Title: Optima
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Permanent Link: http://ufdc.ufl.edu/UF00090046/00020
 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: December 1986
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Bibliographic ID: UF00090046
Volume ID: VID00020
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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13 th International Symposium on
Mathematical Programming

Chuo University
Tokyo, Japan
August 29 September 2, 1988

HE International Symposium
Son Mathematical Programming
is the triennial scientific
meeting of the Mathematical
Programming Society. The 13th
Symposium will be held at Korakuen
Campus, Chuo University, Tokyo,
Japan. Participation is open.
The meeting will offer contrib-
ted as well as invited papers. Each
contributed paper will be presented in
about twenty minutes. Special sessions
including Kantorovich and Beale
memorial sessions will be organized.
State-of-the-art tutorials are
planned, in addition.
Sessions on the following topics
will be organized:
" Linear Programming
" Integer Programming and
Combinatorial Optimization
L Optimization on Graphs, Net-
works and Matroids
L Nonlinear and Nondifferentiable
" Nonconvex and Global
U Large Scale Systems in
Mathematical Programming
O Dynamic Programming and
Optimal Control
L Stochastic Programming and
Optimization under Uncertainty
U Complementarity and Fixed Point
Game Theory
] Multicriterion Optimization
D Computational Complexity
l Heuristics
0 Parallel Computation in
Mathematical Programming

L Implementation and Evaluation
of Algorithms and Softwares
o Mathematical Programming on
Personal Computers
0 Teaching of Mathematical
O Applications of Mathematical
Programming in Economic
Planning, Management,
Engineering, Finance, Policy
Science, Transportation, Energy,
Agriculture, Artificial
Intelligence, Computational
Geometry, VLSI Design, etc.

Papers on all theoretical, comp-
utational and applied aspects of
mathematical programming are
welcome. The presentation of very
recent results is encouraged.
Those who want to present a paper
are invited to submit a title by March
The deadline for abstracts and
registration is May 1,1988.
Notification of acceptance will be
by July 1, 1988.
The Chairman of the local
organizing committee is IRI Masao
(University of Tokyo), and the Vice-
Chairmen are: TONE Kaoru (Saitama
University) and KONNO Hiroshi
(Tokyo Institute of Technology). The
Committee is organized within the
Operations Research Society of Japan.
The Symposium will be
cosponsored by a number of academic
societies, international and domestic,
including IFORS (International
Federation of Operational Research

Societies), APORS (Association of
Asian-Pacific Operational Research
Societies), etc.
Information regarding the sym-
posium will be sent to all those who
have responded to the announcement.
For further information contact:
Organizing Committee for the
13th International Symposium on
Mathematical Programming
c/o The Operations Research Society
of Japan
Gakkai-Center Bldg.
2-4-16 Yayoi, Bunkyo-ku
Tokyo 113, Japan.
-Takao Asano

number 20

List of contents

BOOK REVIEWS/ pages 6-9
CALENDAR/ page 11



PArE 2........ O

Parallel Optimization on
Novel Computer Architectures

The Annals of Operations Research
is planning the publication of a
special Volume on "Parallel
Optimization on Novel Computer
Architectures." The purpose of this
volume is to collect together papers of
high quality on the state-of-the-art
research, implementation and use of
optimization algorithms on parallel
computer architectures. Some
appropriate topics include: parallel
algorithms and their implementation
on novel computer architectures,
numerical optimization on super-
computers and other parallel computer
systems, data structures for parallel
optimization algorithms, and the use
of parallel and vector computers in
expanding the scope of mathematical
programming applications in opera-
tions research.
Authors are invited to submit
contributions by February 28, 1987. For
further information contact Stavros A.
Zenios, Decision Sciences, The
Wharton School, University of
Pennsylvania, Philadelphia, PA
19104, (215) 898-6727 or send electronic
mail to zenios@wharton-10.arpa.
All papers will be refereed, and
there will be no page changes.
-S. Zenios

Fourth EURO
Summer Institute
EURO: The Association
of European Operational
Research Societies
within I.F.O.R.S.
Theme for 1987:
Systems Science
Turku, Finland
June 5 July 21,1987

Admittance is limited to 20
promising young scientists from
European countries. Each participant
will present a research paper on
systems science. There will be invited
lectures, seminars and other research
activities. Papers for a special issue of
EJOR (European Journal of
Operational Research) will be
prepared during the summer institute.
Applicants should send their
curriculum vitae together with an
unpublished paper in the field of
systems science to their national O.R.
Society. These societies will select
their national candidates and submit
them before March 1, 1987, to the
coordinator of the Fourth EURO
Summer Institute. The final choice of
the 20 participants will be made by
the scientific committee.

Peter L. Hammer Honored by Swiss Institute
of Technology Lausanne

Dr. Peter L. Hammer, Director of RUTCOR Rutgers University's Center for
Operations Research at New Brunswick, N.J., was recently awarded the title of
DOCTEUR ES SCIENCES HONORS CAUSA by the Swiss Federal Institute of
Technology in Lausanne. The citation for the award reads:
"In recognition of the dynamic researcher whose fundamental work in discrete
mathematics has revealed profound connections between logic, computer science
and operations research."
-C. Riescher

Ninth Symposium on
Mathematical Programming
With Data Perturbations
The George Washington
Washington, D.C.
May 21-22, 1987

A Ninth Symposium on Math-
ematical Programming with Data
Perturbations will be held at The
George Washington University's
Marvin Center on May 21-22,1987.
Contributed papers in mathemat-
ical programming are solicited in the
following areas: Sensitivity and
stability analysis results and their
applications; Solution methods for
problems involving implicitly defined
problem functions; Solution methods
for problems involving deterministic
or stochastic parameter changes; and
solution approximation techniques an
error analysis.
"Clinical" presentations that
describe problems in sensitivity or
stability analysis encountered in
applications are also invited.
Approximately 30 minutes will be
allocated for the presentation of each
Abstracts should provide a good
technical summary of key results,
avoid the use of mathematical
symbols and references, not exceed 500
words, and include a title and the
name and full mailing address of each
author. The deadline for submission of
abstracts is March 13, 1987. They
should be sent in triplicate to Professor
Anthony V. Fiacco, Department of
Operations Research and the Institute
for Management Science and
Engineering, School of Engineering and
Applied Science, The George
Washington University, Washington
D.C. 20052, Phone: (202) 676-7511.
-Anthony V. Fiacco



0 P TI M A number twenty


Confrenc OTMnmrteDeMER

Martin Beale Memorial

A symposium will be held at the
Royal Society, London, July 6 8, 1987,
in memory of Professor E.M.L. Beale,
sponsored by Imperial College, the
Institute of Mathematics and its
Applications, the Institute of Stat-
isticians, the Mathematical Pro-
gramming Society, the Operational
Research Society, the Royal
Statistical Society, and Scicon
Limited. He was active in all of these
organizations, and their span reflects
not only the breadth of his interests
but also that his achievements ranged
from academic research to real
applications. Much of his career was
motivated by the needs of commerce
and industry; his learned contributions
extended greatly the range of real
problems that can be solved; and he
was highly successful at applying
computer calculations to investigate
mathematical models. The aim of the
symposium is to consider such work,
particularly the interactions between
its various parts.
The invited speakers include: K.C.
Bowen (Royal Holloway College),
G.B. Dantzig (Stanford University),
P.J. Green (University of Durham), P.
Hughes (Logica plc), A. Orden
(University of Chicago), B.D. Ripley
(University of Strathclyde), J.A.
Tomlin (Ketron Inc.), and A.N. Other.
Further, S. Vajda (University of
Sussex) will be the after-dinner
speaker. A number of submitted papers
will also be accepted. The invited
papers will be addressed to all
participants, but the contributed ones
may be specialized, as they will be
presented in parallel sessions and will
be allocated only 25 minutes each
including discussion. If you wish to
contribute a paper, you are invited to
send a summary of about 500 words to
Mrs. B.A. Peberdy (Scicon Limited,
)Vavendon Tower, Wavendon, Milton
Keynes MK17 8LX, England) to arrive
no later than March 1, 1987; not more
than 36 submitted contributions can be
included in the programme.

NATO Advanced Research
Workshop-COAL '87
Algorithms and Model
Formulations in Mathematical
Chr. Michelsen Institute
Bergen, Norway
June 15-19, 1987

The 1987 conference of the
Committee on Algorithms of The
Mathematical Programming Society is
being organized by Chr. Michelsen
Institute and The Department of
Informatics at the University of
Authors are invited to submit
extended abstracts (one page) on recent
advances that combine algorithmic
and modeling aspects of one or more of
the following subject areas: Linear
programming, stochastic program-
ming, network flows, integer
programming and combinatorial
optimization. Papers expressing
viewpoints on the current state and
future development of these subjects
are also welcome.
Deadline for extended abstracts is
February 1, 1987. They should be sent
to Dr. Stein W. Wallace, COAL-87,
Chr. Michelsen Institute, N-5036
FONTOFT-Bergen, Norway.
-S. Wallace

NATO Advanced Study
Mathematical Models for
Decision Support
Val d'Isere, Haute Savoie
July 26 August 6, 1987

The aim of the Advanced Study
Institute is to bring together scientists
working in the fields of Mathematical
Programming, Fuzzy Reasoning,
Relational Data Models and Multi-
Attribute Decision Making to identify
recent research results.
The major focus of the Institute is to
create a better understanding of
mathematical formulation of decision
problems and to develop a framework
for constructing decision support aids
which incorporate software tools,
mathematical models and human
Please send abstracts by March 31,
1987, or requests for further in-
formation to:
Dr. Gautam Mitra, Department of
Mathematics and Statistics, Brunel
University, Kingston Lane, Uxbridge,
Middlesex. U.K. Tel: 0895-74000, ext,
2476/2276/2896. Telex 261173 G.
-G. Mitra

SIAM Conference on Optimization
Houston, Texas
May 18-20, 1987

This is a conference on the state-of-the-art in practical optimization
methods. Topics include The Karmarkar algorithm for linear programming,
general optimization with linear constraints, general optimization with
nonlinear constraints, global optimization methods and parallel optimization
This conference will be proceeded by a short course on Numerical
Optimization on May 17,1987.
For information, contact:
SIAM Conference Coordinator
14th Floor
117 South 17th Street
Philadelphia, PA 19103-5052
Telephone: (215) 564-2929

~ ~


0 P TI M A number twenty


*s Technical Reports & Working Papers o

Cornell University
School of Operations Research and Industrial Engineering
Upson Hall
Ithaca,NY 14853

P. Jackson and R. Roundy, "Constructive Algorithms for
Planning Production in Multi-Stage Systems with Stationary
Demand," TR 632.
J. Muckstadt, "Planning Component Delivery Intervals in
Constrained Assembly Systems," TR 633.
P. Jackson and J. Muckstadt, "Risk Pooling in a Two-Period,
Two-Echelon Inventory Stocking and Allocation Problem," TR 634.
M. Taqqu and W. Willinger, "A Geometric Approach to
Constructing Martingale Measures: The Finite Case," TR 635.
M.Taqqu and W. Willinger, "The Analysis of Finite Security
Markets Using Martingales," TR 636.
D. Crystal, "Tag Systems: A Combinatorial Abstraction of
Integral Dependence," TR 637.
P. Carvalho and L. Trotter, "An Abstract Linear Duality
Model," TR 638.
R. Bechhofer and D. Goldsman, "On the Ramey-Alam
Sequential Procedure for Selecting the Multinomial Event Which
Has the Largest Probability," TR 639.
R. Bechhofer and D. Goldsman, "Truncation of the Bechhofer-
Kiefer-Sobel Sequential Procedure for Selecting the Multinomial
Event Which Has the Largest Probability," TR 640.
A. Chatterjee, M. Cohen, W. Maxwell and L. Miller,
"Manufacturing Flexibility: Models and Measurements," TR 641.
R. Roundy, "A 98%-Effective Lot Sizing Rule for a Multi-
Product, Multi-Stage Production/Inventory System," TR 642.
F. Avram and M. Taqqu, "Generalized Powers of Strongly
Dependent Random Variables," TR 643.
M. Taqqu and C. Czado, "Reproducing Kernel Hilbert Space
for Some Non-Gaussian Processes," TR 644.
D. Duffy and T.J. Santner, "Confidence Intervals for a
Binomial Parameter Based on Multistage Tests," TR 645.
J. Muckstadt and R. Roundy, "Planning Shipping Intervals in
Multi-Item, One-Warehouse, Multi-Retailer Distribution
Systems," TR 646.
J. Muckstadt ,"The Effects of a Biased Estimate of Demand on
Inventory Levels and Customer Service," TR 647.
M. Todd and B. Burrell, "An Extension of Karmarkar's
Algorithm for Linear Programming Using Dual Variables," TR
M. Johnson, "An Analysis of Optimal Production Plans for
Sample GM Component Manufacture Using the MAXSTADT
Planning Package," TR 649.
P. Carvalho, "Discrete Linear Duality," TR 650.

J. Yan, "Graphic Greedoids and Their Duals," TR 651.
J. Yan, "Greedoid Polyhedra," TR 652.
Y. Ikura and G.L. Nemhauser, "Computational Experience
with a Polynomial-Time Dual Simplex Algorithm for the
Transportation Problem," TR 653.
P. Sanchez, "Significant Factor Identification Using Discrete
Spectral Methods," TR 654.
D. Heath and R. Jarrow, "Ex-dividend Stock Price Behavior
and Arbitrage Opportunities," TR 655.
H. Taylor and B. Rodriguez, "Optimal Replacement for Fault
Tolerant Systems," TR 656.
D. Heath, S. Orey, V. Pestien and W. Sudderth, "Minimizing
or Maximizing the Expected Time to Reach Zero," TR 657.
L. Schruben and V. Cogliano, "Frequency Domain
Experiments: Spectral Amplification, Input-Output Correlations
and Model Parameters," TR 658.
W.L. Maxwell, P. Jackson, J. Muckstadt and R. Roundy,
"Production-Distribution Systems Inventory Planning (SIP):
Rationale, Economic and Realities," TR 659.
J.-F. Claver and W.L. Maxwell, "Throughput Analysis of
Closed Loop Material Handling Systems: Deterministic Case,"
TR 660.
R. Bland and D. Jensen, "On the Computational Behavior of a
Polynomial-Time Network Flow Algorithm," TR 661.
T. Santner and D. Duffy, "A Note on Albert and Anderson's
Conditions for the Existence of Maximum Likelihood Estimates
in Logistics Regression Models," TR 662.
R. Roundy, "Rounding Off to Powers of Two in the Economic
Lot Scheduling Problem," TR 663.
D. Heath and P. Sanchez, "On the Adequacy of Pseudo-
Random Number Generators," TR 664.
N.U. Prabhu, "A Class of Ruin Problems," TR 665.
N.U. Prabhu, "Probability Modeling Across the Continents,"
TR 666.
R. Bland, "A Class of Production Planning Problems Solvable
by Network Flows," TR 667.
T.R. McConnell and M. Taqqu, "Dyadic Approximation of
Double Integrals with Respect to Symmetric Stable Processes,"
TR 668.
L. Schruben and V. Cogliano, "An Experimental Procedure for
Simulation Response Surface Model Identification," TR 669.
B. Bhaskaran, "Almost Sure Ordering of Some Continuous
Time Stochastic Processes with Applications," TR 670.


0 P TI M A number twenty


PAGE 5 OPTIMA number twenty DECEMBER 1986

Faculty of Mathematical Studies Washington State University
University of Southampton Department of Pure and Applied Mathematics
Southampton S09 5NH UK Pullman, Washington 99164-2930

V. de Senna and A.K. Shahani, "A Single Inspection Policy for R. Mifflin and J. -J. Strodiot, "A Rapidly Convergent Five Point
the Detection of Failure," No. 107. Algorithm for Univariate Minimization."
H.P. Williams, "Fourier's Method of Linear Programming R. Mifflin, "Concepts of Better Than Linear Convergence in
and its Dual," No. 118. Nonsmooth Minimization."
V. de Senna and A.K. Shahani, "Inspection for the Detection R. Mifflin and J.-J. Strodiot, "A Safeguard Bracketing
of Failure," No. OR1. Techniquefor Obtaining Convergene and Preserving Rapid
V. de Senna and A.K. Shahani, "Age of Onset of Breast T e fr O C a P
Cancer," No. OR2. Convergence in Univariate Minimization.
H.P. Williams, "Invited Survey Presented at NATO
Advanced Study Institute on Computational Mathematical
Programming, Bad Windsheim, West Germany," No. OR3.
H.P. Williams, "Evolution, Game Theory and Polyhedra," No.
S.M. Lewis, A.G. Munford and A.K. Shahani, "Detection of
Failure in the Weibull Case," No. OR5.
A.K. Shahani and V. de Senna, "Two-Test Scheme for the
Detection of Failure," NO. OR6.
H.P. Williams, "Linear and Integer Programming Applied to
Artificial Intelligence," No. OR7.

So- Journals & Studies *

Volume 36, No. 2 I. Diener, "Trajectory Nets Connecting all Critical Points of a
Smooth Function."
A. Sego, "Finding the t- join Structure of Graphs." M.D. Troutt, "A Stability Concept for Matrix Game Optimal
D. Du, and X. Zhang, "A Convergence Theorem of Rosen's Strategies and its Application to Linear Programming Sensitivity
Gradient Projection Method." Analysis.
D. Salane, "Symmetric Minimum-Norm Updates for Use in
Gibbs Free Energy Calculations."
F. Barahona and A. Mahjoub, "On the Cut Polytope."
E. Barnes, "A Variation on Karmarkar's Algorithm for Solving Mathematical Programming Study
Linear Programming Problems." Nonlinear Analysis and Optimization
P. Gill, W. Murray, M. Saunders, J. Tomlin, M. Wright, "On Edited by B. Comet, V.H. Nguyen and J.P. Vial
Projected Newton Barrier Methods for Linear Programming and
an Equivalence to Karmarkar's Projected Method." Y. Chabrillac and J.-P. Crouzeix, "Continuity and
A. Premoli, "Piecewise-Linear Programming: The Compact Differentiability Properties of Monotone Real Functions of
(CPLP) Algorithm." Several Real Variables."
W. Cunningham and J. Green-Krotki, "Dominants and B. Comet, "Regularity Properties of Open Tangent Cones."
Submissives of Matching Polyhedra." G. Haddad, "The Role of Tangent and Normal Cones in the
Viability Theory of Inclusion."
S.M. Robinson, "Local Structure of Feasible Sets in Nonlinear
Volume 36, No. 3 Programming, Part III: Stability and Sensitivity."
B. Gollan, "Eigenvalue Perturbations and Nonlinear
C. McDiarmid, "On the Greedy Algorithm with Random Parametric Optimization."
Costs." J.P. Bulteau and J.P. Vial, "Curvilinear Path and Trust Regions
A.G. Buckley, "Long Vectors for Quasi-Newton Updates." in Unconstrained Optimization: A Convergence Analysis."
S.C. Fang, "Controlled Perturbations for Quadratically A. Auslender, "Numerical Methods for Nondifferentiable
"onstrained Quadratic Programs." Convex Optimization."
J Ph. L. Toint, "Global Convergence of the Partitioned BFGS A. Bihain, V.H. Nguyen and J.-J. Strodiot, "A Reduced
Algorithm for Convex Partially Separable Optimization." Subgradient Algorithm."
M. A. Duran and I.E. Grossmann, "An Outer-Approximation H. Tuy, "Global Minimization of a Difference of Two Convex
Algorithm for a Class of Mixed-Integer Nonlinear Programs." Functions."

PAE6OTIAnme tet ECME18


Network Flows and Monotropic Optimization
By R.T. Rockafellar
John Wiley, New York, 1984
ISBN 0-471-88078-7

Flows in networks form a class of mathematical programming
problems in which duality plays a central role in computation,
theory and interpretation. Starting from flows and potentials in
networks, the author unfolds the underlying combinatorial
structures and convexity properties and shows that these notions
govern a much broader area of mathematical programming,
including linear programming and problems where a
preseparable convex function is minimized subject to linear
constraints. (A convex function is called preseparable if it is the
sum of linear functions composed of convex functions of a single
variable.) He calls this latter optimization problem "monotropic
programming problem," since convex functions of a single
variable vary in one direction only.
The main objective of this book is to forge theoretical links
between problems and procedures that might seem quite
different at first glance, namely network programming, linear
programming and its generalization to oriented real matroids as
well as monotropic programming in its general form. As by-
products many contributions to classical fields and beyond are
presented, for example, a thorough treatment of network flow
problems with nonlinear costs as well as extensions of the simplex
method and of the out-of-kilter method to general piecewise
linear programming. Further, the theory of conjugate convex
functions is developed in a constructive manner with numerous
examples and applications.
The book is organized into eleven chapters: 1. Networks; 2..
Paths and Cuts; 3. Flows and Capacities; 4. Analysis of Flows; 5.
Matching Theory and Assignment Problems; 6. Potentials and
Spans; 7. Networks with Linear Costs; 8. Optimal Flows and

Potentials; 9. Algorithms for Convex Costs; 10. Linear Systems of
Variables and 11. Monotropic Programming.
Every chapter contains exercises (with additional material)
and ends with supplementary comments and references. This
clearly and well-written monograph will serve as an important
contribution which reveals common structures in mathematical
programming governed by duality.
-R. Burkar

Discrete Computational Structures
By R. Korfhage
Academic Press, London, 1983
ISBN 0-12-420860-6

Anyone writing an introductory text for a mathematics or
computer science class is in a dilemma: Is it better to restrict
interest to a small number of topics and study them in depth or to
deal with many themes superficially to keep the book portable?
This book is of the second kind, but it avoids tedious
sequences of definitions. The dilemma mentioned above is
reflected by the fact that some of the (algebraic) chapters in the
first edition have been replaced in this second edition by
chapters treating more current topics and that the word
"polynomial" occurs nowhere in the book in an algebraic context.
The first part presents numerous algebraic structures
together with their machine realizations. The author makes clear
by several examples how much the efficiency of some
manipulations may depend on the particular representations of
the data.
The second part of the volume is devoted to the foundations
of computability and logic and contains introductions to
automata and formal language theory, Boolean algebra, and
propositional and predicate calculus.
The author's style is fluent and readable. The text is nearly
free of formal argument. The main work is relegated to the



OPTIMA number twenty


A~E OTI Anubr wetyDCEBE 18

exercises, many of which are solved in an appendix.
The book makes evident what mathematics and computer
science can do for one another and should therefore motivate
both mathematics and computer science students to examine
interesting topics in detail. However, this is prevented by the poor
reference lists at the end of each chapter.
-Roman K6nig

The Equivalence of Some Combinatorial
Tiatching Theorems
By P.F. Reichmeider
Polygonal Publishing House, Washington, 1985
ISBN 0-936428-09-0

In this work the author explores a set of classical results in
ombinatorics the theorems by Hall, K6nig, Dilworth, Menger
and Ford and Fulkerson which are typically called matching
theorems. A number of (different) proofs, the historical and the
most elegant ones, are presented.
Of course, the results are not new. On the contrary, these
theorems appear in every first course on combinatorics and
graphs. Yet, the primary interest and the value of this book is the
comprehensive discussion of the relationships that exist between
them. Even the fact that these theorems have equivalencies is
well known, and proofs that two specific candidates are related
could be located in the literature. However, what makes this
booklet a nice and welcome contribution is the organisation of
this deep relationship into one compact and really appetizing
-U. Derigs

Linear Programming:
Active Set Analysis and Computer Programs
By M.J. Best and K. Ritter
Prentice Hall, Hemel Hempstead, 1985
ISBN 13-536996-7

In the preface the authors state: "The essential idea of a
solution method for a linear programming problem is to move
om one extreme point of the feasible region to an adjacent one
.n such a way as to improve the objective function value. In
virtually any presentation of the subject, this is illustrated by
graphical examples. Our method of presentation is new in that it

is based on a direct generalization of this geometric notion." This
generalization is the active set analysis.
Although computationally equivalent to the simplex method,
active set analysis provides a clearer understanding of the
mechanics of the method and as such it is a valuable educational
Combined with the very nice printing, the readable style of
writing, a good choice of more advanced topics (GUB, parametric
programming, Bland's rule) and some nice descriptions of
models for applications, there is ample opportunity for
recommendation of this volume. But I have doubts on two points:
First, who is the intended audience? This book is certainly not
intended for either users (too technical) or researchers (too
simple) of LP. Also, in my opinion, business and engineering
students are far better off with a textbook that stresses model
formulations and use of input for and output from LP software,
instead of algorithmic details. The only group for which the text
might be suitable is undergraduate students of mathematics. But
for them I would certainly hope an additional textbook is used to
illustrate what one can do with LP.
Second, one third of the book is an appendix, listing the
computer programs (FORTRAN) of the algorithms described.
While the presentation of the programs is well done (more
comments could be inserted in the coding), its relevance and use
are limited at best. Who copies his own LP codes? Who studies
LP coding in a textbook? I would be surprised if more than a
handful of readers do so.
It seems to have grown into a habit to include listings of
computer programs in a textbook. However, if the programs do
not form an integral part of the course in which the book is used,
they only serve to show that the author can write a computer
In summary, Best and Ritter have produced a good looking
textbook with a nice educational starting point, of which the last
one third is virtually useless and for which the audience is limited.
-J. Telgen




OPTIM A number twenty



OPTIMA number twenty

Integer Programming and Related Areas:
A Classified Bibliography 1981-1984
Lecture Notes No. 243
Edited by R.v. Randow
Springer, Berlin, 1985

This book constitutes the fourth volume of the bibliography
on integer programming and related areas. It covers the following
subjects: theory and methods of general integer programming,
combinatorial and graph-theoretical optimization problems
related to integer programming, and applications of integer
The structure of this volume is much the same as that of the
previous ones. In Part 1 the publications are listed alphabetically
by the first author together with a reference code allowing the
user to identify them. Part 2 is a subject classification with 50 main
subject headings. Part 3 is an alphabetical catalogue of all
authors. The period from mid-1981 to autumn 1984 is covered.
There are 4751 new publications by 3690 authors.
The first three volumes have already proven to be very useful
for anyone working in this field, and it is without any doubt that
this fourth volume will continue to serve as an easy-to-handle and
comprehensive survey of all publications appearing in the field of
integer programming.
-Reinhardt Euler

Linear and Nonlinear Programming
By David G. Luenberger
Addison Wesley, Amsterdam, 1984
ISBN 0-201-15794-2

This is a second edition of the popular book first published in
1973 and notable for being well written and clearly explained. It is
divided into 3 parts.
Part 1 is a self-contained introduction to Linear Programming,
including chapters of Basic Properties, The Simplex Method,
Duality, and Transportation and Network Flow Problems. Part II
covers optimality conditions and algorithms for Unconstrained
Optimization and includes chapters on Basic Properties, Descent
Methods, Conjugate Direction Methods and Quasi-Newton
Methods. Part III extends these ideas to cover Constrained
Optimization, with chapters on Optimality Conditions, Primal
Methods, Penalty and Barrier Methods, Dual and Cutting Plane

Methods, and Lagrange Methods. There are appendices
covering various aspects of mathematical notation, convex
analysis and linear algebra. Each chapter is augmented by
exercises which both illustrate and extend the material in the text
and also by a brief literature survey of relevant references. The
book is in hard cover and is very well produced and set out. Bold
face is used for vector notation.
The material that has been newly introduced in the second
edition includes the section on transportation and network flow in
Part 1. In Part III many of the important developments in
nonlinear programming over the last ten years have been
incorporated into several new sections and a new chapter on
Lagrange methods. Finally, more explanation and applications
exercises have been added to various parts of the book.
The chapter of Transportation and Network Flow is a
welcome addition to Part I which now provides a conventional b '
wide-ranging treatment of linear programming. My mal
criticism of this section is that degeneracy is almost entirely
neglected, apart from an exercise on Bland's rules, which will
tend to perpetuate the point of view that degeneracy is
unimportant in practice misguided in my opinion. Nothing is
mentioned of recent developments in ellipsoid algorithms.
Part II of the book shows its age in that it was largely
conceived in the "DFP era" before the BFGS method attained its
current pre-eminence. The merits of the BFGS method are not
sufficiently stressed, and the advantages of self-scaling methods
are over stated. Nothing is said about developments in trust
region methods, apart from a brief mention of the Levenberg-
Marquardt method. The book also lacks any treatment of the
practically important subject of nonlinear least squares and the
Gauss-Newton method.
Part III has now become something of a hotch-potch of
numerous methods, new and old, for solving nonlinear
programming problems. Perhaps this is inevitable in view of the
uncertain state of the art in this area. The book does say
something about important new subjects such as 11 exact penalty
functions and sequential quadratic programming. However, I feel
that the treatment of quadratic programming itself is unduly
brief. Other subjects whose absence I noted included geometric
programming, integer programming and any general treatment
of nonsmooth optimization.
Overall however, I am sure that the book will continue to sr
well and provide a useful basis for student courses at va.rioG
-R. Fletcher

I~I _Is~l~C_ ~s~ ~I~ _I_ ~I~



1~AGE OPIM nubrt t DEEBE18

Topics on Perfect Graphs
By C. Berge and V. Chvatal
North-Holland, Amsterdam, 1984
ISBN 0-444-86587-X

This book, published in 1984, on the 25th anniversary of
perfect graphs, presents selected results on this topic in a single
volume. These are reprints of classical papers on this subject as
well as surveys and new results.
The editors divided the whole volume into several parts
according to different points of view or techniques polyhedrall
methods, optimization, purely graph theoretical approaches, etc.)
rather than ordering the various contributions chronologically.
Therefore, this book does not provide much insight into how the
field developed over the years (one can find a brief sketch of the
history of perfect graphs in the Introduction), but it does provide
m,! quite complete survey of the important body of work stimulated
by the perfect graph conjecture, leading up to the frontiers of
current research.
-W. Kern

Surveys in Combinatorics 1985
Edited by I. Anderson
London Math. Society, London, 1985
ISBN 0-521-31524-7

This book contains written versions of eight of the nine invited
lectures delivered at the tenth British Combinatorial Conference
held in Glasgow from July 22 26, 1985. The incredible speed at
which they were made available in book form is a tribute to the
efficiency of the publisher and (one suspects) to the ruthless
driving power of the editor. Perhaps this explains why one of the
nine lectures was not included.
The eight that made it in time make agreeable reading. The
OPTIMA public will probably derive most pleasure from the
contributions of G.R. Grimmett on various probabilistic models
for network and electrical flow, of A.J. Hoffman on greedy
algorithms that find the optimal solution, and of N. Robertson
and P.D. Seymour who survey their work on graph minors
including their impressive algorithmic results on the disjoint
fC'onnecting paths problem. In addition, G. Andrews discusses a
ew approach to a class of q-series originally studied by
Ramanujan; J. Beck (who recently received the Fulkerson Prize)
describes some of his beautiful work on the relations between

measure theoretic and combinatorial discrepancy theory; H.J.
Beker reviews adaptive algorithms for communication; J.H van
Lint discusses three open problems from coding theory and
C.St.J.A. Nash-Williams studies existence results for
detachments of graphs.
How useful are proceedings such as these? If at all, then only
if they are produced as quickly as these have been. All the
interesting new results contained here will surely find their way
into the regular journals. Undoubtedly, these journals would also
be delighted to publish authoritative surveys written by experts
such as those assembled on this occasion. So, unless proceedings
are set up to function completely like an introductory textbook,
they serve a very temporary purpose. With that in mind, we can
be grateful to lan Anderson for granting us this quick peek
behind the scenes of some very interesting current research.
-A.H.G. Rinnooy Kan

Mathematical Programming with Data
Perturbations I/II
Edited by A.V. Fiacco
Dekker, New York, 1982
ISBN 0-8247-1543-8/1789-9

The articles in these two volumes are based on papers
presented at the first Symposium on Mathematical Programming
with Data Perturbations. This symposium was held May 24 25,
1979, at the George Washington University and organized by A.V.
Fiacco and S.M. Robinson. The field of mathematical
optimization with data perturbations (also called parametric
optimization) has an increased importance for many topics (e.g.
stochastic optimization, multiobjective optimization, solution
procedures of nonlinear optimization, duality theory, ill-posed
optimization problems, model-building, approximation theory).
Furthermore, the theoretical and numerical results in parametric
optimization are often helpful for solving real-life practical
The reader will find a wide range of important and deep basic
results and applications in both volumes which can be
recommended to mathematicians who are in basic research
and/or applications in mathematical optimization.
-Jtrgen Guddat

-----s ~


OPTIMA number twenty


PAG 10 OPIAnmewnt EEBR18

Nominations for the

George B. Dantzig Prize being taken

This is a call for nominations for the George B.
Dantzig Prize which will be awarded at the annual
SIAM meeting in San Diego, July 18-22, 1988. The
prize is awarded for original work which, by its
breadth and scope, constitutes an outstanding
contribution to the field of mathematical pro-
gramming. The contributions eligible for
consideration are not restricted with respect to the
age or number of their authors, although preference
should be given to the singly-authored work of
"younger" people. The nomination for the award
will be presented by the Prize Committee (Olvi L.
Mangasarian, Chairman, George L. Nemhauser,
Katta G. Murty and Margaret H. Wright) to the

Executive Committees of the SIAM Council and of
the Mathematical Programming Society. Past
recipients of the George B. Dantzig Prize have been:
M.J.D. Powell and R.T. Rockafellar in 1982 and E.L.
Johnson and M.W. Padberg in 1985.
Please send your nominations by May 15, 1987 to
Olvi L. Mangasarian, Computer Sciences Depart-
ment, University of Wisconsin, 1210 West Dayton
Street, Madison, Wisconsin 53706, U.S.A.
Nominations should provide a brief one or two page
description of the nominee's outstanding con-
tributions and a current resume including a list of
-O.L. Mangasarian

Mail to:
c/o International Statistical Institute
428 Prinses Beatrixlaan
2270 AZ Voorburg, The Netherlands

Dues for 1986 include subscription to Vol. 34-36 of

Dues, payable to MPS, Inc., are Dfl. 125 (or $45, or Sw.Fr. 90,
or FF 340, or DM 112, or 28) for continuing members. For
1986, NEW MEMBERS pay ONE-HALF these rates.

Subscription to
is available to all members for Dfl. 45 (or $15, or Sw.Fr. 33,
or FF 120, or DM 40, or 10).
O I wish to enroll as a member of the Society. My
subscriptions) is (are) for personal use only and not for the
benefit of any library or institution.
E New Member?

I enclose payment as follows:
Dues for 1986
MP STUDIES 25 & 26

Name (printed)
Mailing address (please print)

Student Applications: Dues are one-half the above rates. Have
a faculty member verify your student status below and send
application with dues to the above address.
Faculty verifying status

_1_ ~

I~ _______~________e_____s___ _l__sl____l_____s_8_~

_ ~~ ~

O PTI M A number twenty



AGLII OPIM nunetet DECMBE 1986~ ______________

Maintained by the Mathematical Programming Society (MPS)

This Calendar lists noncommercial meet-
ings specializing in mathematical program-
ming or one of its subfields in the general
area of optimization and applications,
whether or not the Society is involved.
(The meetings are not necessarily 'open'.)
Anyone knowing of a meeting that should
be listed here is urged to inform Dr. Philip
Wolfe, IBM Research 33-2, POB 218,
Yorktown Heights, NY 10598, USA;
Telephone 914-945-1642, Telex 137456.
Some of these meetings are sponsored
by the Society as part of its world-wide
support of activity in mathematical
programming.Under certain guidelines
the Society can offer publicity, mailing
lists and labels, and the loan of money to
the organizers of a qualified meeting.
Substantial portions of meetings of other
societies such as SIAM, TIMS, and the
many national OR societies are devoted to
mathematical programming, and their
schedules should be consulted.

April 6-8: "CO87", a Conference on Combinatorial
Optimization, Southampton, U.K.
Contact: Dr. C.N. Potts, Faculty of Mathematical Studies,
University of Southampton, Southampton S09 5NH, United
Kingdom. (Sponsored by the London Mathematical Society.
Deadline for abstracts, 5 January 1987.)

May 18-20: SIAM Conference on Optimization, Houston, TX.
Contact SIAM, 14th Floor, 117 South 17th Street, Philadelphia,
PA. (215) 564-2929.

June 15-19: "COAL '87", NATO Workshop on Algorithms and
Model Formulations in Mathematical Programming, Bergen,
Norway. Contact: Dr. Stein Wallace, Chr Michelsen Institute,
N-5036, FONTOFT- Bergen, Norway.

July 6-8: Martin Beale Memorial Symposium, London, U.K.
Contact Professor MJ.D. Powell, Department of Applied
Mathematics and Theoretical Physics, University of Cambridge,
Silver Street, Cambridge (CB3 9EW, United Kingdom.
Telephone (0223) 337889, Telex 81240.

August 29 September 2: Thirteenth International
Symposium on Mathematical Programming in Tokyo, Japan.
Contact: Professor Masao Iri (Chairman, Organizing Committee),
Faculty of Engineering, University of Tokyo, Bunkyo-ku, Tokyo
113. Official triennial meeting of the MPS.

27 October 1986

_ ~ 1_11~ _~ _I~ I~


AGE 11

OPTIMA number twenty


Jan Karel Lenstra, Centre for Mathematics and Computer
Science, Amsterdam, is the new Chairman of the MPS
Executive Committee....The MPS Council now consists of:
Michel Balinski (Chairman), Alex Orden (Vice Chairman),
Al Williams (Treasurer), and the four members-at-large,
Martin Grotshcel, Karla Hoffman, Masao Iri, and Robert B.
Schnabel....IFORS XI will be held August 10 14, 1987 in
Buenos Aires, Argentina. Contact: M.E. Thomas, ISyE,
Georgia Tech., Atlanta, GA....OR Letters announces a
special software section. Contact: Harvey Greenberg,
Associate Editor, Math Department, Campus Box 170,
University of Colorado at Denver, Denver, CO 80202,
phone (303) 556-8464.....Donald Hearn (Florida) will be on
sabbatical at MIT (Sloan School) during 1987.

Deadline for the next O P T I M A is April 15, 1987.

Books for review should be
sent to the Book Review
Editor, Prof. Dr. Achim
Bachem, Mathematiches
Institute der Universitit
zu K61n, Weyertal 86-90,
D-5000 Kiln, West Germany.

Journal contents are subject
to change by the publisher.

Donald W. Hearn, Editor
Achim Bachem, Associate Editor
Published by the Mathematical
Programming Society and
Publication Services of the
College of Engineering,
University of Florida.
Composition by Lessie McKoy,
Graphics by Lise Drake.

303 Weil Hall
College of Engineering
University of Florida
Gainesville, Florida 32611


I -~ s -



OPTI M A number twenty

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