Title: Optima
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00090046/00037
 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: July 1992
 Record Information
Bibliographic ID: UF00090046
Volume ID: VID00037
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.


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PRIZE for fundamental contributions to the theory of
operations research and management science was
awarded by the Operations Research Society of
America and The Institute of Management Sciences
to Alan J. Hoffman and Philip Wolfe at the joint
meeting of the societies in Orlando, Florida, April 29,
1992. The following citation is from the ORSA office
press release.
"Alan Hoffman and Phil Wolfe have had distinguished careers in
mathematicalprogramming. Their common bond is having worked
together for more than 25 years in the Mathematical Sciences De-
partment of the IBM Thomas J. Watson Research Center.They have
been intellectual leaders of the mathematical programming group
at IBM. This was one of the first industrial groups in the field and
it has continued to produce work of the highest quality in theory,
algorithms and software.
"Throughout his career, Alan Hoffman has worked on linear pro-
gramming and combinatorial optimization. He has brought to bear
a deep knowledge of algebra and combinatorics and much math-
ematical insight to the solution of a multitude of problems in this
"In1951, Hoffman was the co-author of one of the first computational
studies establishing the efficiency of the simplex method for solv-
ing linear programming problems. By the mid 1950s PAGEELEVEN M


Von Neumann








~--- -~-- -~II--~-' I--~- I-

PAE2 ubr hrt-eenJLY29


Oberwolfach Conference



January 26 February 1, 1992
The conference which was organized by P.
Gritzmann (Trier), V. Klee (Seattle) and P.
Kleinschmidt (Passau), was attended by 39
participants, who gave a total of 37 lectures.
The conference reflected the interesting
developments in the area of Applied and
Computational Convexity which give this
young field of mathematics its clear profile.
The roots of this field lie jointly in geometry,
in mathematical programming and in
computer science. Typically, the problems
are algorithmic in nature, the underlying
structures are geometric with special
emphasis on convexity, and the questions
are usually motivated by practical applica-
tions in mathematical programming,
computer science, and other less obviously
mathematical areas of science.
According to the concept of this conference,
the participants belonged to four different
fields; classical convexity theory, math-
ematical programming, computational
geometry and computer science.

The talks dealt with various topics of the
wide spectrum of subjects covered by
Applied and Computational Convexity. A
couple of lectures were devoted to convex
polytopes and polyhedral combinatorics,
where polyhedral approaches are utilized
for solving large-scale combinatorial
optimization problems.
Linear programming was the subject of
another group of lectures. Average case
analysis of LP-algorithms, new randomized
approaches to linear programming, and
questions concerning its parallel complexity
were studied.
Geometric aspects of nonlinear optimization
were scrutinized in some other talks while
yet other lectures dealt with lattice point
problems, partly from the point of view of
integer programming. Another complex
covered at the conference dealt with
concepts of classical convexity like mixed
volumes of convex bodies and their rela-
tions to problems in computer algebra or
mathematical programming.
Some other talks were devoted to questions
in geometric probing that are related to
various problems in numerical analysis or
computer tomography. In this context the
algorithmic theory of convex bodies played
an important role. Various concrete practical
applications were studied, including a
problem of chromosome classification.
Also presented were some algorithmic
approaches for the construction of certain
tilings that are relevant for the study of
In addition, various open problems were
stated which led to vivid discussions.
The conference showed that even though
the participants belonged to different fields
that have quite different tool-boxes, ap-
proaches and ideas for solving their

problems, there is a deep and dose connec-
tion which is centered around the basic
concept of convexity. We are certain that the
further study of these concepts will lead to a
fruitful further development of the field of
Applied and Computational Convexity.
In the following we list the speakers
and the titles of their talks.
Imre BArAny: On the number of convex lattice
polygons. Joint work with J. Pach and A.
Louis J. Billera: Fiber polytopes and transpor-
tation polytopes. Joint work partly with B.
Sturmfels and A. Sarangarajan.
Jiirgen Bokowski: Spatial polyhedra without
diagonals. Joint work with Amos Altshuler
and Peter Schuchert.
Vladimir G. Boltyanski: The Helly dimension
of convex bodies.
Karl Heinz Borgwardt: Improvements in the
average-case analysis of the simplex-method
based on geometrical properties of randomly
generated polyhedra.
Ludwig Danzer Strategies for the generation
of PENROSE-tilings with defects, which
(hopefully) will not lead into dead ends.
Klaus Donner Best L2-approximation with
order convex and cone star-shaped sets in
MR-tomographic images.
Martin Dyer Random walks and unimodular
linear programs. Joint work with A. Frieze.
Giinter Ewald: Projections of polytopes onto
Miroslav Fiedler An application of simplex
geometry to graphs and resistive electrical
Richard J. Gardner Determination of convex
polytopes by X-rays. Joint work with Peter


Number ThirtySeven


JULY 1992

PAGE 3 Number Thirty-Seven JULY 1992

Peter Gritzmann: Polytope containment and
determination by linear probes. Joint work with
Victor Klee and John Westwater.
Martin Henk: Approximating the volume of
convex bodies. Joint work with U. Betke.
Reiner Horst: Global optimization and the
geometric complementarity problem.
Alexander Hufnagel: On the complexity of
computing the volume of a zonotope. Joint work
with Martin Dyer and Peter Gritzmann.
Gil Kalai: The diameter of graphs of convex
polyhedra and a randomized simplex algorithm.
Victor Klee: Three unsolved problems concern-
ing cubes.
Peter Kleinschmidt: Methods of automated
chromosome classification. Joint work with
Ilse Mittereiter, Christian Rank.
Jeffrey C. Lagarias: The spectral radius of a set
of matrices and matrix norms. Joint work with
Yang Wang.
D. G. Larman: A Ramsey theorem for convex
sets in the plane.
Jim Lawrence: Transversals and the Euler
Carl Lee: Generalized stress and rigidity.
Horst Martini: The generalized Fermat-
Torricelli problem.
Nimrod Megiddo: Parallel complexity of
linear programming.
Giinter Meisinger: On the face and flag
numbers of convex polytopes.
Shmuel Onn: Permutation polytopes.
Panos Pardalos: Minimization of separable
convex functions subject to equality and box
constraints. Joint work with N. Kovoov.
Richard Pollack: Arrangements, spreads and
topological projective planes. Joint work with
J. E. Goodman, R. Wenger, and T.

Bill Pulleyblank: On splittable sets. Joint
work with F.B. Shephard and B.A. Reed.
Alexander Schrijver The stable set and odd
path polytopes. Joint work with P.D.
Ron Shamir: Unimodal separable minimization
subject to partial order constraints. Joint work
with Endre Boros.
Gyirgy Sonnevend: Analytic centers for
semiinfinite sets of convex inequalities.
Josef Stoer On the complexity of continuation
methods following an infeasible path.
Berd Sturmfels: Product formulas for sparse
resultants. Joint work with Paul Pedersen.
Emo Welzl: A randomized LP-algorithm with a
subexponential number of arithmetic operations.
Joint work with Jirka Matousek and Micha
J.M. Wills: A lattice point problem.
Giinter M. Ziegler: Subspace arrangements
and their homotopy types. Joint work with
Rade T. Zivaljevic.




October 15-16, 1992,
Hotel Seepark, Seestrasse 47
CH-3602 Thun, Switzerland
This tutorial is organized by SVOR/ASRO
(Swiss Association of Operations Research),
in collaboration with ETG/PES (Power
Engineering Society) member of the SEV
(Swiss Institute of Electrical Engineers).

Permanently increasing requirements in
power supply necessitate efficient control of
electric power systems. An emerging subject
of importance is optimization which is the
challenging principal theme of the an-
nounced tutorial.
Modelling Aspects of Unit Commitment
and Optimal Power Flow will provide
insight to electric energy systems engineer-
ing and to its associated problem statement.
Due to the nature of the underlying optimi-
zation problems recent developments in
advanced and well-established Mathemati-
cal Programming Methodologies will be
presented, illustrating in which way
dynamic, separable, continuous and
stochastic features might be exploited. In
completing the various methodologies a
number of presentations will state experi-
ences with optimization packages currently
used for unit commitment and optimal
power flow calculations.
One of the interesting objectives of this
tutorial is the fruitful communication to
be expected between operations research
experts, analysts of the application's side
and users in the power industry.

Unit Commitment; (Hydro-) Thermal
Optimization; Optimal Power Flow;
Optimization Packages for Unit Commit-
ment and Optimal Power Flow; Dynamic
Programming; Interior Point Methodology;
Lagrangian Optimization Methodology;
Stochastic Programming.

_ _s I~ ~ ~I_ ~ _s~ ~ I~ I

Number Thirty-Seven

JULY 1992




Dr. H. Braun (BASF, Germany), Prof.
G.B. Dantzig & Dr. G. Infanger (Stanford
University, USA), Dr. K. Kato (ECC, USA),
Dipl. Ing. K. Linke & Dipl. Ing. H.H.
Sanders (VEW, Dortmund, Germany),
Prof. K. Neumann (University of Karlsruhe,
Germany), Dr. A. Papalexopoulos (PG&E,
USA), Prof. R.T. Rockafellar (University
of Washington, Seattle, USA), Dr. E.
Steinbauer, Dipl. Ing. A Schadler
(STEWEAG, Austria), Prof. J.-P. Vial
(University of Geneva, Switzerland), Dr.
R. Bacher (ETH Zurich, Switzerland), Prof.
H. Glavitsch (ETH Zurich, Switzerland).

Organizing Committee:
Dr. Karl Frauendorfer (University of
Zurich, SVOR/ASRO), Prof. Dr. Hans
Glavitsch (ETH Zurich, ETG/PES), Dr.
Rainer Bacher (ETH Zurich, ETG/PES).
For registration and further
information please contact:
Dr. Karl Frauendorfer, Institute of Opera-
tions Research, University of Zurich,
Moussonstr. 15, CH-8044 Zurich, Switzer-
land, Tel: +41-1-257 3772; FAX: +41-1-252
1162; E-mail: K193302@czhrzula (earn or






Erice, Italy

April 29 May 1, 1993
This meeting will highlight recent
developments in the theory of integer
programming and combinatorial
Topics will include:
Accommodation for the participants and the
facilities for the Conference will be provided
by the "Ettore Majorana" Centre for
Scientific Culture. The Centre is located in
Erice, a small medieval village on top of a
mountain (750 meters above sea level) on
the western edge of Sicily.

For further information including
registration details, please contact:
Giovanni Rinaldi
Consiglio Nazionale delle Ricerche
Istiituto di analisi dei sistemi ed Informatica
Viale Manzoni 30, ROMA, Italy.
E-mail: rinaldi@ iasi.rm.cnr.it Fax: (39)6-
Instructions for Contributors
Persons wishing to submit a paper should
send eight copies of an extended abstract
before September 30, 1992 to:
Professor L.A. Wolsey
University Catholique de Louvain
Voie du Roman Pays 34
1348 Louvain-la-Neuve, Belgium.
The extended abstract should be from five to
ten pages in length (typed, double-spaced), i.e.,
about 2,000 words, and not a complete paper. It
must provide sufficient details concerning the
results and their significance to enable the
program committee to make its selection.

September 30,1992 Deadlinefor
submission of extended abstracts of papers.
December 31,1992 Notification
of acceptance of papers.
February 28,1993 Deadline for
submission of full text of accepted papers.
April 29-May 1st, 1993 The Conference.

_ I I


Number Thirty-ieven

JULY 1992

Numbcra~a ll Thirty-Sc-'en JULY 199

Technical Reports

Workng Papers




RUTCOR Rutgers Center
for Operations Research
Busch Campus, Rutgers
P.O. Box 5062, New Brunswick,
New Jersey 08903, USA

Irvin J. Lustig, Roy E. Marsten and David F.
Shanno, "The Interaction of Algorithms and
Architectures for Interior Point Methods," RRR
Ronald M. Harstad and Michael H.
Rothkopf, "Optimal Use of Governmental
Monopoly Power," RRR 37-91.
Ilan Adler and Ron Shamir, "Greedily
Solvable Transportation Networks and Edge-
Guided Vertex Elimination," RRR 39-91.
Endre Boros, Peter L. Hammer and Ron
Shamir, "Balancing Problems in Acyclic
Networks," RRR 40-91.
Endre Boros, Peter L. Hammer, Toshihide
Ibaraki and Kazuhiko Kawakami, "Identify-
ing 2- Monotonic Positive Boolean Functions in
Polynomial Time," RRR 41-91.
Fred S. Roberts, "On the Indicator Function of
the Plurality Function," RRR 43-91.
Fred S. Roberts and Yonghua Xu, "On the
Optimal Strongly Connected Orientations of
City Street Graphs IV: Four East-West Avenues
or North-South Streets," RRR 44-91.
Guoli Ding, A.Schrijver and P.D. Seymour,
"Disjoint Paths in a Planar Graph A General
Theorem," RRR 45-91.

Guoli Ding, A. Schrijver and P.D. Seymour,
"Disjoint Cycles in Directed Graphs on the
Torus and the Klein Bottle," RRR 46-91.
Christodoulos A. Floudas, Pierre Hansen
and Brigitte Jaumard, "Reformulation of Two
Bond Portfolio Optimization Models," RRR 47-
Fred S. Roberts, "Limitations on Conclusions
Using Scales of Measurement," RRR 48-91.
N.V.R. Mahadev, Fred S. Roberts and
Prakash Santhanakrishnan, "3-Choosable
Complete Bipartite Graphs," RRR 49-91.
Pierre Hansen and Keh-Wei Lih, "Heuristic
Reliability Optimization by Tabu Search," RRR
Frank K. Hwang, Uriel G. Rothblum and
Larry Shepp, "Monotone Optimal Multi-
Partitions Using Schur Convexity With Respect
To Partial Order," RRR 51-91.
Frank K. Hwang and Uriel G. Rothblum,
"Majorization and Schur Convexity with
Respect to Partial Orders," RRR 52-91.
Uriel G. Rothblum, "Using A Characterization
of Feasibility of Transportation Problems to
Establish the Pairwise Connectedness of Rn with
Respect to Partial Orders," RRR 53-91.
Joel E. Cohen and Uriel G. Rothblum,
"Nonnegative Ranks, Decompositions and
Factorizations of Nonnegative Matrices," RRR
Tamra J. Carpenter and David F. Shanno,
"An Interior Point Method for Quadratic
Programs Based on Conjugate Projected
Gradients," RRR 55-91.
Benjamin Avi-Itzhak and Shlomo Halfin,
"Servers in Tandem with Communication and
Manufacturing Blocking," RRR 56-91.

Rainer E. Burkard, Karin Dlaska and Bettina
Klinz, "The Quickest Flow Problem," RRR 57-
Pierre Hansen and Maolin Zheng, "Upper
Bounds for the Clar Number of a Benzenoid
Hydrocarbon," RRR 58-91.
Maolin Zheng, "On Clar Graph," RRR 59-91.
Shaoji Xu and Jianzhong Zhang, "An Inverse
Problem of the Weighted Shortest Path Prob-
lem," RRR 60-91.
Yves Crama and Frits C.R. Spieksma,
"Scheduling Jobs of Equal Length: Complexity
and Facets," RRR 61-91.
Pey-Chun Chen, Pierre Hansen, Brigitte
Jaumard and Hoang Tuy, "Weber's Problem
with Attraction and Repulsion," RRR 62-91.
Denise Sakai, "No-Hole K-Tuple (R+ )-
Distant Colorings," RRR 63-91.
Yves Crama, Pierre Hansen and Brigitte
Jaumard, "Complexity of Product Positioning
and Ball Intersection Problems," RRR 64-91.
Denise Sakai, "Minimizing the Number of
Holes in 2-Distant Colorings," RRR 65-91.
Denise Sakai, "Two Results About Niche
Graphs," RRR 66-91.
Denise Sakai, "Labelling Chordal Graphs with
a Condition at Distance Two," RRR 67-91.
J. Long and A.C. Williams, "On the Number
of Local Maxima in 0-1 Quadratic Programs,"
RRR 68-91.
Peter L. Hammer and Alain Hertz, "On A
Transformation which Preserves the Stability
Number," RRR 69-91.
Andras Prekopa, "Inequalities on Expectations
Based on the Knowledge of Multivariate
Moments," RRR 70-91.

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

JULY 1992

Numberc~ Th irt v Sevenn


Dynamic Optimization, The Calculus of
Variations and Optimal Control in Economics
and Management,
Second Edition
by M.I. Kamien and N.I. Schwarz
North-Holland, Amsterdam, 1991
ISBN 0-444-01609-0
The flier which accompanies this book states that: "The first edition of this vol-
ume has served as the classic text in economics, mathematical methods in eco-
nomics and dynamic optimization, management science, mathematics and en-
gineering. Now, with this second edition, a new genera tion of readers will ben-
efit from the book's clear exposition and many worked examples." This not so
modest recommendation raises high expectations. After having studied the
book, the current reviewer comes to the conclusion that the book lives up to
these expectations. Let us have a closer look.
For those who are familiar with the first edition, the second edition contains
new developments. The most noticeable addition is a section on differential
games. Other additions deal with comparative dynamics, integral state equa-
tions and jumps in the state variable. The book consists of two parts; calculus
of variations and optimal control. The first part, on the calculus of variations,
is split up into 18 sections. The second part, on optimal control, is split up into
23 sections. The average length of each section is about seven pages (the
maximum length is 15 pages which occurs only once). Most sections deal with
standard, separate, topics which are easily accessible. Thus a clear exposition
has been obtained. Most of the sections contain worked out examples. The sec-
tions contain exercises and conclude with some information on further read-
ing. Apart from these two parts there are two extensive appendices, one on cal-
culus and nonlinear programming and one on differential equations. Without
being exhaustive, let me mention the contents of some sections. In the part on

JULY 1992

Number Thirty-Seven

JULY 1992

Number Thirty-Seven

the calculus of variations we have the Euler equation, second order conditions,
the Legendre condition, transversality condition, free end value, finite and
infinite horizon, sensitivity, corners and the Weierstrass-Erdmann corner
conditions, inequality constraints, graphical aids. The part on optimal control
deals amongst others with the distinction between'state' and 'control', neces-
sary conditions, sufficiency conditions, discounting, the current-value Ham-
iltonian, infinite horizon, bounded controls,bang-bang control, singular solu-
tions, Pontryagin maximum principle, state variable inequalities, delays in the
differential equation, dynamic programming, stochastic optimal control, dif-
ferential games (two person, Nash), open-loop and feedback strategies.
In both parts only continuous time formulations are considered. Most sections
deal with scalar problems (the'state' x is one-dimensional). According to the
preface, the style is such that the "focus is on providing the student with the
tricks of the trade on an informative intuitive level." Indeed, I think that this
book is an excellent first introduction to the field of dynamic optimization.
Though most of the examples have an economic flavor, the emphasis is on the
solution techniques) and therefore this book is not only interest-arousing for
economists and management scientists, but also for (applied) mathematicians
and engineers.
The prerequisites are rather modest; calculus, some basic knowledge of
nonlinear programming and of the theory of differential equations. The text
is suitable for undergraduates in the mathematical sciences and for beginning
graduates of the economic and managerial sciences. Some mild criticisms that
the novice might not realize that the examples have been carefully designed
suchasto make analyticalinsight possible. For more complicated problems one
definitely needs numerical techniques which are not treated.
Another point that puzzles me somewhat is that the dynamic programming
approach is somewhat hidden in the part on optimal control. One could easily
devote a separate third part to dynamic programming which would have em-
phasized the difference between open-loop and feedback solutions. In the
current set up this difference hardly shows up which is a pity (the difference
in these solutions becomes visible only in the section on differential games).
Notwithstanding this criticism, the novice will "benefit from the book's clear
exposition and many worked examples."

Handbook of Theoretical Computer Science
Volume B
Edited by J. van Leeuwen
North-Holland, Amsterdam, 1990
ISBN 0-444-88074-7
The Handbook of Theoretical Computer Science is designed to provide a wide
audience of professionals and students in computer science and related dis-
ciplines with an overview of the major results and developments in the theo-
reticalexplorationofmodemdevelopments incomputerand software systems.
The current version of the Handbook is presented in 2 volumes: Vol. A: Algo-
rithms and Complexity; Vol. B: Formal Models and Semantics.
This reflects the divisionbetweenalgorithm-orientedanddescription-oriented
research that can be witnessed in theoretical computer science. The volumes
can be used independently, and together they give a unique impression of the
core areas of research in theoretical computer science as it is practiced today.
In my opinion, the handbook is a basic and very important book.
Volume B, called Formal Models and Semantics, is divided into 19 chapters:

Indeed, I think
that this book is
an excellent first
introduction to
the field of


I ---~-P~

AGE 8 Number Th

Finite Automata (Perrin), Context-Free Languages (. Berstel and L. Boasson),
Formal Languages and PowerSeries (A. Salomaa), Automata onInfinite Objects
(W. Thomas), Graph Rewriting: An Algebraic and Logic Approach (B.
Courcelle), Rewrite Systems (N. Dershowitz and J.-P. Jouannaud), Functional
Programming and Lambda Calculus (H.P. Barendregt), Type Systems for Pro-
grammingLanguages (J.C. Mitchell), Recursive Applicative ProgramSchemes
(B. Courcelle), Logic Programming (KR. Apt), Denotational Semantics (P.D.
Mosses), Semantic Domains (C.A. Gunter and D.S. Scott), Algebraic Specifi-
cations (M. Wirsing), Logics of Programs (D. Kozen and J. Tiuryn), Methods
andLogics forProvingPrograms (P. Cousot),Temporaland ModalLogic (E.A.
Emerson), Elements of Relational Database Theory (P.C. Kanellaiks), Distrib-
uted Computing: Models and Methods (L Lamport and N. Lynch), Operational
and Algebraic Semantics of Concurrent Processes (R Milner).

Stability, Duality and Decomposition in General
Mathematical Programming
by O.E. Flippo,
CWI Tract 76, Centre for Mathematics and Computer
Amsterdam, 1991
ISBN 90-6196-398-2
This book presents a new general framework for primal and dual decompo-
sition methods. Books about decomposition are scarce, and most literature on
decomposition is based on practical applications. This book, however, is out-
spokenly theoretical in its approach. The author states that the approach is one
of abstraction and the analysis is more conceptual than algorithmic in nature.
No applications or computational results are presented or discussed. There-
fore, the book is mainly addressed to readers interested in theoretical aspects
of decomposition.
The main goal of the book is to give new generalizations of the traditional de-
composition methods of Benders and Dantzig and Wolfe. It consists of three
parts, each self-contained with anintroduction, a summary and a reference list.
The topics of the three parts are stability, general duality theory and general
decomposition methods. General duality theory isanessential prerequisite for
the general decomposition methods, and stability is an essential condition for
thegeneraldecompositionmethods to converge, so the first two parts are mainly
prerequisites to the third part, where the new decomposition methods are
presented and analyzed.
In the first part, right-hand-side perturbations are considered, and stability is
definedascontinuity ofthevalue-function (the perturbationfunction). Anum-
ber of results are given containing sufficient conditions for stability, and the
necessity of these conditions is also discussed.
The second part presents general duality theory. It is shown to contain
Lagrangean duality, augmented Lagrangean duality and integer linear pro-
gramming duality as special cases. Special consideration is given to the ques-
tion about one-to-one correspondence between primal constraints and dual
variables, which is shown to hold in the case of additively separable dual
solutions, and, if the dual functions are finite, in the case of stability, or in the
case of a bounded integer program.
The third part presents two new, very general decomposition procedures, vari-
able decompositionandconstraint decomposition,whichare shown to be dual
to each other.

- ~---- I---~--~~-`-~-~


Number ThirtywSeven

JULY 1992

JULY 1992

Number Thirty-Seven

The key idea in variable decomposition is a new and seemingly simple refor-
mulation, when constructing the subprogram. Usually some "difficult" vari-
ables x are fixed to some 2, which means that these variables are eliminated
from the problem. Here the constraints = reintroduced explicitly andx kept
as variables. The standard derivation of the master problem is then carried
through, keeping this special problem formulation. This generalization elimi-
nates the need for any additional assumptions about separability or the Prop-
erty P introduced by Geoffrion, something which is needed in former exten-
sions of Benders decomposition (due to what the author calls the "inappropri-
ate" formulation of the problem by directly fixing x to ).
The rather simple trick of using the constraints x = R explicitly has the effect of
expanding the dual space. If the subproblemis actually going to be solved that
way, i.e., without eliminating the fixed variables, the subproblemwillbecome
larger that the original problem. From this point of view it is unfortunate that
the practical efficiency of this decomposition method is not discussed at all.
The algorithm is given as a framework, without specifying many details. De-
compositionprocedures by the followingauthors are shown to fit into the frame-
work: Benders (partially linear programs), Balas, Lazimy (both mixed-integer
quadratic programs with a convex structure), Geoffrion (partially convex pro-
grams), Wolsey (no explicit constraints), Burkard, Hamacher and Tind (sepa-
rable algebraic optimization) and the outer approximation approach of Duran
and Grossman.
The method is shown to have finite convergence if the primal or dual solutions
generated belong to finite sets. Examples are bounded integer sets (primally
finite)orlinearprograms (duallyfinite). Conditions forasymptotic convergence
are also given, and results for e-optimal solutions are given, which allows for
inaccurate solutions of the sub- and master programs.
By applying this approach to a mixed-integer nonlinear program with under-
lying convex structure, a separation into a mixed integer linear program and
a convex nonlinear program is obtained, ie., the integer requirements are sepa-
rated from the nonlinearities.
The constraint decomposition procedure presented uses general dual func-
tions, instead ofaffine functionswithordinary Lagrange multipliers, and gen-
eralizes the methods of Dantzig and Wolfe (LP), Dantzig (convex programs)
and Burkard, Hamacher andTind. The subprogramis a "generalized" Lagran-
gean relaxation. Convergence results similar to those for variable decompo-
sition are given.
Finally, generalizations of the two primal-dual decompositionmethods-cross
decomposition and Kornai-Liptak decomposition- are presented, using both
variable and constraint decomposition.
Abook about decomposition is always welcome. Thisbook is wellwritten with
a certain elegance of style. It is in fact Flippo's PhD.-dissertation, and this is
obvious by the repeated discussions about which results are new contributions
and which are not. This might also explain the somewhat argumentative style
in which the author promotes his ideas.
In conclusion, this book describes an interesting generalization of primal and
dual decomposition methods. It might not quite qualify as the generalization
which subsumes all others, but is an interesting contribution and can be rec-
ommended to everyone interested in theoretical aspects of decomposition

This book describes
an interesting
generalization of
primal and dual
methods. It might
not quite qualify as
the generalization,...
but is an interesting
contribution and can
be recommended to
everyone interested
in theoretical aspects
of decomposition



Number Thirty-Seven

Vol. 55, No. 1

Michael J. Todd, "On Anstreicher's Combined
Phase I-Phase II Projective Algorithm for Linear
J.F. Pekny and D.L. Miller, "A Parallel Branch
and Bound Algorithm for Solving Large
Asymmetric Traveling Salesman Problems."
Michele Conforti and M.R. Rao, "Properties
of Balanced and Perfect Matrices."
G. Di Pillo, F. Facchinei and L. Grippo, "An
RQP Algorithm Using a Differentiable Exact
Penalty Function For Inequality Constrained
J.H. Dula, "An Upper Bound on the Expecta-
tion of Simplical Functions of Multivariate
Random Variables."
U. Passy and E.Z. Prisman, "A Duality
Approach to Minimax Results for Quasi-Saddle
Functions in Finite Dimensions."
A.G. Robinson, N. Jiang and C.S. Lerme,
"On the Continuous Quadratic Knapsack
Yin Zhang, "Computing a Celis-Dennis-Tapia
Trust-Region Step for Equality Constrained

)urna ls

Vol. 55, No. 2

Michele Conforti and M.R. Rao, "Structural
Properties and Decomposition of Linear
Balanced Matrices."
Martin Dyer and Alan Frieze, "Probabilistic
Analysis of the Generalised Assignment
Ephraim Korach and Michal Penn, "Tight
Integral Duality Gap in the Chinese Postman
Alan J. King and R.Tyrrell Rockafellar,
"Sensitivity Analysis for Nonsmooth General-
ized Equations."
Rachelle S. Klein, Hanan Luss and Donald
R. Smith, "A Lexicographic Minimax Algo-
rithm for Multiperiod Resource Allocation."
Asim Roy and Jyrki Wallenius, "Nonlinear
Multiple Objective Optimization: An Algorithm
and Some Theory."

Vol. 55, No. 3

Pierre Hansen, Brigitte Jaumard and Shi-Hui
Lu, "Global Optimization of Univariate
Lipschitz Functions: I. Survey and Properties."
Pierre Hansen, Brigitte Jaumard and Shi-Hui
Lu, "Global Optimization of Univariate
Lipschitz Functions: II. New algorithms and
Computational Comparison."
Dimitri P. Bertsekas and Jonathan Eckstein,
"On the Douglas-Rachford Splitting Method
and the Proximal Point Algorithm for Maximal
Monotone Operators."

Graham R. Wood, "The Bisection Met
Higher Dimensions."
M. Gr6etschel and Zaw Win, "A Cutt
Plane Algorithm for the Windy Postmar
Dorit S. Hochbaum, Ron Shamir and
George Shanthikumar, "A Polynomia
Algorithm for an Integer Quadratic
Nonseparable Transportation Problem."

Vol. 56, No. 1

S. Frank Chang and D. Thomas McCormick,
"A Hierarchial Algorithm for Making Sparse
Matrices Sparser."
Shinji Mizuno, "A New Polynomial Time
Method for a Linear Complementarity Problem."
Douglas J. White, "A Linear Programming
Approach To Solving Bilinear Programmes."
Hiroshi Konno and Takahito Kuno, "Linear
Multiplicative Programming."
Jerzy Kyparisis and Chi-Ming IP, "Solution
Behavior for Parametric Implicit
Complementarity Problems."
Chi-Ming Ip and Jerzy Kyparisis, "Local
Convergence of Quasi-Newton Methods for B-
Differentiable Equations."
Silvia Vogel, "On Stability in Multiobjective
Programming-a Stochastic Aproach."


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

JULY 1992

hod in



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


Hoffman &

Wolfe Receive

Von Neumann


his interest in applying linear programming to the solution of combinatorial optimization problems
had clearly emerged, and in 1956 his paper with J. Kruskal on unimodular matrices appeared. He has
been a very active contributor to the derivation of combinatorial min-max results using linear program-
ming duality and total unimodularity.
"Alan Ho ffman haswritten papers with atleast seven other von Neumann prize winners, so it is verylikely
that he represents the node of highest degree in the graph of von Neumann collaborators. Hislong stand-
ing tenure in the field is documented by having had papers in the first volume of SIAM Journal (1953),
Management Science (1954) and Naval Research Logistics Quarterly (1954). Remarkably, he has sustained
a high level of research activity for more than forty years. He has done substantial work in linear program-
ming, network flows, unimodularity, blocking and antiblocking polyhedra, balanced matrices, greedy
algorithms, eigenvalue estimation and other areas of mathematics.
"Philip Wolfe has published more than 60 papers on the subject of mathematical programming. The
pioneering work on using lexicography to resolve cycling in the simplex method for linear programming,
done with co-workers G. Dantzig and A. Orden, was published in 1955. In 1956, M. Frank and Wolfe
published the seminal paper that gives a linearly convergent algorithm for quadratic programming. His
1959 paper The simplex method for quadratic programming' exemplifies the idea of using the simplex
method as a building block for solving nonlinear problems. The restricted pivot selection scheme of this
paper has had a strong influence on algorithmic developments in quadratic programming and linear
"Phil Wolfe isalso aco-authorof whatmaybe the firstpaper inlarge-scale optimization,namelyhis paper
with Dantzig on the decomposition principle of linear programs. This idea has had an enormous impact
on theory and computation and is still an active area of research today.
"Phil Wolfe also contributed to numerical analysis, computational complexity, game theory and software
systems. In addition to being well-known for his fundamental contributions to the simplex method, de-
composition and quadratic programming,he also developed the mostrobust optimization algorithm ever
written, but was too modest to take credit for it. See Anonymous, 'A new algorithm for optimization,'
Mathematical Programming 3,1972."

cfJpplic tionforcJWembershi*

Mail to:

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--- -------s_

JULY 1992


Number Thirty-Seven

The second meeting of the Nordic Section of
PMPS will be August 14-16, 1992. Contact Jens
Clausen, email: clausen@diku.dk. %The first
Soviet-Italian Conference on Methods and Ap-
-plications of Mathematical Programming will
be held Sept. 7-11,1992, Cetraro, Cosenza, Italy.
Contact is Dr. Francesco Lampariello, email:
itasov@irmiasi.bitnet or fax: 39 6 770031. IJA
course on Interior Point Methods in Optimiza-
tion is being organized by INRIA for October 7-9,
1992, in Rocquencourt, France. The main speak-
ers are C.C. Gonzaga and J.Ph. Vial. Contact
Frederic Bonnans, email: bonnans@
femat.inria.fr. $The 16th IFIP Conference on
System Modeling and OptimizationwillbeJuly
5-9,1993, Compiegne, France. Contact the Sec-
retariat, email: symposia@inria.fr or fax: (33) (1)
39 63 56 38. A Sixth Workshop on Computer-
Aided Scheduling of Public Transport will be
held in Lisbon, Portugal, 6-9 July, 1993. Contact
the Secretariat, e-mail: paixao@ul.pt or fax: (01)
397 83 08. $Deadline for the next O P T I M A is
October 1,1992.

Books for review should be
sent to the Book Review Editor,
Professor Dolf Talman
Department of Econometrics
Tilburg University
P.O. Box 90153
5000 LE Tilburg

Journal contents are subject
to change by the publisher.

Donald W. Hearn, EDITOR
Elsa Drake, DESIGNER



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