P TI MA N3
MATHEMATICAL PROGRAMMING SOCIETY NEWSLETTER July r991
an Karel Lenstra, Eindhoven Univer-
Jsity of Technology professor and one of the
organizers of the 14th MPS Symposium,
has been elected Chairman of the Society for the
period 1992-1995. He will be Vice Chairman
until he replaces current chairman George
Nemhauser of Georgia Tech in August of 1992.
Joining Lenstra on the Council will be Leslie E.
Trotter of Cornell who continues as Treasurer
through August 1995. The four new Council
Members-at-Large are Clovis C. Gonzaga,
COPPE-Federal University of Rio de Janeiro;
Masakazu Kojima, Tokyo Institute of Technol-
ogy; Bernhard Korte, University of Bonn; and
Stephen M. Robinson, University of Wiscon-
sin. They will serve from the 14th Symposium
until the 15th (August 1991 to August 1994).
K, P T I M A
Conference on Optimization
The next SIAM Conference on
Optimization will be held May 11-13,
1992, in Chicago, Illinois. The
conference is sponsored by the SIAM
Activity Group on Optimization.
The major themes for the 1992
SInterior point methods
*Algorithms for optimization problems
*Network optimization methods
*Parallel algorithms for optimization
The conference will be held at the Hyatt Regency
Hotel, which is located near many of the cultural
and gastronomical attractions of Chicago.
The call for papers will be mailed on July 19,
1991. Abstracts for presentations are due on
October 11, 1991. Please make a note of the
dates May 11-13, 1992. See you in Chicago!
Jorge Mor6 (Co-chair), Argonne National
Jorge Nocedal (Co-chair), Northwestern
Jane Cullem, IBM Thomas J. Watson
Donald Goldfarb, Columbia University
Society for Industrial and
3600 University Science Center,
Philadelphia, PA 19104-2688
The Fourth International Workshop
on Generalized Convexity will be
held in Pscs, Hungary, August 31-
September 2, 1992, and is organized
by S. Kornl6si, P6cs; T. Rapcsik,
Budapest; and S. Schaible,
Conference themes include:
* Characterizations of various kinds of
* Generalized monotone maps
*Optimality and duality
* Fractional programming
* Multi-criteria optimization
*Numerical solution methods
*Applications in economics, business
administration, and stochastic systems
Prof. S. Koml6si
Faculty of Economics
Janus Pannonius University
Rik6czi ut 80
H-7621, P6cs, Hungary
Telephone 36-72-11433; Fax 36-72-33129
+European Journal of
Special Issue on Lotsizing
Models for Production
The need for lotsizing emerges when, for
technical or economic reasons, successive
processes (such as production and con-
sumption) are not or cannot be synchro-
nized. Although technological develop-
ments have increased the capacity of
industrial organizations to synchronize
operations, lotsizing remains a very
important coordination tool when full
synchronization is impossible. European
Journal of Operational Research (EJOR)
devotes a special issue on lotsizing models for
production planning. Submitted papers may
focus on new theoretical developments
concerning lotsizing models, but contribu-
tions discussing applications of lotsizing
models and techniques in practice are
especially welcomed. For example, contribu-
tions may deal with, but are not restricted
to, the following topics:
1. Models and solution procedures for
lotsizing in capacitated environments.
2. Procedures for reduction of setup time and
3. Interaction between dynamic lotsizing and
4. Lotsizing and maintenance.
5. Interrelation between product line design
6. Lotsizing and safety stocks in MRP or DRP
7. Mathematical complexity results and
mathematical programming-based algorithms
for lotsizing problems.
I M_ -1157l
8. Interaction between lead-times and
9. Decision support systems for lotsizing.
10. Models and solution procedures for
lotsizing in complex (multilevel) product
11. Lotsizing and restrictions imposed by
environmental constraints (e.g., pollution
Guest editors for the special issue are Marc
Salomon, Roelof Kuik, and Luk N. Van
Wassenhove. Authors should follow
standard guidelines for EJOR as stated in
each issue of the journal. All papers will be
evaluated using the EJOR standard review
process. Four copies of the manuscript
should be sent to:
Rotterdam School of Management
P.O. Box 1738
Deadline for submission of papers is March 1,
1992. Additional information concerning this
special issue can also be obtained from Marc
*Special Issue of
on "Applications of
Discrete Optimization in
Editor: Thomas Lengauer, University of
Paderborn, Paderborn, Germany.
In recent years, there has been an impressive
cross-fertilization between research in
discrete optimization and related research in
computer science. Methodological advances
in computer science have revealed that
many optimization problems reduce to
classical questions discussed in the area of
discrete optimization. On the other hand,
new applications have propelled the
progress in developing methods for solving
large optimization problems.
This issue of Mathematical Programming B
aims at presenting original contributions to
the area of discrete optimization that arise
from applications in computer science. A
nonexclusive list of applications is
Layout design of VLSI circuits (e.g.,
floorplanning, placement, global routing,
detailed routing, cell synthesis)
High-level synthesis of VLSI systems (e.g.,
scheduling and resource allocation)
VLSI architectures for solving discrete optimiza-
New developments in computing:
Code optimization for innovative architectures
Parallel algorithms and architectures for solving
discrete optimization problems
Optimization problems in running parallel
computers (e.g., resource allocation, load
balancing, message distribution)
Submitted papers should present original
research contributions, detail the optimiza-
tion methods, but also discuss thoroughly
the relevance of the models and results for
the respective application. A validation of
the research results normally will be
composed of both theoretical analyses and
experimental data about normal editorial
process. All submissions will undergo the
normal Mathematical Programming
The final drafts of accepted papers must
adhere to the format specified by Math-
ematical Programming B, described at the
end of each issue. Four copies of submis-
sions should be sent to:
Prof. Thomas Lengauer
Department of Computer Science and
Mathematics (FB 17)
University of Paderborn
Fax: +49 5251 60 3836
The deadline for submission is September 30,
1991. The final papers will be sent to the
publisher in the fall of 1992. The issue is
scheduled to appear in the first half of 1993.
CONTINUES ON FOLLOWING PAGE
*Special Issue of
Mathematical Programming B
on "Applications of
We are planning to edit a special issue of
MPB that will focus on real-world applica-
tions of combinatorial optimization. We
seek contributions that address practical
problems, describe their mathematical
modeling, the theory developed for the
structural understanding of the model, and
the algorithms designed and implemented
for solving the problem.
The latter may be exact optimization
algorithms or problem-specific heuristics
that take the special application into
account. A report of the computational
performance of the algorithms and the
quality of the solutions obtained is indis-
pensable. We are not interested in numeri-
cal studies on random problems. What
counts is the theoretical and algorithmical
treatment of practical instances from the real
Papers should be submitted to either one
of us (addresses are listed below). The
deadline for submission is December 31,
1991. All submitted papers will be
refereed under the usual criteria of
Rainer E. Burkard
Institute fiir Mathematik
Technische Universit~t Graz
8010 Graz, Austria
Institute fir Mathematik
8900 Augsburg, Germany
You can now reach 27 of the
Nordic MPS members by
one e-mail message to
The idea is that other MPS
members can inform Nordic MPS
members about such items as
Planned visits to the region
If you plan to tour the region by giving
talks at different universities, one
message will put you in contact with
almost all universities where math-
ematical programming is taught.
More precisely, you will reach leading
researchers at the following institutions:
Norway: The University of Bergen,
The University of Trondheim, The
Norwegian Computing Center Oslo
Sweden: Linkoping University, The
Royal Institute of Technology Stockholm,
University of Umea
Finland: Helsinki School of Economics
Denmark: University of Copenhagen,
University of Aarhus, The Business
School in Aarhus, The Technical
University of Denmark
Iceland: The University of Iceland
Stein W. Wallace, leader of the Nordic
Section of MPS, may be reached via
or by phone: + 47-7-593609
School of Operations Research
and Industrial Engineering
Ithaca, NY 14853-3801
S. Mizuno, M.J. Todd, Y. Ye: "Anticipated
Behavior of Long-Step Algorithms for Linear
Programming," TR 882.
R. Barton and L.W. Schruben: "Graphical
Methods for the Design and Analysis of
Simulation Experiments," TR 883.
R. Barton: "Experiments in Computing Finite
Difference Derivatives when Optimizing Low
Accuracy Functions," TR 884.
J.S.B. Mitchell and C.H. Papadimitriou: "The
Weighted Region Problem: Finding Shortest -
Paths Through a Weighted Planar Subdivision,"
S. Rachev and S. Resnick: "Max-Geometric
Infinite Divisibility and Stability," TR 886.
A.G. Loerch and J.A. Muckstadt: "An
Approach to Production Planning, Schedul-
ing, and Due-Date Quotation in Cyclically
Scheduled Manufacturing Systems," TR 887.
D.M. Ryan: "The Solution of Massive General-
ized Set Partitioning Problems in Aircrew
Rostering," TR 889.
M. Todd and L. Khachiyan: "On the Com-
plexity of Approximating the Maximal Inscribed
Ellipsoid for a Polytope," TR 893.
E.M. Arkin, S. Khuller and J. Mitchell:
"Optimal Enclosure Problems," TR 895.
J. Mitchell and E. Wynters: "Optimal Motion
of Covisible Points Among Obstacles in the
Plane," TR 896.
E.C. Sewell and L.E. Trotter, Jr.: "Stability
Critical Graphs and Even Subdivisions of K,,"
P.L. Jackson and J.A. Muckstadt: "Llenroc
Plastics: Market Driven Integration of Manufac-
turing and Distribution Systems," TR 898.
L. Tuncel: "On the Complexity of Preflow-Push
Algorithms for Maximum Flow Problems," TR
R. Barton: "Graphical Tools for Experiment
Design: A Brief Survey," TR 902.
M. Todd: "A Low Complexity Interior-point
Algorithm for Linear Programming," TR 903.
E. Sewell: "Stability Critical Graphs and the
Stable Set Polytope," TR 905.
M. Todd: "Combining Phase I and Phase II in a
Potential Reduction Algorithm for Linear
Programming," TR 907.
C. Ko and R. Bland: "Characterizations of
Camion Trees and Depth-first Search Trees by
Excluded Configurations," TR 909.
P.J. Heffernan: "Linear-Time Algorithms for
Weakly-Monotone Polygons," TR910.
Y. Herer: "Submodularity and the Travelling
Salesman Problem," TR 915.
Y. Herer and R. Roundy: "Heuristics for a
One Warehouse Multi-Retailer Distribution
Problem with Performance Bounds," TR 916.
L. Liao and C. Shoemaker: "The Proof of the
Quadratic Convergence of Differential Dynamic
Programming," TR 917.
D.B. Shmoys and E. Tardos: "Computational
Complexity," TR 918.
C.N. Potts,D.B. Shmoys and D.P.
Williamson: "Permutation vs. Non-permuta-
tion Flow Shop Schedules," TR 919.
J.S.B. Mitchell, G. Rote, G. Woeginger:
"Minimum-Link Paths Among Obstacles in the
Plane," TR 920.
D.B. Shmoys, C. Stein, J. Wein: "Improved
Approximation Algorithms for Shop Scheduling
Problems," TR 921.
J. Renegar: "Computational C'npl it ,i of
Solving Real Algebraic Formulae," TR 922.
A.W.J. Kolen and J.K. Lenstra: "Combinato-
rics in OR," TR 925.
D. Gusfield and E. Tardos: "A Faster
Parametric Minimum Cut Algorithm," TR 926.
C. Ko: "An Algorithm to Find a 2-Isomorphic
Depth-First Search Image of a Tree," TR 927.
M.A. Hariga and P.L. Jackson: "Time Variant
Lot Sizing Models for the Warehouse Scheduling
Problem," TR 930.
M.A. Hariga and P.L. Jackson: "Time
Invariant Lot Sizing Models for the Warehouse
Scheduling Problem," TR 931.
M.A. Hariga and P.L. Jackson: "The Ware-
house Scheduling Problem Formulation and
Algorithms," TR 932.
C. Akkan, M. Fret, D.C. Heath, P.L. Jackson,
K. Levesque, and S. Tlakula: "Chip Assign-
ment Algorithms for Dynamic Wafer Design in
Semiconductor Manufacturing," TR 935.
J.S.B. Mitchell: "Algorithmic Approaches to
Optimal Route Planning," TR 937.
J. Renegar: "Is It Possible to Know a Problem
Instance is Ill-Posed? Some Foundations for a
General Theory of Condition Numbers," TR
J. Muckstadt and R. Bowman: "Stochastic
Analysis of Cyclic Schedules," TR941.
E. Arkin, K. Kedem, J.S.B. Mitchell, J.
Sprinzak, M. Werman: "Matching Points into
Noise Regions, Combinatorial Bounds and
Algorithms," TR 942.
H. Cohen: "The Wild Card Option in Treasury
Bond Futures is Relatively Worthless," TR 943.
S. Mizuno, M. Todd, Y. Ye: "On Adaptive-
Step Primal-Dual Interior-Point Algorithms for
Linear Programming," TR 944.
J. Muckstadt and R. Bowman: "Stochastic
Analysis of Cyclic Schedules, Algorithms and
Examples," TR 945.
M.J. Todd and L. Tuncel: "A New Triangula-
tion for Simplicial Algorithms," TR 946.
S. Tayur: "Controlling Serial Production Lines
with Yield Losses Using Kanbans," TR 947.
J.S.B. Mitchell and E.L. Wynters: "Finding
Optimal Bipartitions of Points and Polygons,"
CONTINUES ON FOLLOWING PAGE
PAG 6 umbr tirt~-fur ULY99
R. Roundy and D. Sun: "An Improved
Algorithm for Finding Optimal Lot Sizing
Policies for Finite Production Rate Assembly
Systems," TR 949.
M.J. Todd: "Projected Scaled Steepest Descent
in Kojima-Mizuno-Yoshise's Potential Reduc-
tion Algorithm for the Linear Complementarity
Problem," TR 950.
M.J. Todd and J.-P. Vial: "Todd's Low-
Complexity Algorithm is a Predictor-Corrector
Path-Following Method," TR 952.
J. Mitchell: "An Optimal Algorithm for
Computing Visibility in the Plane," TR 953.
Centrum voor Wiskunde en
Dept. of OR, Statistics, and System
PO Box 4079
1009 AB Amsterdam
L.J.J. Bruggen, J.K. Lenstra, P.C. Schuur, "A
Variable Depth Approach for the Single-Vehicle
and Delivery Problem with Time," Memoran-
dum COSOR 90-48 Technische Universiteit
Eindhoven, Faculteit Wiskunde en 1990.
G.A.P. Kindervater, J.K. Lenstra, M.W.P.
Savelsbergh, "Sequential and Parallel Local
Search for the Time-Constrained Traveling
Salesman," Report EUR-CS-90-06, Erasmus
Universiteit Rotterdam; Memorandum
J.H.M. Korst, J.K. Lenstra, E.H.L. Aarts, J.
Wessels, "Periodic Multiprocessor Scheduling,"
Memorandum COSOR 90-49 Technische
J. van den Berg, R. Meester, "Stability
Properties of a Flow Process in Graphs," Report
90-58, TU Delft.
F.A. van der Duyn Schouten, S.G. Vanneste,
"Two Simple Control Policies for a Multi-
Component Maintenance System," Research
report KUB, FEW 455 1990.
O.J. Boxma, H. Levy, "Cyclic Reservation
Schemes for Efficient Operation of Multiple-
Queue Single-Serv," Report Raymond and
Beverly Sackler, Faculty of Exact Sciences,
Tel Aviv Universit 1990.
A.M.H. Gerards, "On Tutte's Characterization
of Graphic Matroids a Graphic Proof," CWI
Report BS R9028.
F.B. Shepherd, "Near-Perfect Matrices," CWI
Report BS R9034.
G. Ding, A. Schrijver, P.D. Seymour,
"Disjoint Paths in a Planar Graph a General
Theorem," CWI Report BS R9012.
G. Ding, A. Schrijver, P.D. Seymour,
"Disjoint Cycles in Directed Graphs on the
Torus and the Klein Bottle," CWI Report BS
A. Frank, A. Schrijver, "Edge-Disjoint Circuits
in Graphs on the Torus," CWI Report BS
A. Schrijver, P.D. Seymour, "A Simpler Proof
and a Generalization of the Zero-Trees Theo-
rem," CWI Report BS R9015.
B.J.B.M. Lageweg, J.K. Lenstra, B. Veltman,
"Multiprocessor Scheduling with Communica-
tion Delays," CWI Report BS R9018.
S.L. van de Velde, "Dual Decomposition of
Single-Machine Scheduling Problems," CWI
Report BS R 9009.
S.L. van de Velde, "Duality-Based Algorithms
for Scheduling Unrelated Parallel Machines,"
CWI Report BS R 9010.
J.A. Hoogeveen, H. Oosterhout, S.L. van de
Velde, "New Lower and Upper Bounds for
Scheduling Around a Small Common Due
Date," CWI Report BS R9030.
J.A. Hoogeveen, "Analysis of Christofides'
Heuristic: Some Paths are More Difficult than
Cycles," CWI Report BS R 9005.
J.A. Hoogeveen, S.L. van de Velde, "Polyno-
mial-Time Algorithms for Single-Machine
Multicriteria Scheduling," CWI Report BS R
A.W.J. Kolen, J.K. Lenstra, "Combinatorics in
Operations Research," CWI Report BS R9024
Research memorandum RM 90-27,
Rijksuniversiteit Limburg; Memorandum
J.A. Hoogeveen, S.L. van de Velde, "A New
Lower Bound Approach for Single-Machine
Multicriteria Scheduling," CWI Report BS
A. Schrijver, "Tait's Flyping Conjecture for
Well-Connected Links," CWI Report BS
J. van den Berg, E. Kranakis, D. Krizanc,
"Computing Boolean Functions on Anonymous
Networks," CWI Report CS R9011.
J.W. Cohen, "The Two-Dimensional Random
Walk, its Hitting Process and its Classification,"
CWI Report BS R9003.
J.W. Cohen, "On the Attained Waiting Time,"
CWI Report BS R9016.
J.W. Cohen, "On the Random Walk with Zero
Drifts in the First Quadrant of R2," CWI
Report BS R9022.
P. Wartenhorst, "Bounds for the Interval
Availability Distribution," CWI Report BS
M. Kuijper, J.M. Schumacher, "Realization
and Partial Fractions," CWI Report BS R9032.
M. Kuijper, J.M. Schumacher, "Minimality of
Descriptor Representations under External
Equivalence," CWI Report BS R 9002.
K. Dzhaparidze, P.J.C. Spreij, "On Second
Order Optimality of Regular Projective
Estimators: Part I," CWI Report BS R9029.
K. Dzhaparidze, "On Iterative Estimators,"
CWI Report BS R9036.
R. Helmers, P. Janssen, N. Veraverbeke,
"Bootstrapping U-Quantiles," CWI Report BS
D.M. Bakker, "Gradient Projection for
Nonparametric Maximum Likelihood Estimation
with Interral Censored Data," CWI Report BS
D.M. Bakker, "Two Nonparametric Estimators
of the Survival Function of Bivariate Right
Censored Observations," CWI Report BS
V.V. Korolyuk, "Central Limit Theorem for
Non-Homogeneous Processes with Independent
Increments," CWI Report AM R9026.
R. Helmers, "A Local Limit Theorem for L-
Statistics," CWI Report BS R9033.
A.J. Baddeley, R.P.C. Rodgers, "Nested
Monte Carlo Study of Random Packing on the
Sphere," CWI Report BS R9023.
R E V
No one would deny the important role combinato- L
rics plays in contemporary mathematics, though its
position is not always easy. Pure theoretists don't want to
see deep theorems there, while practical computer scientists
find combinatorics too theoretical. Nevertheless, or better just
because of this, I agree with the authors that each student of
mathematics or computer science should pass at least one semester of
combinatorics during his or her university curriculum. The book under
review is a good introductory test which contains basic and most important
combinational and graph theoretical notions and approaches and is accom-
panied by 885 problems. It can be fruitfully used for courses at junior level
for students of mathematics and at junior or senior level for students of
computer science or other engineering sciences (a combinatorics course for
senior students of mathematics should contain deeper theorems).
The book consists of 10 chapters, each of which is divided into two to six sec-
tions. Two groups of problems (called Problems and Advanced Problems)
are presented at the end of each section; most difficult problems are marked
by asterisks. Another group of review problems, a brief summary and bib-
liography conclude each chapter. Solutions or hints to odd numbered prob-
lems are provided at the end of the book. As a result of this 'parity revealing
strategy', there are a few nontrivial problems left without hints which, on
the other hand, may provide good influence on the students while forcing
them to work a bit harder. However, the majority of the problems are more
or less straightforward and should be suitable for all students. Special ex-
ercises for computer oriented students (called Supplementary Computer
Projects) conclude many of the sections.
The subjects covered by the book are the following (SCP in parentheses
indicates presence of Supplementary Computer Projects in the particular
1 Combinatorial Problem Solving 1.1. Deduction (SCP), 1.2 Induction (SCP),
1.3 Sets and Relations (SCP), 1.4 Functions (SCP) (Pigeonhole principle);
2 Basic Counting Principles 2.1 Sequential Counting, 2.2 Case-by-case
Counting,2.3Selections (SCP) (Permutations and combinations without rep-
etition), 2.4 Selections with Unlimited Repetition (Permutations and com-
binations with repetition, and distri-
W S butions), 2.5 Binomial Coefficients
(Pascal's triangle),2.6 Permutations of
3 The Principle of Inclusion-Exclu-
sion 3.1 The Union of Overlapping
Sets (SCP),3.2 Counting Restricted Ar-
rangements (Derangements, combi-
nations with limited repetition,
Euler's phi function), 3.3 Distributions (SCP) (Dis-
tributions of distinct/identical objects to distinct/
S4 Combinatorial Algorithms 4.1 Algorithms (SCP), 4.2 As-
ymptotic Analysis of Algorithms, 4.3 Enumerating Permuta-
tions and Combinations (SCP) (Lexicographic order);
5 Graphs 5.1 Graph Models (SCP) (Basic notions, degree sequence), 5.2 Paths
and Connectedness, 5.3 Circuits and cycles (SCP) (Eulerian trails and circuits,
Hamiltonian paths and cycles), 5.4 Planar Graphs (Euler's formula and
Kuratowski's theorem), 5.5 Graph Colorings (SCP) (Five color theorem,
6 Graph Algorithms and Searching 6.1 Breadth First Search (SCP) (Shortest
path, bipartite graphs), 6.2 Trees (SCP) (Depth first search, spanning trees,
Cayley's theorem), 6.3 Tree Algorithms (SCP) (Binary search, minimum-
weight spanning tree, sorting);
7 Generating Functions 7.1 Generating Function Models, 7.2 Calculating
Coefficients (SCP), 7.3 Partitions (SCP), 7.4 Exponential Generating Func-
8 Recurrence Relations 8.1 Recurrence Relation Models (SCP) (Fibonacci and
Catalan numbers), 8.2 Homogeneous Linear Recurrences (SCP) (Solving
linear recurrences via characteristic equation), 8.3 Nonhomogeneous Lin-
ear Recurrence Relations (SCP);
9The Polya Theory of Counting9.1 Symmetry Groups and Burnside's Theo-
rem, 9.2 The Cycle Index;
10 Graph and Network Algorithms 10.1 Directed Graphs (SCP) (Tourna-
ments, directed Euler tours), 10.2 Networks (The earliest starting time algo-
rithm, criticalpathanalysis, compaction of an integratedcircuitdesign),10.3
Network Flows (The labeling algorithm, matching and Hall's marriage
As seen from thecontents, most of thebasic areas of combinatorics and graph
theory are covered. On the other hand, some sections might be richer even
at this introductory level, e.g. Chapter should reveal few examples of using
differentiation when evaluating generating functions. Some Ramsey theory
CONTINUES ON T)LLOWING PAGE
with Problem Solving
Bradley W. Jackson and
-- -- -- q; wm.i --
I0 m ,~ -
should be included, for instance, as an extension of the pi-
geonhole principle in Section 1.4. Though the book is writ-
ten mainly for computer science students, it contains just a
brief note about NP-completeness theory, without defini- ___
tions and withoutexamples of reductions betweenproblems R v
from NP. A very few formulations occur which are not
completely correct from the formal point of view; namely,
the proof of Burnside's theorem (Section 9.1) is incorrect.
-JAN KRATOCHVIL, PRAGUE
Handbooks in Operations Research and
Management Science, Vol. 1
G. L. Nemahuser, A. H. G. Rinnoy Kan and
M. J. Todd, Editors
IS BN 0-444-87284-1
This is the first volume of a series of books dedicated to optimization meth-
ods. It is very appropriately called a handbook, since it possesses the prin-
cipal characteristics of this typeof text; itcontains the fundamental arguments
of the discipline which are treated with much clarity. On the other hand, it
is much more than a handbook because it presents simply a number of recent
and important acquisitions to the discipline.
The choice of optimization as the subject of the first volume is suitable be-
cause, as the authors themselves maintain, optimization models have often
been demonstrated to be the key for many applications of mathematics in
various fields like engineering, economics, industrial management of ser-
vices, transportation, communication.
The presence in the book of models and methods, whether of continuous or
combinatorial optimization, underlines the necessity of their wider interac-
tion at both didactic and research levels. Stochastic programming, either as
models or as an approach for treating complex deterministic models is most
welcome as are multi-objective models.
The first chapter is devoted to unconstrained optimization. Based on classic
methods, such as Taylor approximations and Newton-type methods, it
contains recent approaches like the one which uses trust regions. Special
attention is paid to computing aspects, including large-scale problems, data-
fitting applications, and parallel computation.
The second chapter contains an updated exposition of the main topics of
linear programs and related problems. Besides the classic simplex method,
which is presented also in a very attractive geometrical way,
D R tworecently proposed polynomial algorithms are described:
Khachian's ellipsoid method and Karmarkar's projective
one. As in the preceding chapter, techniques for handling
SW s large-scale problems are discussed.
The third chapter deals with constrained nonlinear program-
ming, with both equality and inequality constraints and, in
particular, the quadratic case. The reader is led to rapid un-
derstanding of the main approaches,like those based on Lagrang-
ian multiplers, penalty, augmented Lagrangian and barrier-function
methods. Special attention is devoted to numerical aspects.
Chapter four treats network flow optimization problems which have been
shown to be instrumental in several operations research applications. The
attention is focused on the three fundamental topics of this field, namely the
shortest path, the maximum flow, and the minimumcost flow problems. The
computational complexity of the algorithms is discussed.
The fifth chapter leads the reader through the important and complex sub-
ject of polyhedral combinatorics, whose aim is to reduce the feasible region
as an integer linear problem to a polyhedron so that the combinatorial prob-
lem collapses to a linear program. Min-max relations receive special atten-
tion, as well as several other important topics, like polarity, blocking and
The sixth chapter contains the main tools for solving integer programs whose
polyhedral properties have been investigated above. Principal attention is
devoted to cutting plane methods, in particular Gomory fractional cuts.
Several other fundamental topics are discussed, e.g. duality, computational
complexity, and methods for handling large-scale problems, such as branch-
Chapter seven treats those optimization problems where differentiability
of the involved functions is not guaranteed. The first part seeks to motivate
such a theory, showing classic and recent situations where the assumption
of differentiability would lead to rough approximations. Then two main
approaches for handling nondifferentiable optimization, i.e. subgradientand
bundle methods, are described. Remarks on directions for future develop-
ments, which close the chapter, are very suitable because of the fast devel-
opment of this subject.
The eighth chapter is concerned with stochastic programming, i.e. optimi-
zation problems where some of thedata are random variables. The firstpart
is dedicated to the motivation of stochastic models. Indeed, in recent years
we have seen, from economics to physics, from biology to engineering, an
increasing demand for a stochasticapproach to real problems, some of these
initially handled as deterministic ones. The main tools of stochastic program-
ming are thus presented here in an appropriate position. Anticipative and
adaptive models are described in detail. Then we meet re- -- concepts used in most of the methods for solving
course problems and optimality conditions. The last part I multiextremal global optimization problems that authors
contains approximations,solution procedures, stability,and believe to be promising for further research. These concepts
incomplete information. are applied to derive algorithms for solving wide classes of
The ninth chapter deals with global optimization, i.e. meth- R S v 1 w problems that are often encountered in applications.
ods for finding a global extremum in an optimization prob- The book is divided into three main parts with 11 chapters.
lem. The several available approaches to this difficult task Each chapter starts with a summary of its contents.
are discussed, in particular, partition and search as a gener- Following the lines of the authors a short review of the
alization of branch-and-bound methods, approximation and contents of these three parts is given below.
search, generating random directions, and techniques for improving Part A, "Introduction and Basic Techniques" (chapters I-IV), deals with
local optima. the main classes of globaloptimization problems and develops some of their
The tenth chapter deals with optimization problems having more than one
objective function. Starting from a survey of useful results on binary rela-
tions, the chapter introduces a variety of approaches drawn from multi-
objective optimization, including goal programming, interactive methods,
utility functions, and special simplex methods for the linear case.
by R. Horst and H. Tuy
The concern of this excellent book is to consider the global optimization
problems for which standard nonlinear programming techniques fail be-
cause of the existence of local minima that are not global. These global
optimization problems are called multiextremal global optimization prob-
lems. The authors emphasize that the solution methods for the multiextremal
global optimization have to be significantly different from standard
nonlinear programming techniques which can at most locate local minima
and cannot decide whether a local solution is global. For these reasons they
provide useful tools for transcending local optimality restrictions. Particu-
larly important is special emphasis placed on the systematical clarification
and unification of various approaches for solving global optimization prob-
lems. Such various approaches and a large number of algorithms are the
consequences of the recent rapid expansion in computer technology.
First of all, this original and interesting book gives a survey of the most
important methods and results in the theory and practice of global optimi-
zation. Moreover, authors provide many of their own new results. Several
methods are interpreted as applications and combinations of certain recent
basic approaches serving as suggestions for the development of new pro-
cedures. The book also presents the state of the art in certain deterministic
basic properties and applications. Some fundamental concepts thatunify the
various general methods of solutions such as outer approximation, concav-
ity and branch and bound are reviewed there.
A thorough study of methods for solving concave minimization problems
and some related problems having reverse convex constraints is the topic
of Part B, "Concave Minimization" (chapters V-IX). Three main categories
of the methods for concave minimization cutting methods, successive
approximation methods and successive partition methods are studied in
detail in this part. The authors emphasize the fact that cutting planes play
a dominant role in cutting methods. Relaxation and restriction are the main
aspects of successive approximation, and branch and bound concepts usu-
ally serve as a framework for successive partition. Moreover, they also
discuss decomposition approaches to large scale problems and specialized
methods adapted to problems with a particular structure such as quadratic
problems, separable problems, bilinear programming, complementarity
problems and concave network problems.
Part C, "General Nonlinear Problems" (chapters X-XI), concentrates on the
study of methods of solution for very general global optimization problems.
Severalouter approximation algorithms, branch and bound procedures and
their combinations are developed for solving d.c. programming (d.c. is an
abbreviation for the difference of two convex functions) and Lipschitzian
optimization problems. Finally, the authors discuss many interesting appli-
In summary, the motivation and the presentation of the topics are of excel-
lent clarity. Thus this book could be highly recommended for research in
global optimization as well as for engineers having to solve practical
multiextremal optimization problems. It is of interest to students and re-
~I ~ I
Vol. 50, No. 2
A. Griewank, "The Global Convergence of
Partitioned BFGS on Problems with Convex
Decompositions and Lipschitzian
A.R. Conn, N.I.M. Gould and Ph.L. Toint,
"Convergence of Quasi-Newton Matrices
Generated by the Symmetric Rank One
W. Romisch and R. Schultz, "Distribution
Sensitivity in Stochastic Programming."
J.A. Filar, T.A. Schultz, F. Thuijsman and
O.J. Vrieze, "Nonlinear Programming and
Stationary Equilibria in Stochastic Games."
Y. Ye, "An O(n3L) Potential Reduction
Algorithm for Linear Programming."
R. Horst, N.V. Thoai and H.P. Benson,
"Concave Minimization via Conical
Partitions and Polyhedral Outer
Vol. 50, No. 3
A.V. Goldberg, M.D. Grigoriadis and R.E.
Tarjan, "Use of Dynamic Trees in a Net-
work Simplex Algorithm for the Maximum
D.A. Bayer and J.C. Lagarias, "Karmarkar's
Linear Programming Algorithm and
M. Kojima, S. Mizuno and A. Yoshise,
"An 0(4nL) Iteration Potential Reduction
Algorithm for Linear Complementarity
A. Lent and Y. Censor, "The Primal-Dual
Algorithm as a Constraint-Set-Manipula-
M.C. Ferris, "Finite Termination of the
Proximal Point Algorithm."
A. Dekkers and E. Aarts, "Global Optimi-
zation and Simulated Annealing."
I. Pitowsky, "Correlation Polytopes:
Their Geometry and Complexity."
Vol. 51, No. I
B.C. Eaves, A.J. Hoffman and H. Hu,
"Linear Programming with Spheres and
Hemispheres of Objective Vectors."
D. Goldfarb and D. Xiao, "A Primal
Objective Interior Point Method for Linear
K. Paparrizos, "A Feasible (Exterior Point)
Simplex Algorithm for Assignment
J.R. Brown, "Solving Knapsack Sharing
Problems with General Tradeoff Functions."
H. Yabe and T. Takahashi, "Factorized
Quasi-Newton Methods for Nonlinear Least
J-S. Pang, "A B-Differentiable Equation-
Based, Globally and Locally Quadratically
Convergent Algorithm for Nonlinear
Programs: Complementarity and Varia-
tional Inequality Problems."
M. Werman and D. Magagnosc, "The
Relationship Between Integer and Real
Solutions of Constrained Convex
I~AGE 11 number thirty-four JULY 1991
Jon Lee (OR Department, Yale)
will spend the 1991-92 academic
year at CORE. I Clyde Monma
has been promoted to division
manager of Bellcore's mathemat-
ics, information sciences and
operations research division.
IPatrick Harker has become the
youngest faculty member in
Wharton's history to achieve the
rank of professor. He has also
been named a White House
Fellow by President Bush for the
period September 1991-August
1992. 'cDadline for the next
OPTIMA is October 1, 1991.
Books for review should be
sent to the Book Review Editor,
Prof. Dr. Achim Bachem,
Mathematiches Institute der
Universitiit zu K6ln,
Weyertal 86-90, D-5000 Koln,
Journal contents are subject
to change by the publisher.
Donald W. Hearn, EDITOR
Achim Bachem, ASSOCIATE EDITOR
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