada and Germany, and more
than 30 participants each from Italy,
Japan, The Netherlands and the
United Kingdom.
Complete rosters and addresses of
participants, updated final program
schedules, and additional abstract
books are available for a U.S. $5 han
dling and postage charge by writing
to: XVISMP, Department of Indus
trial and Operations Engineering,
1205 Beal, University of Michigan,
Ann Arbor, MI 481092117, USA.
Additional copies of the proceedings
book of tutorial papers also are avail
able at this address for U.S. $20. All
checks should be made payable to
University of Michigan. JOHN BIRGE
~
PAGE 2
N9 44
NOV 1994
Haunted Labyrinth:
Symposium Invocation Music
by WE. Bolcom
S I
4
i OR thefirsttime, the world
premiere ofa musicalcom Beale/Orchard
position has taken place at Hays Prize
an inauguration ceremony
ofan International Symposium on After a very close competition in
Mathematical Progammi. volving many excellent nominations,
Mathematical Programming.
the Beale/OrchardHays prize com
William E. Bolcom, a Distinguished mittee is pleased to announce the
University Professor at the University award of the 1994 prize to Andrew
ofMichigan, composed the piece, R. Conn of IBM, Yorktown
"Haunted Labyrinth," especially for Heights; Nicolas I.M. Gould of the
the Symposium. The music was per Appleton Rutherford Laboratory,
formed by pianist Robert Conway. Oxfordshire; and Philippe L. Toint
Sof the Facultes Universitaires Notre
Thecomposition, basedonB.C. Eaves' Dame de la Pai, Namur, for their.
Dame de la Paix, Namur, for their
ghost story interpretation ofcomple book titled: LANCELOT: A Fortran
mentary pivot algorithms for the lin Packagefor LargeScale Nonlinear
ear complementarity problem (LCP), Optimization, Springer Verlag, Ber
followedthepath ofiteratesforanLCP lin, 1992.
oforder5fromapaperbyKattaMurty. As the authors say in their introduc
Bolcom, born in Seattle, entered the tion, LANCELOT (Large And Non
University of Washington at age 11, linear Constrained Extended
where he studied piano and composi Lagrangian Optimization Tech
tion. He has earned many honors niques) was created out of the neces
including the 1988 Pulitzer Prizefor sity for accurate modeling of physi
c r cs w i cal, scientific, statistical and eco
Music for compositions written in
nomic phenomena, which led to
every period of his life. Commissions
everlarger and more ,! i r,,,
have come from orchestras such as the nonlinear optimization problems.
nonlinear optimization problems.
New York Philharmonic and the However, necessity needs to be rec
Vienna Philharmonic. Chambermu ognized, and complemented by the
sic and concert composed by Bolcom courage, determination and ability
include a sonata for cellist Yo Yo Ma to undertake a major research effort
andpianistEmanuelAx, and aflute spread over several years and na
concertoforJames Galway andthe St. tions.
Louis Symphony Orchestra. To summarize briefly several of the
Bolcom has taught composition at the achievements in the course of this
UniversityofMichigan SchoolofMusic project:
since 1973. He has been afullprofes i) Significant work on the structure
sor there since 1983. In 1994, he was of largescale nonlinear optimization
named the Ross Lee Finney Distin problems, and on algorithmic ap
proaches for large problems, i.e.
guished University Professor ofMusic. preaches for large problems, i.e.
their joint paper, "A globally conver
K. AARDALa L
gent augmented Lagrangian algo
NOV1994
PAGE 3
N 44
i'
I 
I I .;
PAi 4 No44 NOV 1994~P
rithm for optimization with general
constraints and simple bounds,"
SIAMJournal on Numerical Analysis,
No. 28, pp 545572, 1991.
ii) The development of a uniform
input representation for nonlinear
programs. The authors were not en
amored of the MPS format, but
were convinced by the user commu
nity that if LANCELOT were to get
the widest possible use on real prob
lems, total compatibility with the
mps format was required. Thus they
deserve commendation.
iii) The development of a code suffi
ciently robust that it efficiently
solves, without tuning, the widest
range of nonlinear programming
problems of any code yet devised.
iv) The creation and distribution of
the CUTE test environment, which
is a major asset to the field.
v) The quality of the documentation
provided by the book.
vi) The decision to distribute
LANCELOT in return for a new
problem from the user, thus making
the software easily available and si
multaneously promoting research.
1
1 4.
t7
CONN (I.) AND TOINT
RECEIVE THEIR PRIZES FROM
WOLSEY.
UIIi
1M I
LEMAIR CHIAL (I.) AND WETS RECEIVE
THEIR AWARDS FROM TODD.
t I'
"\\. ,f
' In conclusion, the
committee hopes and
believes that
t LANCELOT is only
a beginning, and, given
ihlat necessity has re
.ived such a helping
I .rnd, many others in the
1,1 Id will be encouraged to
I !.le the many problems
,, ;ig out for a solution.
R. MEYER, DAVID F.
S3, ROBERT VANDERBEI AND
LAURENCE A. WOLSEY (CHAIR)
m The 1994 Dantzig Prize
The 1994 Dantzig Prize was awarded jointly to Claude
Lemarechal, INRIA, Rocquencourt, for his exceptional work in developing
and analyzing numerical methods in nonsmooth optimization; and to Roger
J.B. Wets, University of California at Davis, for his outstanding contribu
tions to all aspects of stochastic programming, and to variational convergence
in the approximation of infinitedimensional problems.
The George B. Dantzig Prize, jointly administered by the Mathematical Pro
gramming Society and the Society for Industrial and Applied Mathematics, is
awarded to one or more individuals for research which, by virtue of its origi
nality, breadth and depth, is having a major impact on the field of math
ematical programming. The 1994 prize committee consisted of M.
Gr6etschel, E.L. Johnson, R.T. Rockafellar and M.J. Todd (chair). Below fol
lows an extract of the report of the committee. Interviews with both
Lemar&chal and Wets will appear in the next issue of OPTIMA.
Claude Lemarechal:
Lemarechal is the individual most re
sponsible for the state of the art in
computational nonsmooth optimiza
tion. This is a significant area not
only because of the existence of
r1 .....hl..i' ,i I I functions arising
I directly in applications, but also be
i '  cause decomposition methods for
I solving very large scale smooth prob
'.\/ lems (for example, those treated by
stochastic ,.....' ,,ri', ) lead di
rectly to the need to solve lowerdi
T mensional nonsmooth problems. The
tools of convex and, more generally,
Snonsmooth analysis are necessary to study
such problems, but also needed are numerical
methods that try to emulate the attractive behav
ior of methods for smooth optimization. Starting with some key papers, (e.g.
"An extension of Davidon's methods to nondifferentiable problems," in
Math. Prog. Study 3 (1975) and "An algorithm for minimizing convex func
tions," in Proceedings of the IFIP 74) Lemarechal has been the central figure in
this new branch of mathematics. He initiated or participated in most of the
significant developments in this area, especially in the algorithmic sector.
The bundle concept certainly is his decisive contribution to numerical
nonsmooth optimization. In a series of papers, he thoroughly investigated and
rigorously developed this idea and its variants (e.g. "Bundle methods in
nonsmooth optimization," in Nonsmooth Optimization, Lemarechal and
Mifflin (eds.), Pergamon Press, 1978; "On a bundle algorithm for nonsmooth
optimization," in Nonlinear Programming 4, Mangasarian, Meyer and
Robinson (eds.), Academic Press, 1981). Until recently, the corresponding
code MI FC1 was the only mathematically rigorous and efficient method for
the minimization of general nonsmooth nonconvex functions. This code has
been used successfully by numerous scientists and practitioners all over the
world. More recent codes (by Kiwiel and Schramm/Zowe) are based on the
same philosophy, with only minor additions to the bundle concept.
~ .~
PAGE 4
No 44
NOV 1994
M
PAGL 5 N0 44 Nov1994""
Lemarechal's work is Il..... imagi
native and sometimes even specula
tive. He 1 ,. I ; ..! at pushing
new ideas, which are .,'. 1. far
from practical realization, but which
might open the way for future
progress in nonsmooth optimization.
Lemarechal clearly realized that
'secondorder elements' (whatever
this means for nondifferential func
tions) are a must for any further sub
stantial computational progress. A
series of papers is devoted to this sub
ject, e.g., "Some remarks on the con
struction i. I order algorithms
in convex optimization," J ofApplied
Math. and Optim. 10(1983), "The
eclipsing concept to \ T a
multivalued mapping," Optimization
22(1991).
He recently has published, with J.B.
HiriartUrruty, the twovolume book
Convex Analysis and Minimization Al
""' i . "Verlag, 1993), giv
ing a comprehensive and accessible
account of these developments. Fur
ther, he has been involved in signifi
cant work on forcing global and fast
local convergence of algorithms for
nonlinearly constrained problems and
on quasiNewton methods.
Lemarechal always has been con
cerned with the practical use of math
ematical programming algorithms.
He has long been the president of
MODULOPT, which provides a li
brary of computational methods and
test problems, most from reallife ap
plications. He has worked on solving
problems arising in fields as diverse as
flight trajectories; transonic fluid me
chanics; meteorology; and molecular
biology, leading to discretizations
with hundreds or thousands of
variables.
Roger J.B. Wets:
Wets is recognized as the leading fig
ure in the area of stochastic program
ming. His studies on the theoretical
underpinnings of the subject include
fundamental investigations into the
geometry of the solution set, the
properties of the value function, con
ditions for existence and stability of
*. .,;,i l ..1n,,.... and the structure
of dual problems (see e.g., "Program
ming under uncertainty: the solution
set," in SIAMJ. Appl. Math. 14
(1966), "Stochastic convex program
ming: basic .l. ; ,.." in PacificJ.
M ath. 63 (1' '. i.. "',I .1.,i, in
twostage stc1 ,*...,rn.r ,,, "*
in SIAMJ. . I ".,
One of the key ,, ; 1 is that sto
chastic r. r ... 1', e an additional
multiplier type that does not arise in
determ in l.I. 1i...kl ,.., .i,!L. 1. as
sociated i 11 . .. , .... .fthe
. . .. t, r ... s ...
On ii I 1,...,,i,,;,. .1. ofstochastic
programming, Wets' contributions
include the basic and fundamental
Lshaped method, a very efficient
method for the simple recourse prob
lem, and the recent progressive hedg
ing algorithm (see "Lshaped linear
programs with application to optimal
control and stochastic program
ming," in SIAMJ. Appl. Math. 17
(1969), "Solving stochastic programs
with simple recourse," in Stochastics
10 (1983), and "Scenarios and policy
aggregation in optimization under
uncertainty," in Math. ofO.R. 16
(1991)). These methods have been
used effectively in a variety of appli
cations, and their use is expanding as
computational power to handle such
large models grows. The last method
cited exhibits considerable scope for
exploiting parallel computing.
Nonanticipativity multipliers are
crucial in it.
Through the analysis of statistical
properties of optimization problems
depending on random variables in
cluding generalized laws of large
numbers Wets has laid the founda
tion for ; ... T.. 1 ,1 or otherwise sim
plifying the probability distribution
in a stochastic programming prob
lem. The central concept here, which
he has spent a substantial part of his
career in developing, is epiconver
gence. This refers to a kind of conver
gence of optimization problems or
subproblems, feasible solution set and
objective function together, that en
sures convergence of solutions, thus
fitting into a larger subject known as
variational convergence. From early
theoretical work (see "Convergence
of convex functions, variational in
equalities and convex optimization
problems," in VariationalInequalities
and Complementarity Problems, John
Wiley, 1980) he has proceeded to use
epiconvergence to answer questions
in the design of numerical methods
that rely on random sampling or par
titioning of the probability space to
reduce dimensionality in the repre
sentation of a problem's stochastic
structure (see "Epiconsistency of
convex stochastic programs," in
Stochastics 34 (1991)). The epi
convergence approach is emerging
as a basic tool also in other areas of
optimization where the underlying
problems have an infinite
dimensional aspect.
Wets also has been very active in ap
plications ranging from the environ
ment (lake pollution) to finance (as
..r I .,lIr, management). He has
done consulting work for the Frank
Russel investment system, which re
ceived the runnerup award in the
1993 Edelman Prize for Management
Science Achievement, on the man
agement of Lake Balaton eutrophica
tion (see "Stochastic optimization
models for lake eutrophication man
agement," in Operations Research 36
(1988)), and on the World Bank
model for developing countries. He
has been a driving force more gener
ally in promoting the use of stochas
tic programming models by others
in applications where deterministic
modeling can lead to unsatisfactory
results. A theme in this effort has
been his close involvement in recent
years with the ongoing development
of stochastic programming codes
at IBM.
In addition to their own research,
both Lemardchal and Wets have very
successfully nurtured and inspired
their areas, encouraging and working
with younger scientists, organizing
conferences, editing proceedings, and
writing survey papers introducing the
field to other researchers. Both
nonsmooth optimization and sto
chastic programming have substantial
literatures from East Europe, and
Lemarichal and Wets have done
much to make this work known and
appreciated in the West, through
conferences, joint authorship or edit
ing, their extended participation in
the programs of IIASA, and their ex
tensive visits throughout the world.
F =antzig Prize F u
George B. Dantzig, one of
the founders of the field of math
ematical programming, celebrated
his 80th birthday on Nov. 8 of this
year. One possibility to honor
George Dantzig on his birthday is
to contribute to the George B.
DantzigPrize fund. TheDantzig
Prize was established in 1979 by
the Meathematical Programming
Society and the Society for Indus
trial andAppliedMathematics
(SIAM). The prize is awarded to
recognize original broad and deep
research making a major impact
on the field. The Dantzig Prize
represents a continuing tribute to
George not only to his distinguished
work, but also to him as an esteemed
colleague, teacher and fiend. Ifyou
wish to contribute to the fund, please
send a check payable to "SIAM
Dantzig Prize Fund" to:
Professor Richard W. Cottle
Department of Operations Research
Stanford University
Stanford, California 943054022
USA
Checks in foreign currency also are
welcome! Contributions are tax
deductible under the tax laws of
the United States.
`
PAGE 5
N? 44
Nov1994
PAGE 6 N0 44 NOV 1994a
j .I
(1 to rt.) THOMAS, SEYMOUR,
ROBERTSON.
KALAI AND BILLERA (below) RECEIVING
THEIR PRIZES FROM SCHRIJVER,
Citation:
For a long time, numerical analysts
have studied vector spaces of splines,
or piecewise polynomial functions.
Billera's paper gives a new approach,
expressing the spaces in question as
graded components of a commuta
tive ring or module. This leads to a
proof of Strang's conjecture of 1973
concerning the dimension of the
space of differentiable functions on a
1994 Fulkerson Prize
Citations
The 1994 Fulkerson Prize Commit
tee consisted of: Alan J. Hoffman,
Alexander Schrijver (chair) and Eva
Tardos.
The committee was appointed by
the American Mathematical Society
and the M athematical 7..... ....... :, .
Society to submit a recommendation
of the papers) that should be
awarded a 1994 D. Ray Fulkerson
Prize.
The specifications read:
"Papers to be eligible for the
Fulkerson Prize should have been
published in a recognized journal
during the six calendar years preced
ing the year of the Congress. The ex
tended period is in recognition of
the fact that the value of fundamen
tal work cannot always be immedi
ately assessed. The prizes will be
given for single papers, not a series
of papers or books, and in the event
of joint authorship the prize will be
divided. The term "discrete math
ematics" is intended to include
graph theory, networks, mathemati
cal programming, applied combina
torics and related subjects. While re
search work in these areas usually is
not far removed from practical ap
plications, the judging of papers will
be based on their mathematical qual
ity and significance."
This Committee considered papers
published in one of the six years
from 1988 through 1993. Calls for
nominations were published by No
tices ofthe American Mathematical
Society, ORIMS Today, OPTIMA,
Mathematical ''. 1
SIAMNews. Moreover, several re
searchers (including most members
of editorial boards of journals in dis
crete mathemat
ics) were re
quested directly
(by mail or in
person) to sub
mit nomina
tions. /
The committee
reviewed 13 eli
gible articles, in
cluding some
nominations
consisting of a
set of papers,
and found most l.
of high quality. '
Extensive dis
cussion between
the three mem
bers of the committee and consulta
tion with some specialized experts
led to the unanimous conclusion
that the following three papers
should be awarded a 1994 D. Ray
Fulkerson Prize:
L. Billera, "Homology of Smooth
Splines: Generic Triangulations and
a Conjecture of Strang," Transac
tions ofthe American Mathematical
Society, pp 325340, No. 310, 1988.
plane twomanifold that are piece
wise polynomial of degree at most r.
B'.. 1.. .'s highly unexpected tech
niques solve several problems that
stuck others attempting to solve the
Strang conjecture. Not only did
Billera's techniques prove Strang's
conjecture, they also yield lower
bounds for dimensions larger than
two, and it opens up a new field of
algebraic techniques (modules in
stead of vector spaces) to be used for
splines. The article is exemplary in
its effectiveness of creating bridges
between pure mathematics (commu
tative algebra, Groebner basis meth
ods) and a central field of applied
mathematics (the computation of
splines).
G. Kalai, "Upper Bounds for the
Diameter and Height of Graphs of
Convex Polyhedra," Discrete and
Computational Geometry, pp 363
372, No. 8, 1992.
PAGE 6
N? 44
NOV 1994
Ali!
r ,
P.
PAGE 7 N0 44 Nov1994EWIC
Citation:
In Kalai's paper, an upper
bound on the diameter of a d
dimensional polytope with n facets
is proved. It is a completely unex
pected breakthrough in the long
standing and important Hirsch con
jecture of 1963, which states an up
per bound of nd. Despite consider
able efforts by several researchers
over more than three decades, the
best known upper bound was until
recently exponential in the dimen
sion. Kalai's methods are of a sur
prising elegance and simplicity, and
will stimulate further important re
search on the complexity of linear
programming and on understanding
the structure of polyhedra.
N. Robertson, P.D. Seymour and
R. Thomas, "Hadwiger's Conjecture
for K_6Free Graphs,"
( .... . 1 1* 1 M .. 13,
1993.
Citation:
This paper gives a proof of
Hadwiger's conjecture (1943) for
K_6free graphs, stating that every
graph not containing K_6 as a mi
nor is fivecolorable. It thus forms a
breakthrough in the area of graph
colorability. The proof is very deep
and ingenious, and it provides a lot
of techniques applicable to other
problems on graph colorings, paths
and minors (while the proof is quite
independent of the graph minors
project). The proof consists of a re
duction to the fourcolor theorem,
thus giving several interesting tools
for understanding Hadwiger's con
jecture beyond planarity. The lucid
and transparent style of presenting
deep and original arguments adds to
the quality of the paper as a master
piece of pure and hard combinato
rics.
The 1994 Fulkerson Prize recipients
were honored in an award ceremony
held at the opening the 15th Inter
national MPS Symposium in Ann
Arbor, MI, August 1994.
ALEXANDER SCHRIJVER, CHAIR
1994
Tucker Prize
Citations
The A.W. Tucker prize is awarded
by the Mathematical Programming
Society for an outstanding paper
authored by a student. The 1994
prize committee consisted of An
drew Conn, William Cunningham,
Clovis Gonzaga, Thomas Liebling
(chair), and JeanPhilippe Vial. The
committee proposed Dick den
Hertog, Jiming Liu and David
"' 1. ....i.. as the three finalists. All
finalists presented their work at a
special session of the symposium. At
the business meeting the next day,
David 11 .. .... was announced as
the winner. The committee's moti
vation follows. An interview with
Williamson starts to the right. Inter
views with Dick den Hertog and
Jiming Liu will appear in the next is
sue of OPTIMA.
David P. Williamson, Massachu
setts Institute of Technology, "On
the Design of Approximation Algo
rithms for a Class of Graph Prob
lems."
Williamson's extremely wellwritten
thesis presents new, interesting and
creative techniques that have impli
cations for rather broad classes of
problems. It presents an original ap
plication of duality for heuristics de
sign with guaranteed performance
for a family of problems that, aside
from the (easy) matching problem,
includes notoriously hard ones such
as the generalized Steiner problem
and the prizecollecting traveling
salesman problem. While the perfor
mance bounds given are the best
known, they underestimate the ac
tual performance of the heuristic,
which turns out to be very robust for
practical problems. Several associ
ated papers already have had wide
infliifnce
Dick den Hertog, Delft University
of Technology, "Interior Point Ap
proach to Linear, Quadratic and
Convex Programming Algorithms
and Complexity."
The candidate worked in a particu
larly active and competitive area in
which many wellknown researchers
keep making contributions that are
! i, r to follow and classify for the
nonspecialist. His beautifully writ
ten thesis represents a reconciling
and unifying treatment. It also in
cludes a generalization of those con
tributions, bringing out the simplic
ity of the underlying ideas. Also
noteworthy are the results produced
by the candidate in the area of large
step methods for convex program
ming. It is quite remarkable that it
should have been a graduate student,
like den Hertog, rather than a more
senior researcher, who uncovered
such basic results and treated the
subject in such breadth and depth.
His texts have become a standard
reference in the area.
Jiming Liu, The George Washing
ton University, "Five Papers on Sta
bility and Sensitivity Analysis of
Generalized Equations and Varia
tional Analysis."
Liu has obtained highly original re
sults related to perturbed variational
problems; in particular, some of the
results on growth condition in varia
tional inequalities are real extensions
of what was known before. His work
on sensitivity of solution points (not
optimal values, a much easier prob
lem) to local perturbations will be
helpful for improved design of mod
els and algorithms, for a better un
derstanding of their asymptotic be
havior. For instance, in bilevel pro
gramming, Liu's results on some
form of differentiability may prove
very useful in the design of algo
rithms. His work already has found
its way to the scientific literature,
with five singly authored publica
tions in firstrate journals.
The Winner of the
1994 Tucker Prize
David P. Williamson received his
Ph.D. from Massachusetts Institute of Tech
nologyin September 1993. Thethesis, "Onthe
Design ofApproximation !' .. ' for a
Class of Graph Problems, "was supervised by
MichelX. Goemans.
The research lies in the intersection between
computer science and combinatorial optimi
zation, an area that has been particularly
active in the last couple ofyears. The main
result of the thesis is the development of a
tion algorithms for combinatorial problems.
been done ad hoc, by using the specific struc
ture of the considered problem. When
1i .. .* ,. : ofan 'approximation al
gorithm,': ... .' .
polynomialtime, andthatgeneratesafeasible
solution that is within factor a ofthe value
ofan optimalsolution. Thefactorc .. . .'
referred to as the performance guarantee'of
the algorithm.
Currently .. 'holds a postdoc posi
Operations Research at Cornell University.
Eii PRIZi

N? 44
NOV1994
PAGE 7
PAGE 8 N0 44 NOV 1994I
OPTIMA:Allyouruniver
sity degrees are fom MIT.
How did you chose MIT?
DW: When I looked for
colleges, I applied to five
places; among others Cal
Tech, Stanford and MIT. It
ended up that I got accepted
everywhere. I was accepted
early to MIT, so I had a
couple of months to think
about going there. I didn't
think I was going to get in,
so itwas, I .. I, 
did. Then it came down to
thinking about MIT versus
Cal Tech. Cal Tech was
too narrow and too high
pressure, and then MITver
sus Stanford. I decided in
the end I wanted to go to a
technical school, because in high school I
was tired of people not understanding that
I liked science. So, I went to MIT.
OPTIMA: Were there anyspecific events or
in combinatorialoptimization andcomputer
science?
bines mathematics and computer science in
the mathematics department, and since I
liked both, that's what I went into. But the
person who really influenced me for work
ing on combinatorial optimization was
David Shmoys. He was my undergraduate
advisor as well as my Masters thesis super
visor. MIT assigns undergraduate students
to people in their areas arbitrarily, and I
ended up with David. It turned out that he
also taught a course in complexity theory
that I took the first semester he was my un
tla p... .1 ; .., lt.. 1....1 ....,I ha ,
him and during one summer I started
working for him doing research that even
left MIT just as I was entering graduate
school.
0i' i 1 .l : And then you met Michel
Goemans?
DW: No, I actually didn't meet Michel
until a couple ofyears later. David had been
in touch with Michel, so I had heard ofsome
of the things Michel did through him. It
wasn't until some time later that I met
Michel, and a little later that I decided that
I'd better start working with him!
OPTIMA:. ,. . ,
with Michel Goemans, didyou already work
on similar topics?
DW: One of the reasons I wanted to work
with him was that I had already duplicated
some of his results, done special cases of
 ,;,,,. ,1, n I, ..1 .... .. ;., :_ . general
ity. We were thinking of similar things, so
I I ..... ,l I,, it would be better to "join
forces" than to keep duplicating someone
else's research.
01I' Ii: I '. One majorproblem on design
ing approximation algorithms has been the
lack of. You have su
developed a famework into which
many combinatorialproblems fit. What was
the main .. . ... developments?
DW: It was a particular paper by Agrawal,
Klein and Ravi (7' .. of the 23rd
AnnualACMSymposium on TheoryofCom
puting, pp 134144,1991) in which they use
a kind of primaldual technique for solving
a specific problem, except they were not
using linear programming. Michel and I
1, ,, 1,I .. 1 ,,J.1 try to make the linear
programming part of it explicit and see what
happened. Then we also saw itwas possible
.. . I; .. 11,.. ,I ..,;,1n ., I.... ..... ..... . .1,, ,
what they were trying to do, and also make
itconceptuallysimpler.' i ,. ,II, I ..
OPTIMA: Thecombinatorialproblensyou
consider are viewed as graph problems, and
they are modeled as a special type ofcovering
problem. You then consider the linear pro
gramming relaxation of that model, and its
corresponding dual. One ofyour key results is
thedevelopmentofaprimaldualapproxima
oftwo. C...' ,..
"two "?
D W : . l, ........ . I,, . . .
trying to construct a forest, and you do so
by increasing dual variables to determine
which edges to add next. The cost of the
edges in your final forest can be shown to
be no more than twice the sum fall the dual
variables: The main intuition here is that the
relation between the cost of the forest and
the dual variables has to do with the aver
age degree of the forest, and the average
degree is always no more than two. Thesum
of the dual variables is a lower bound on the
integer program you are trying to solve, so
you know that your solution is always no
more than two times optimal.
OPTIMA:T ,' ,'
the main impact ofyour results?
DW: The hope is that people will be able
to take this idea of applying the primaldual
method to solve integer programs approxi
mately. It's not that it wasn't done before,
but we give a new way of thinking about it.
The other thing is that some of the problems
considered in my thesis are problems people
are really interested in, such as the surviv
able network design problem. The approxi
mation algorithm we give for that problem
has already been implemented by people at
Bellcore, and is used in one oftheirsoftware
packages.
OPTIMA: Iguess there are still combina
torialproblemsthatdo notfit intoyourframe
your method even more to handle more gen
eral classes?
DW: The ideas I wrote about can still be
applied to other problems. People are think
ing more about coming up with other, dif
ferent, unifying frameworks, and they have
been more successful in doing that in the
past couple of years. There is a little bit of
overlap in the sense that people have been
using linear programming duality to help
them solve other types of problems.
OPTIMA: For many problems, you see
quite a big gap between the best known
worstcase bound and the known limit of
approximability. Do we lack tools for devel
oping approximation ',: with a
sharp bound, or to prove tight limits of
approximability?
DW: I think that a lackoftools on both sides
is part ofthe problem. Itwas only in the past
few years that the result by Arora, Lund,
Motwani, Sudan, and Szegedy came up
(; . ,,... ..!
on Foundations of Computer Science, pp 2
13,1992) and peoplewere able to prove any
substantial bounds on approximability on
a number of problems. Well, even the
bounds that are known now are not always
so substantial they are along the lines of
'you can't approximate suchandsuch a
problem to within 1 percent of optimum
unless P=NP.' Still, no onewas able to prove
any constant gap before for many of these
problems, so it is a tremendous result. In
terms of being able to prove sharp bounds,
probablysome new tools are needed. How
ever, new tools also are necessary for design
ing algorithms. For instance, Michel and I
wrote a paper right after I finished my the
sis in which we made a big step forward for
the maximum cut problem. That was by
using the tool ofsemidefinite programming,
which people in computer science hadn't
used atall'. F ... 1, ..... I 1,.. ;n ., thatit
really helped in terms of being able to ap
proximate the maximum cut problem, and
some of the satisfiability problems.
OPTIMA: Mathematical programming
and operations research receive a lot ofinput
from other fields such as computerscience and
mathematics. Whatisyour opinion on thedi
rection ofdevelopmentfor mathematicalpro
gramming?
DW: It is hard for me to say because my
trainingwas mostlyas computer scientist,
so I don't have the perspective of someone
who has been in operations research. But,
because ofwhere I am, I tend to see the cross
fertilization between mathematical pro
gramming and computer science, which is
very lively! Since I am a computer scientist,
I think there are a lot of great ideas from
mathematical programming and operations
research that can be used in computer sci
ence, and which computer scientists are not
so familiar with.
OPTIMA: Inyourparticular area, what's
the main open question?
DW: Is P=NP? IfP=NP,I am needless! The
Arora paper was the last thing that got ev
erybody in the field excited, although it is
not clear how that result can be applied to
take the next step to proving that P is not
equal to NP. Actually, there was a recent
result on something bit lower down in the
complexity hierarchy. Mulmuley showed
that one couldseparatestrongly polynomial
time from NC, for an appropriate definition
of NC that allows only arithmetic opera
tions (7 '. .fthe 26thAnnualSym
posium on Theory of Computing, pp 603
614, 1994). It sounds like a nice result, but
I find it hard to evaluate.
OPTIMA: Whatareyourplansfor the near
future?
DW: I am going to start at IBM inJanuary.
I will be doing research and working on
applied problems within. My job is in an
optimization group headed by Bill
I.,111. 1, I.I ,,I. There is a computer science
group nearby, so I will probably be work
ing a bit with some of them as well.
KAREN AARDAL
 ~ ~
PAGE 8
N? 44
NOV 1994
'AE9N04 OV 9
Working Group on Generalized
Convexity Formed
The recent International Symposium on Mathematical Programming in Ann
Arbor included for the first time an entire track of sessions on generalized
convexity, with more than 25 lectures.
During the conference, the international Working Group on Generalized
Convexity (WGC) was formed. Its activities will be guided by the Interna
tional Scientific Committee, consisting of the .il.. ;,,' members: C.R.
Bector (Canada), B.D. Craven (Australia), J.P. Crouzeix (France), J.B.G.
Frenk (The Netherlands), S. Komlosi (Hungary), J.E. MartinezLegaz
(Spain), P. Mazzoleni (Italy), and S. Schaible (USA, Chair).
The committee will attempt to guide the generalized convexity community
in establishing itself within worldwide academia. It will engage in proposing
future events, such as international and regional conferences, and it will try
to improve communication among its members. Anyone interested in par
ticipating in WGC should contact its chair, Siegfreid Schaible, Graduate
School of Management, University of California, Riverside, CA 92521,
USA; fax to (909) 7873870; or email to schaible@ucracl ucr. edu.
New
Society
Officers
Elected
At the Mathematical Program
ming Symposium in Ann Arbor,
Chairman Jan Karel Lenstra
reported on the recent MPS
elections. The new officers and
council members are:
John Dennis (ViceChairman
until August 1995; Chairman,
19951998);
Clyde Monma (Treasurer,
19951998);
Aharon BenTal, Bob Fourer,
Toshihide Ibaraki and Eva
Tardos (Council Membersat
Large, 19941997).
______ ______ _____
Laurence Wolsey Receives
the EURO Gold Medal
Laurence A. Wolsey, C.O.R.E.
University Catholique de Louvain, a
distinguished member of the Math
ematical Pr. .. .. ..I.,.I .. Society, re
ceived the EURO Gold Medal at the
EURO meeting in (CI, .. in July
1994. The medal was jointly awarded
to Jean Pierre Brans, Vrije
Universiteit Brussel.
The EURO Gold Medal is conferred
on a prominent person or institution
either for a remarkable role played in
the promotion of operations research
(OR) in Europe, or for an outstand
ing contribution to the OR science.
Wolsey has been one of the main
contributors to the development of
the theory and the computational as
pects of polyhedral combinatorics.
His work on polyhedral solution
4 Faculty Position
THE JOHNS HOPKINS
UNIVERSITY
Department ofMathematical Sciences
The Department ofMathematical Sciences atTheJohns Hopkins Universityin
vites applications for an anticipated facultyposition to begin in Fall 1995. The core
areas of the department are Discrete Mathematics, Matrix and NumericalAnaly
sis, Operations Research and Optimization, and Probability and Statistics. Can
didates with a strong background in one of these areas or in the area of numerical
mathematics are encouraged to apply. Especiallywelcome are applicants who can
interact effectivelywith faculty and students in the School ofEngineering, particu
larly in such thrust areas as information, biomedical, environmental and materi
als sciences. A broad and outstanding mathematical background is essential.
Applicants at alllevels will be considered. Selectionwill reflect demonstration (for
senior applicants) and promise (forjunior applicants) of excellence in research,
teachingandinnovative applications.A Ph.D. is required. Applications in theareas
of algebra, analysis, geometry, number theory and topology will not be accepted
bythe Mathematical Sciences Department, which is distinctfrom theMathematics
Department.
Minorityandwomen candidates are encouraged to apply. TheJohns Hopkins Uni
versity is an Affirmative Action/Equal Opportunity Employer.
Applicants are requested to send initially only a curriculum vitawith acoverletter
describing professional interests and aspirations. Recommendation letters, tran
scripts, preprints and reprints are to be furnished only upon request. Please send
applications no later thanJan. 15, 1995, to: Faculty Search Committee, Depart
ment of Mathematical Sciences, TheJohns Hopkins University, 220 Maryland
Hall, Baltimore, MD 212182689.
methods has led to the development
(with T.J. Van Roy) of the software
package, MPSARX, for general
mixedinteger programming.
The work on MPSARX was awarded
the OrchardHays (now the Beale/
OrchardHays) prize in 1988 for "ex
cellence in computational math
ematical programming" by the Math
ematical Programming Society.
Wolsey's book, Integer and Combina
torial Optimization, Wiley, 1988, co
authored by G.L. Nemhauser, was
awarded the 1989 Lanchester Prize
by the Operations Research Society
of America.
Wolsey is coordinator of the research
project, "Algorithmic approaches to
large and complex combinatorial op
timization problems," within the Sci
ence and Human Capital and Mobil
ity programs of the European Com
munity, involving many of the lead
ing research groups in Europe. Since
1986, he has been responsible for the
European Doctoral Programs in
Quantitative Methods in Manage
ment, which is an exchange program
for graduate students between eight
European universities.
Wolsey has long been an associate
editor of Mathematical Programming
Series A, and is, since 1990, a co
editor. He also has been a member
of Council, and a Publications Com
mittee Chairman of the Mathemati
cal I't..c ... i,. i, Society.
KAREN AARDAL
NOV1994
NQ44
PAGE 9
9
PAGE~ 10 N 44NOV199
Obituaries
Stepan Karamardian
(193394)
On July 10, 1994, Stepan
Karamardian died in Oakland,
CA, from a sudden heart attack. He
was 61. Stepan received his Ph.D.
from the University of California,
Berkeley, in 1966 under G.B.
Dantzig with a thesis titled "Dual
ity in Mathematical Program
ming. "He then joined the faculty of
UC Irvine and later UC Riverside,
taking on increasingly more admin
istrative duties.
ROM 198290, Stepan served as
Dean of the Graduate School of
Management at UC Riverside. He
oversaw the enlargement of the fac
ulty and student body and the estab
lishment of an undergraduate degree
in business administration and the
MBA degree, at the same time im
proving the research environment of
the school. After having taken an
early retirement in 1990, Stepan
joined a UC team that was to estab
lish the American University of Ar
menia, where he held administrative
positions until his death. His Arme
nian background, as well as his ad
ministrative and academic experience,
were of great value in his last assign
ment. He is survived by his wife,
Seta, of San Francisco, and three
daughters.
Stepan became internationally known
early in his career through his contri
butions to nonlinear
complementarity theory, which he
studied in the broader context of
mathematical programming, fixed
point theory and variational inequali
ties. He also worked on problems re
lated to generalized convex functions
and generalized monotone operators.
In his last two published articles,
Stepan focused on generalizations of
monotonicity for operators
(Karamardian and Schaible, JOTA
1990; and Karmardian, Schaible,
Crouzeix, JOTA 1993). Together, we
opened up a new area of research
which has stimulated several research
groups abroad within a short period
of time. Such results relate back to
generalized convexity as .II as to
complementarity problems and varia
tional inequalities.
In the mathematical programming
community, Stepan will be remem
bered as a mathematician of high cali
ber, whose contributions have signifi
cantly broadened the theoretical basis.
SEIGFRIED SCHAIBLE
Sept. 20, 1994
In Memoriam:
Eugene L. Lawler
Eugene L. Lawler died on Sept. 2,
1994, aged 61, after an eight
month battle with cancer. He is
survived by his wife, Marijke, his
son, Stephen, and his daughter,
soninlaw and granddaughter, Su
san, Matthew and Janna Rose Sur
prise. He will be dearly missed by
his students, colleagues and friends.
ENE obtained an A.M. at
Harvard University in 1957
and was a Senior Electrical Engineer
at Sylvania Electric Products in
Needham, MA, from 1959 until
1961. He went back to Harvard to
obtain a Ph.D. in 1962. Gene then
taught at the University of Michigan
in Ann Arbor from 1962 until 1970,
and at the University of California at
Berkeley since 1971. He combined
an illustrious career of highly influen
tial research with a history of dedi
cated service to both universities.
For more than 30 years, Gene has
been studying algorithmic issues in
combinatorial optimization. His con
tributions have been fundamental in
giving the discipline the breadth and
depth it has now attained. Of all of
his work, his textbook, Combinatorial
Optimization: Networks and Matroids
(1976), has had the most pronounced
impact. It brought the most impor
tant results in the area together and is
notable for its lucid writing style. It
gave new clarity to II,,,, i., I... l
results, brought the reader to the
forefront of the field, and made the
challenges of the future both appar
ent and accessible. It is one of the
classics of the area. The book, The
Traveling Salesman Problem: A
Guided Tour of Combinatorial Opti
mization (1985), which he edited
with three younger colleagues, also
became a benchmark reference.
It is hard to separate Gene's contribu
tions as an expositor and as a re
searcher. His great gift in investigating
a computational approach to a prob
lem was his ability to extract the essen
tial difficulty, achieve a deeper insight,
and then solve a more general problem
in a simpler way. To some extent, his
expository talent came from the rela
tive 1111 ni,; he had in absorbing new
ideas. For him to understand other
people's work, especially when it was
written in a complicated way, he often
had to wrestle with it to arrive at a bet
ter understanding and a simplification
of the result.
Gene's papers on branchandbound
(with D.E. Wood) and dynamic pro
gramming (with J.M. Moore) are
classics; the former, in fact, was se
lected as a citation classic in 1987.
Both papers, rather than introducing
radically new techniques, brought a
new level of usefulness and under
standing to important algorithmic
I ..' i',.. Since the mid70s, Gene
was particularly interested in se
quencing and scheduling. Prior to his
work, the area was a rather
unmathematical hodgepodge, with
little systematic understanding of the
types of methods and techniques.
Gene's work stimulated and unified
the area greatly. Most recently, he
had turned his attention to combina
torial problems in computational bi
ology, which is an area of growing
importance.
Gene was a phenomenal educator,
providing the intuition that made
difficult results easily accessible. He
was constantly available for every new
idea and always ready to interest his
students in whatever he currently was
thinking about.
Gene had an enormous influence on
the atmosphere of the Computer Sci
ence Division at Berkeley. He never
lost sight of the mission of a university
and never backed away from difficult
tasks. Gene was the social conscience
of the Division. He helped the indi
vidual student fight the bureaucracy,
reformed what the university taught
and to whom it taught, and made the
university a more humane and stimu
lating place to study. This year he was
awarded the Berkeley Citation, the
campus's highest accolade.
Gene Lawler was a remarkable man
who was ready to discuss intelligently
nearly any current issue and did so in
a thoughtprovoking way. We will all
miss him very much.
Gene's family welcomes donations to
the Eugene L. Lawler Fellowship for
Disadvantaged Students. ( I .. ,
payable to UC Regents, can be sent
to: ( Ih i, I,, 's Office, Computer
Science Division, 387 Soda Hall,
University of California, Berkeley,
CA 94720.
I 
NI 44
NOV 1994
PAGE 10
'\_(_L~L N0 44 Nov1994IB
CONF
Forthcoming
Conferences
ENCE
'fAPMOD95 International
Symposium on Applied Math
ematical Programming and
Modeling, Brunel University,
Uxbridge, Middlesex, U.K.,
April 35, 1995
IThe Fourth Conference on
Integer Programming and
Combinatorial Optimization,
Copenhagen, Denmark,
May 2931, 1995
IThe Hebrew University of
Jerusalem International Con
ference on Game Theory and
Applications, in Honor of
Robert J. Aumann on his
65th Birthday, Jerusalem,
June 2529, 1995
IVII International Conference
on Stochastic Programming,
Nahariya, Israel, June 2629,
1995
IThe Fifth Conference on
Integer Programming and
Combinatorial Optimization,
Vancouver, Canada,
June 1996
international Workshop on
Parallel Algorithms for Irregu
larly Structured Problems,
Lyon, France, Sept. 46, 1995
XXVI International Sympo
sium on Mathematical Pro
gramming, Lausanne,
Switzerland, Aug. 1997
_. 
NOV1994
IPAGE 1 1
NQ 44
1
IVII International Conference
on Stochastic Programming
Nahariya, Israel, June 2629,
1995
First Announcement and
Call for Papers
The VII Conference on Stochastic
I .....; sponsored by the
Committee for Stochastic Program
ming of the Mathematical Program
ming Society, will be hosted by the
TechnionIsrael Institute of Tech
nology, and held in Nahariya, Israel
(near Haifa). A number of tutorial
and stateofthe art reviews will be
presented by invited speakers.
For more details, please contact:
' 1', Schnapp, Faculty of Industrial
Engineering and Management,
Technion, Haifa, Israel. fax: 9724
235194; email:
ierns01@technion.ac. il.
IThe Hebrew University of
Jerusalem International Con
ference on Game Theory and
Applications
in Honor of Robert J. Aumann
on his 65th Birthday
Jerusalem, June 2529, 1995
The academic committee includes
Kenneth J. Arrow, Jacques Dreze,
John C. Harsanyi, Sergiu Hart,
Michael Maschler, Andreu Mas
Colell, Abraham Neyman, Ariel
Rubinstein, David Schmeidler,
Eytan Sheshinsky and Menahem
Yaari. Partial financial support may
be available. If you would like to
participate and/or to receive further
announcements, please write to:
Center for Rationality and Interac
tive Decision Theoralem
Feldman *.,;il;. Givat Ram
91904 Jerusalem, Israel.
Phone: +9722584135/6; Fax:
+9722513681; email:
RATIO@VMS.HUJI.AC.IL
'APMOD95 International
Symposium on Applied Math
ematical Programming and
Modeling
Brunel University, Uxbridge,
Middlesex, U.K., April 35,
1995
APMOD95 is the third in a series of
successful events. This year's sympo
sium will be held at Brunel Univer
sity from April 35, 1995. This se
ries of events compliments the trien
nial Mathematical Programming
Society Symposia and has built up
a good tradition: in particular, the
APMODs are followed by refereed
publications and have been well
liked by the participating scientists.
The main topics will be LargeScale
Linear ,..' "...... .. Integer Pro
gramming, Nonlinear Programming
and Modeling Systems. Contribu
tions from America and Eastern
countries are invited and solicited.
The symposium is set up to attract
specialists with different back
grounds, such as hardware manufac
turers, industrial research I .
software houses and academic
researchers.
The deadline for abstracts is Jan. 14,
1995. Notice of acceptance of papers
will take place by Feb. 14, 1995. For
more information and more dead
lines, contact Molly Demmar, De
partment of Mathematics and Statis
tics, Brunel University, Uxbridge,
Middlesex, UB8 3PH. Tel: +44 895
274000 ext. 2421.
Fax: +44 895 203303; email:
molly.demmar@brunel.ac.uk.
international Workshop on
Parallel Algorithms for Irregu
larly Structured Problems
Geneva, Aug. 29Sept. 2, 1994
Extensive research has been carried
out concerning different ways for
the automatic extraction of parallel
ism of several problems. Efficient
solutions have been found to many
problems, but others still lack effi
cient and automatic methods for
their solution and remain open to
research in parallel algorithms.
Call for Papers
Mathematical Programming Series B special issue on Applica
tions of Computer Science Techniques in Combinatorial Opti
mization, edited by Jan Karel Lenstra, Alexander Rinnooy
Kan, and David Shmoys.
With this special issue we intend to honor the memory of Eugene L. Lawler,
who died in September 1994. We solicit papers that illustrate the application
of concepts and methods from computer science to problems in combinato
rial optimization. These problems may find their origin in a diversity of areas,
such as distribution and production planning, computer system design and
control, and computational biology. Computer science techniques for the
design, analysis and implementation of combinatorial algorithms include
polynomialtime optimization methods, data structures, issues of problem
complexity, the derivation of guaranteed and probabilistic performance guar
antees, and the study of local search methods.
All papers will be reviewed in accordance with the standards of Mathemati
cal ..,. Please submit contributions to this issue :..I! ,', the
submission guidelines of the journal before June 30, 1995 to:
Jan Karel Lenstra or David B. Shmoys
Department of Mathematics School of Operations Research
and Computing Science and Industrial Engineering
Eindhoven University of Technology Cornell University
P.O. Box 513 ETC Building 232
5600 MB Eindhoven Ithaca, NY 14853
The Netherlands U.S.A.
jkl@win.tue.nl shmoys@cs.cornel l.edu
Among this latter category, often are
seen irregularly structured problems
that resist parallelization by both au
tomatic and manual manipulation.
To discuss such issues, the first in
ternational joint workshop on Paral
lel Algorithms for Irregularly Struc
tured Problems was held at the Uni
versity of Geneva from Aug. 29
Sept. 2, 1994. The workshop was
organized by Afonso Ferreira (LIP,
Lyon) and Jose Rolim (University of
Geneva). This meeting consisted of
presentations of the state of the art
in research concerning irregularly
structured parallel algorithms, and
surveys of potential research areas.
It provided a collaborative working
and research environment. Talks in
cluded such topics as scheduling,
parallel data structures, branch and
bound, randomized algorithms, dis
crete optimization, load balancing,
automatic synthesis and approxi
mated methods.
The list of speakers included:
A. Gerasoulis, Rutgers University
T. Haagerup, Max Plank Institut,
Saarbruecken
G. Kindervater, Erasmus University
L. Kucera, Charles University,
Prague
V. Kumar, University of Minnesota
R. Lueling, University of Paderborn
G. Megson, New Castle University
P. Pardalos, University of Florida
V. Prasanna, University of Southern
California
C. Roucairol, University of
N ,_, II.,
This workshop was sponsored by IFIP,
EATCS, 3eme Cycle Romand
d'Informatique, Fonds National Suisse
de la Recherche Scientifique, IBM
Switzerland, Centre Universitaire
SI i .i ... I' ., I de l'Universite de
Geneve, and by the Laboratoire
d'Informatique Theorique de l'Ecole
Polytechnique de Lausanne.
Proceedings of the workshop will be
published. The next workshop will be
held in Lyon, France, Sept. 46, 1995.
NQ 44
PAGE 12
NOV 1994
SP OC111___1 _11 __
OPTIMA Readers:
20/ Off
Selected SLIA I Titles
Sociei juur
Indu qrlata and
.4pphledi
Malbaemalcs
Nonlinear Programming
Clk I L Migjtiriari
Th,; rinrnt i the I'; ht the .inwc
in I rr rici Ic no n ihin et J' iu ii
11. __JovE n th A,crdr~clencerink n.friurain
*piinhiand iiilne th~. r .tnp I'roariuind
1, k pri idcs id,L r the lur,rid.nIL rA
Jee t., ;Tud. .'nru I' u h p
Contend.
rel.,c o it,, Elim Pr; i P CiirJrlr 1
7 7~~~~~ 2 u (1r : o C r o7 m
u.,' t,.ra in d 4/.rar:e C ar&__r
al ,: E.1':r 1 C Pr .: :.I Iid t 1n
,..12,.' t111Ci ',~i C I.,r r ll O'n .111 h Criro,
.ii./Li:i/t Q~,r,,i tiz n I .'t XkwI W i n
i i .,'!! 'lfs Irun tt!,Itiehli2dUL i '2
coaF F!,,. ncfi P; IiuiL: ,r 111ai Cq ''qrwnlit
f 7LrIh'. '" I h.ipe Ic i I lIJi)riced1.A n L'UN9riL Of
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i r t ; r' .oa B .
i~l'.t 11,Kc n L _.I, Order Code CLI0i
InteriorPoint Polynomial Algorithms in
Convex Programming
Yurii Nesterov and Arkadii Nemirovskii
with a foreword by Stephen Boyd
Studies in Applied Mathematics 13
In this book, the authors describe the first unified theory of
polynomialtime interiorpoint methods. Their approach provides a
simple and elegant framework in which all known polynomialtime
interiorpoint methods can be explained and analyzed.
Contents
Chapter 1: SelfConcordant Functions and Newton Method; Chapter 2: Path
Following InteriorPoint Methods; Chapter 3: Potential Reduction Interior
PointMethods; Chapter 4: How to Construct SelfConcordant Barriers; Chapter
5: Applications in Convex Optimization; Chapter 6: Variational Inequalities
with Monotone Operators; Chapter 7: Acceleration for Linear and Linearly
Constrained Quadratic Problems; Bibliography; Appendix 1; Appendix 2.
1994 / ix + 405 pages / Hardcover / ISBN 0898713196
List Price $68.50 / OPTIMA Reader Price $54.80 / Order Code AM13
Optimization Software Guide
Jorge J. More and Stephen J. Wright
Frontiers in Applied Mathematics 14
Here is a reference tool that includes discussions of developments in
optimization theory, and names software packages that incorporate
the results of theoretical research. After an introduction to the major
problem areas in optimization and an outline of the algorithms used
to solve them, a data sheet is presented for each of the 75 software
packages and libraries in the authors' survey.
For a complete table of contents or excerpts available in uncompressed
PostScript form access gopher.siam.org or contact SIAM Customer Service.
1993 / xii + 154 pages / Softcover
ISBN 0898713226 / List Price $24.50
OPTIMA Reader Price $19.60 / Order Code FR14
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'AGE 14
"The second chapter is prob
ably closest to the interests
of the reader of OPTIMA: it
contains the algorithms in
linear algebra that the au
thor needs, including lattice
basis reduction algorithms."
N? 44
A Course in ComputationalAlgebraic
Number Theory
by Henri Cohen
SpringerVerlag, Berlin, 1993
ISBN 3540556400
Algebraic numbers are numbers such as the cube root of two, the golden ratio, or roots
of unity. Algebraic number theory is the study of arithmetic properties of number sys
tems that consist of such numbers. It first came up in the first half of the 19th century,
in connection with generalizations ofGauss' quadratic reciprocity law. Algebraic num
ber theory has important applications to the solution ofdiophantine equations, such
as Fermat's equation x" +y=z"; to arithmetic algebraic geometry; and, to mention a recent
development, to the problem of decomposing large numbers into prime factors, which
is related to cryptography.
Cohen's book offers, in more than 500 pages, far more than the title promises. In addition
to algorithms in algebraic number theory, one finds algorithms in elementary number
theory, algorithms for polynomial factorization and algorithms related to elliptic curves.
There is a thorough and uptodate treatment of primality testing and factorization.
The second chapter is probably closest to the interests of the reader of OPTIMA: it
contains the algorithms in linear algebra that the author needs, including lattice basis
reduction algorithms.
The book can be used in several ways. The minimum prerequisites are a basic knowl
edge of elementary number theory and a feeling for algorithms. In principle, one can
learn algebraic number theory from the book, since the algorithms presented often yield
.. ... I ,,i.. i, ,, , i, I ,11 ... ..m ore conceptual, but less constructive
treatments. The student who likes to learn by example acquires the proper tools for
numerical experimentation. At the same time, . ".., r .I be able to use the book
as a compendium of algorithms in number theory; what cannot be found here most
likely is yet to be developed.
5 __________________________________________ .
NOV 1994
. . ...
R E V I E W S
Nov1994
_____________________________________________________________
The attitude of the book is that of the pure mathematician for whom 1: .,. .... are
tools rather than objects of study. Thus, the emphasis is on the practicality and the
mathematical justification of the algorithms, rather than on complexity issues, which
, 1. ...il, 1 I h . . I r 11 .1 . I,, r l .. ,, I .. .. t II .." .11 ,r .. ,r I... r h. r. I I
he knows that his readers skip passages printed in quasialgol or in typewriter font, and
he has been wiser than many in avoiding both.
The style of the book is lively and informal, rather than polished, with many asides,
exercises and stimuli for further research. It is highly recommended to anybody inter
ested in knowing what is going on in this area.
H.W. LENSTRA JR.
Optimization in Industry,
Mathematical Programming and
Modeling Techniques in Practice
edited by Tito A. Ciriani and Robert C. Leachman
John Wiley and Sons, Chichester, 1993
ISBN 0471934925
In 1991, the IBM Europe Institute held a seminar on Optimization in Industrial
Environments, aiming at an overview of new achievements in mathematical program
ming modeling and its implications for optimization technology. Seventeen presen
tations held at that seminar are documented in this book.
How should one review this diverse. I:........ of articles? I admit I found it .r!,._,,l
to answer this question. Should I attempt to characterize each individual article? Or
is a grouping according to optimization techniques used more interesting? Or a cat
egorization according to industry? At any rate, the sequence as presented in the book
seems completely arbitrary; I could not find any logic behind it. So let me group the
articles in my own way and that is by industry application.
Ti,.. i ...p is about thecomputerindustry. Ti,. I i, .. 1,, .11.. ; ."M od
eling Techniques for Automated Production Planning in the Semiconductor Indus
try," by R.C. Leachman. He describes the information flow and production planning
in a semiconductor industry (Harris Corp.) The 20 timeperiod planning model cov
ersahorizonof 18 ..... Il 1, 1 ;Fr ., .... I ,, .. ':,, ........ .... wouldinvolve
half a million constraints and variables. Instead, a heuristic decomposition scheme is
proposed, including five modules, in which three use LP, the largest LP involving
isstudiedin" ; I' !... ,,i ... .... "byL.F.EscuderoandP.V.Kamesam.The
main goal is to determine the I" ..... i,.. i .. I' ., the volume and location
of stock levels in such a way as to hedge against uncertainty in demand while meeting
specified servicelevel requirements. A scenario approach is used, leading to a stochas
tic programming model. Computational results are said to be quite encouraging. "Op
timization in Microelectronics Manufacturing," by H. Fromm, C. E'ill,. I .. I, and
A. Wollensak, describes optimization of a .1i ',, I center using linear combinatorial
optimization. Next, they discuss the loading of batches of parts on processing equip
ment using queuing models, which is treated in more detail in "RealTime Scheduling
of Batch Operations," by C.R. Glassey, F. Markgraf and H. Fromm. They conclude
from simulation results that a decision process based on arrival forecasts (look ahead)
"This book presents an illus
tration of presentday use of
optimization techniques in in
dustry and demonstrates the
economic impact these tech
niques have, despite the diffi
culties encountered during
practical implementation."
PAGE 15
N 44
N? 44
can lead to substantial inventory and waiting time reductions. "The Job Sequencing
Ordering Problem on a Card Assembly Line," by L. Escudero and A. Sciomachen,
presents a 01 algorithm for a job sequencing problem, and reports on computational
experience with it. "A Linear Approach to 'I ........ the Production of Mainframe
Computers," by C. Monvoisin, advocates an LP approach with two objectives (maxi
mize production, minimize inventory) for production planning of IBM mainframes.
Three articles deal with problems in the oil industry. "Optimization in Refinery Sched
uling: [..i. I. ... i .. Solution," by K. Ballintijn, deals with a multiperiod LP model
for refinery scheduling to which integer variables are added to reduce the number of
unnecessary switches in production modes on the refinery plants. The other two ar
ticles deal with the so. I .1 .1 ...h. , problem in refinery scheduling: If several differ
ent refinery streams are .1 ,.., into a single tank from which material also is taken
for various destinations, and if each flow possesses distinct qualities satisfying mixing
rules when brought together, then the production model becomes nonlinear. "In the
1'...hI.. Problem," M I.il '*.... ' 'I .... method for solving such prob
lems. R. Main, in "Large Recursion Models: Practical Aspects of Recursion Techniques,"
warns, however, that some recursion techniques which work for small models give poor
results when applied to larger models. He adds that at present there does not appear
to be a technique better than recursion.
The consumer product industries are represented in two articles. The first one is by
A. Gascon, R.C. Leachman and A.A. DeGuia and is titled, "Optimal Planning and
ControlofC ..... 1,, .I .... I I, j i .. Itdescribes a hierarchyofcomputer
based decision supports systems for the planning and control of household product
inventories. The highest level computes forecasts of monthly shipments, based on
multivariate regression ofseasonality and promotional activity data. In the second level,
an LP model is used to translate the demand forecasts into monthly production. An
inhouse developed heuristic does the scheduling of production cycles on individual
packaging lines at each plant. Benefits from, and difficulties with, the introduction of
i., 1. ', i, .... ..'. . ... ofthispaperarem missing, i. ..,i., i .
LP. The other article, "Mixed Integer Programming in Production Scheduling: A Case
Study," by R. Ashford and R. Daniel, gives an MIP model '., il 1. ..il;..._ of the
production of cartons for the storage of liquid products. The authors point out the big
improvements of the model outcomes over manually produced schedules and empha
Two studies represent the aerospace industry. "CrewPairing Optimization at Ameri
can Airlines Decision Technologies," by R. Anbil, C. Barnhart, L. Hatay, E.L. Johnson
and V.S. Ramakrishnan, describes the problem of partitioning a flight schedule of an
airline into sequences of flight legs beginning and ending at a crew base with an over
night rest period in the middle. Using LPs with a few million columns, the company
S ,, h ,i .... ,,,r,,, ll]. r l, il., ,rh[ hL  ,l ,,,, l... i . .. 1 .. 'p airing m models.
"Nonlinear Optimization il... ;.,'I,, for Mixed Integer Programming Problems:
Applications and Results," by G. Fasano, develops an approach for solving linear 0
1 programming problems by reformulating the problem as a quadratic nonlinear
optimization problem and solving this in a branchandbound manner. It claims
successful application to ... Ii. optimal configuration layout problems containing
3,500 01 variables.
I ,I.; ,, I .. ,, .i, ,, theoreticallyoriented papers. In "MonteCarlo (Importance)
Sampling within a Benders DecompositionAlgorithm for Stochastic Linear Programs,"
G. Infanger gives a complete presentation of the use of Benders decomposition and
__ _ _ _ _ __ _ __ _ _ _ _ _ _ __ _ _ _ _ _ _
PAGE 16
NOV 1994
Nov1994
"Because of the many
examples, the book is
extremely suitable for
private study. Almost no
foreknowledge is needed
to read this book, which
has a very nice and clear
layout. I think the book is
especially suitable for be
ginning students in math
ematics and areas related
to mathematics, such as
computer science and
management science..."
importance sampling for solving twostage stochastic linear programs with recourse.
He has tested the approach on problems, such as expansion planning of electric utili
ties and portfolio management, and states that the technique c ,, I ,', 11.. 26 or more
stochastic parameters. "Combinatorial Models for Manufacturing: Optimizing Flow
i f,, .. ... r ,,ni.. ;11. r .,;.. ,, 7 ... ."byA.Agnetis,C.ArbibandM .Lucertini,
shows the correspondence between flow management problems in FPS and optimi
zation techniques, such as dynamic, linear and integer programming, and costflow
problems in networks. In "Solution of LargeScale Linear I',. .i.. A Review of
Hardware, Software and Algorithmic Issues," R. Levkovitz and G. Mitra discuss se
and the suitability of these '1 .il... on the various computer architectures. They
conclude that ti,. 1 ,i .. now seem to be the seamless integration of simplex and
interiorpoint methods, and the exploitation of parallel and novel computer architec
tures in future generations of solvers. This paper presents a fine overview of the current
state of largescale LP. T.A. Ciriani, in "Model Structures and Optimization Strate
gies," tests MIP preprocessing capabilities of MPSX/370 and OSL on various large
models. He observes that model structures are important for solution I' .. .. and
concludes that MIP preprocessing techniques can efficiently reduce optimization time.
This book presents an illustration of presentday use of optimization techniques in
industry and demonstrates the economic impact these techniques have, despite the
difficulties encountered during practical implementation.
A.T, LANGEVELD
Discrete and Combinatorial
Mathematics, an Applied Introduction,
Third Edition
by R.P. Grimaldi
AddisonWesley, Reading, USA, 1994
ISBN 0201549832
The author writes in the preface that the major purpose of this book is "to provide an
introductory survey in both discrete and combinatorial mathematics...intended for the
beginning student." In 17 chapters, which are divided into four parts, he introduces
the reader to various areas of discrete mathematics.
The first part consists of seven chapters discussing some fundamentals of discrete
mathematics. As in just about every book of this type, the first chapter is about the
fundamentals of counting: permutations, arrangements, binomial coefficients, the
binomial theorem and distributions. Also, Chapter 5, "Relations and Functions," is
mostly about counting I ....r. r. .; of functions from finite set A to some finite set
B, yielding, for example, the :ii i';_l numbers. The last two sections of this chapter,
about the order of complexity of algorithms, have only the notion of a function in
common with the preceding sections. Some chapters are just about formalizations of
intuitive notions, such as Chapters 2 and 3, about logic (explaining what a proof is)
and set theory (some basic definitions), respectively. Chapter 6, on languages and finite
state machines, is an isolated chapter and seems to be superfluous. Chapter 4, about
1. in.. ... i.. dni t i, .,, ..a. i. i..,,, a... .. n.. .1 m them atical induction
(including recursive definitions and harmonic, Fibonacci and Lucas numbers) and some
___________________________________________ I ___________________________________________
PAGE 17
N 44
NOV 1994
ring properties of the integers: division algorithm, prime numbers, gcd, Icm, Euclid
ean algorithm and factorization. Finally, Chapter 7 introduces partially ordered sets,
including lattices, and equivalence relations.
Part 2 of the book treats some more advanced methods of counting, such as the prin
ciple of inclusion and exclusion (Chapter 8,. 11..., some results of Chapter 3 and
the Stirling numbers and discussing derangements and arrangements with forbidden
... .._ .. I ,. ,, i, r. (C hapter9 ,.. ,, ,,1 ... .. .1,..... 'C hap ter
," i.ii ,.i; .. i.. i different types of recurrence relations, Catalan numbers and
the complexity of divideandconquer algorithms.
The third part consists of the topics found in every book with a title like "Introduction
toGraphTheory."', n. .. ;1 i...... 1n ...... ...,r .. .1l .....basicdefinitions,
Euler circuits, planarity, Hamilton cycles and graph coloring (Chapter 11). Chapter
12 is about trees and Chapter 13 discusses some optimization problems in graphs such
as Dijkstra's shortestpath algorithm, the minimalspanning tree algorithms of Prim
and Kruskal, the maxflow mincut theorem and the theorem of KonigHall.
Part 4 discussessom e further l,. I .I... .. ..... 1 .. i ,, i n I.i. l t. 1.1 I I I. i ,. 14,
especially the integers modulo n) and Boolean algebra (chapter 15). Chapter 16 intro
duces the notion of a group, with coding theory and Polya's method of enumeration
as applications. Finally, in Chapter 17, the finite fields are constructed and combina
torial designs such as latin squares and block designs (including affine and projective
planes) are discussed.
There are a large number of examples with detailed explanations in the text. Maybe
it is a matter of taste, but I think the number of examples is a bit overdone, totaling
more than 600. As a consequence, the t. I. ..I .r ,, r Iir 1 ,1 .i. .. ....... ..... of
examples and the pace is somewhat slow. At the end of each section and each chapter
there is an abundance of exercises, .1 ;,... .. ... 1,700. The solutions of the odd
numbered exercises are given at the end. In each chapter, the last section provides a
roughsum m ary: ; .1 .,; i.. '. ,' .. ; .. .. I; !.. .. .... I. j. .late(U .S.
oriented) references for further study.
The book has three appendices which discuss exponential and logarithmic functions
able sets (A3). It is not clear to me why these appendices were added. It seems more
natural to assume that these subjects are treated in other courses.
Except for the three appendices, 87 extra examples and more than 300 extra exercises,
the differences between this edition and the second edition are marginal.
Because of the many examples, the book is extremely suitable for private study. Almost
no foreknowledge is needed to read this book, which has a very nice and clear layout.
I think the b.. ; ,ll, 1;.1.1 f. i ..,,,,,,, .,r ,,,,,... l, ,,. .;and areas
related to mathematics, such as computer science and management science, lII..., I.,
I prefer a more concise treatment of the subjects for mathematics students.
RENI PETERS
PAGE 18
No 44
NF4 o19
November 1994
OPTIMA Expanding with new Editors
OPTIMA will be expanding in 1995, by decision of the MPS Coun
cil. Joining Don Hearn, Editor, and Dolf Talman, Book Review Edi
tor, willbe: Karen Aardal, Features Editor; and Faiz AlKhayyal, Soft
ware & Compu station Editor. 'li K.1 i. n will have primary responsibili
ties for feature articles and Faiz will solicit and prepare articles on
computational news. [Karen has made several contributions to this
issue and Faiz will start a column in OPTIMA 45, the spring 1995 issue.
MPS members are encouraged to submit articles and general inter
est items to the editors. [Deadline for the next OPTIMA is Feb. 1.1995.
Donald W. Hearn, EDITOR
email:hearn@ise. ufl. edu
Karen Aardal, FEATURES EDITOR
Department of Econometrics
I1! .1 I, University
P.O. Box 90153
5000 LE Tilburg
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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
Richard Jones, ASSISTANT EDITOR
Elsa Drake, DESIGNER
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