Title: Optima
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Permanent Link: http://ufdc.ufl.edu/UF00090046/00044
 Material Information
Title: Optima
Series Title: Optima
Physical Description: Serial
Language: English
Creator: Mathematical Programming Society, University of Florida
Publisher: Mathematical Programming Society, University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: November 1994
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Bibliographic ID: UF00090046
Volume ID: VID00044
Source Institution: University of Florida
Holding Location: University of Florida
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Symposium on

conference notes 11-12

book reviews


gallimaufry 19





P~ct 2 N0 44 NOV 1994



r ..n .\-i.:

',,, ""' ...... Mathematical Program-
ming, Aug. 14-19, 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 Prize-winning 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
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 48109-2117, 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



N9 44

NOV 1994

Haunted Labyrinth:

Symposium Invocation Music

by WE. Bolcom

S- I


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/Orchard-Hays 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 Large-Scale 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
ever-larger 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 large-scale 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-
gent augmented Lagrangian algo-



N 44

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 545-572, 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 4.




1M I


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.

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 infinite-dimensional 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 lower-di-
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.

~ -.-------~


No 44

NOV 1994


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
'second-order 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
He recently has published, with J.-B.
Hiriart-Urruty, the two-volume 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 quasi-Newton 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 real-life 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
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
two-stage stc-1 ,*...,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
L-shaped method, a very efficient
method for the simple recourse prob-
lem, and the recent progressive hedg-
ing algorithm (see "L-shaped 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 epi-conver-
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
epi-convergence 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 "Epi-consistency 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 runner-up 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 94305-4022
Checks in foreign currency also are
welcome! Contributions are tax-
deductible under the tax laws of
the United States.



N? 44


PAGE 6 N0 44 NOV 1994a

j .I

(1 to rt.) THOMAS, SEYMOUR,


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
The 1994 Fulkerson Prize Commit-
tee consisted of: Alan J. Hoffman,
Alexander Schrijver (chair) and Eva
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
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
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 325-340, No. 310, 1988.

plane two-manifold 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
G. Kalai, "Upper Bounds for the
Diameter and Height of Graphs of
Convex Polyhedra," Discrete and
Computational Geometry, pp 363-
372, No. 8, 1992.


N? 44

NOV 1994

r ,


PAGE 7 N0 44 Nov1994EWIC

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 n-d. 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_6-Free Graphs,"
( .... -. 1 1* 1 M .. 13,
This paper gives a proof of
Hadwiger's conjecture (1943) for
K_6-free graphs, stating that every
graph not containing K_6 as a mi-
nor is five-colorable. 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 four-color 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-
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.


Tucker Prize


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 Jean-Philippe 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-
Williamson's extremely well-written
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 prize-collecting 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

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 well-known researchers
keep making contributions that are
! i, r to follow and classify for the
non-specialist. 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 first-rate 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 post-doc posi-

Operations Research at Cornell University.



N? 44



PAGE 8 N0 44 NOV 1994I

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

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
0i' i 1 .l : And then you met Michel
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 134-144,1991) in which they use
a kind of primal-dual 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

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 primal-dual
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
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
worst-case 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
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 such-and-such 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-
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
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.

----- -----~ ~-----


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. Martinez-Legaz
(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) 787-3870; or e-mail to schaible@ucracl ucr. edu.





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 (Vice-Chairman
until August 1995; Chairman,
Clyde Monma (Treasurer,
Aharon Ben-Tal, Bob Fourer,
Toshihide Ibaraki and Eva
Tardos (Council Members-at-
Large, 1994-1997).

______ ______ _____

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



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
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 21218-2689.

methods has led to the development
(with T.J. Van Roy) of the software
package, MPSARX, for general
mixed-integer programming.
The work on MPSARX was awarded
the Orchard-Hays (now the Beale/
Orchard-Hays) 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.





PAGE~ 10 N 44NOV199


Stepan Karamardian
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 1982-90, 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
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.
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,
son-in-law 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 branch-and-bound
(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 mid-70s, 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
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 thought-provoking 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


'\_(_L~L N0 44 Nov1994IB





'fAPMOD95 International
Symposium on Applied Math-
ematical Programming and
Modeling, Brunel University,
Uxbridge, Middlesex, U.K.,
April 3-5, 1995
IThe Fourth Conference on
Integer Programming and
Combinatorial Optimization,
Copenhagen, Denmark,
May 29-31, 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 25-29, 1995
IVII International Conference
on Stochastic Programming,
Nahariya, Israel, June 26-29,
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. 4-6, 1995
XXVI International Sympo-
sium on Mathematical Pro-
gramming, Lausanne,
Switzerland, Aug. 1997

_. ----



NQ 44


IVII International Conference
on Stochastic Programming
Nahariya, Israel, June 26-29,
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
Technion-Israel Institute of Tech-
nology, and held in Nahariya, Israel
(near Haifa). A number of tutorial
and state-of-the 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: 972-4-
235-194; e-mail:
ierns01@technion.ac. il.

IThe Hebrew University of
Jerusalem International Con-
ference on Game Theory and
in Honor of Robert J. Aumann
on his 65th Birthday
Jerusalem, June 25-29, 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: +972-2-584135/6; Fax:
+972-2-513681; e-mail:

'APMOD95 International
Symposium on Applied Math-
ematical Programming and
Brunel University, Uxbridge,
Middlesex, U.K., April 3-5,
APMOD95 is the third in a series of
successful events. This year's sympo-
sium will be held at Brunel Univer-
sity from April 3-5, 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 Large-Scale
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
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; e-mail:

international Workshop on
Parallel Algorithms for Irregu-
larly Structured Problems
Geneva, Aug. 29-Sept. 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
polynomial-time 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,
G. Kindervater, Erasmus University
L. Kucera, Charles University,
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
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. 4-6, 1995.

NQ 44


NOV 1994

SP OC111___1 _11 __

OPTIMA Readers:

20/ Off

Selected SLIA I Titles

Sociei juur
Indu qrlata and

Nonlinear Programming
Clk I L Migjtiriari

Th,; rinrnt i the I'; ht the .inwc

in I rr- rici I-c no n- ihin et J' iu ii
1-1. __JovE- n th A,crdr~clencerink n.friurain
*p-iinhiand 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
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 1-n

,..12,.' t111Ci ',~i C I.,r r ll O'n .111 -h Criro,

.ii./Li:i/t Q~,r,,i tiz n I .'t Xk-wI W i n
i- i .,'!! 'lfs I-run tt!,Itiehli2dUL i '2

c-oaF F!,,. ncfi P; IiuiL: ,r 111ai Cq ''qrwnlit
f 7LrIh'. '" I h.ipe Ic- i I lIJi)riced1.A n L'UN9riL Of

_F 'ft 1'S._h 1 ...'L i.a Pr..pkrte: --IP -A

i r t- ; r' .oa- B .
i~l'.t 11,Kc n L _.I, Order Code CLI0i

Interior-Point 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
polynomial-time interior-point methods. Their approach provides a
simple and elegant framework in which all known polynomial-time
interior-point methods can be explained and analyzed.
Chapter 1: Self-Concordant Functions and Newton Method; Chapter 2: Path-
Following Interior-Point Methods; Chapter 3: Potential Reduction Interior-
PointMethods; Chapter 4: How to Construct Self-Concordant 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 0-89871-319-6
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 0-89871-322-6 / List Price $24.50
OPTIMA Reader Price $19.60 / Order Code FR14

Also of

SIAM Journal on
Contains research and exposi-
tory articles on the theory and
practice of optimization, and
papers that link optimization
theory with computational prac-
tice and applications.
Published quarterly.
J.E. Dennis, Jr., Rice University
(through 12/31/94)
M.L. Overton, Courant Institute
ofMathematical Sciences
(beginning 1/1/95)
1995 List Price
$216.00 domestic / $246.00 overseas
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Si iTJ


- -------- -- ---------~-~--

'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
Springer-Verlag, Berlin, 1993
ISBN 3-540-55640-0
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 up-to-date 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

. . ...




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 quasi-algol 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.

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 0-471-93492-5
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 time-period 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 service-level 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 "Real-Time 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 present-day use of
optimization techniques in in-
dustry and demonstrates the
economic impact these tech-
niques have, despite the diffi-
culties encountered during
practical implementation."


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 0-1 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
in-house 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. "Crew-Pairing 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 branch-and-bound manner. It claims
successful application to ... Ii. optimal configuration layout problems containing
3,500 0-1 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

__ _ _ _ _ __ _ __ _ _ _ _ _ _ __ _ _ _ _ _ _


NOV 1994


"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 two-stage 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 cost-flow
problems in networks. In "Solution of Large-Scale 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
interior-point 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 large-scale 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 present-day use of optimization techniques in
industry and demonstrates the economic impact these techniques have, despite the
difficulties encountered during practical implementation.

Discrete and Combinatorial

Mathematics, an Applied Introduction,

Third Edition
by R.P. Grimaldi
Addison-Wesley, Reading, USA, 1994
ISBN 0-201-54983-2
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 ___________________________________________


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 divide-and-conquer 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 shortest-path algorithm, the minimal-spanning tree algorithms of Prim
and Kruskal, the max-flow min-cut theorem and the theorem of Konig-Hall.
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.


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 Al-Khayyal, 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
e-mail:hearn@ise. ufl. edu
Department of Econometrics
I1! .1 I, University
P.O. Box 90153
5000 LE Tilburg
The Netherlands
e-mail: aardal@kub. nl
Georgia Tech
Industrial and Systems Engineering
Atlanta, GA 30332-0205
e-mail: faiz@isye. gatech. edu
Department of Econometrics
Tilburg University
P.O. Box 90153
5000 LE Tilburg
The Netherlands
e-mail: talman@kub. nl
Elsa Drake, DESIGNER

Journal contents are subject to change
by the publisher.

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N? 44


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