PTI MA
MATHEMATICAL PROGRAMMING SOCIETY NEWSLETTER
Number 15
May 1985
12th International Symposium on
Mathematical Programming Maclaurin Building at M.I.T.
The 12th International Symposium
on Mathematical Programming will be
held from August 5 to August 9 at MIT.
Over 600 papers on a wide range of
theoretical and applied topics have been
scheduled for presentation. The program
will contain sessions on all aspects of
mathematical programming and will in
clude speakers from more than 20
countries in North America, Europe,
South America, and Asia.
Distinguished researchers have been
invited to make onehour presentations
on topics of current interest in mathe
matical programming, including:
N. Christofides, "Vehicle Sched
ling andRouting."
R. Cottle, "On Linear Comple
mentarity Problems."
G. Dantzig, title to be announced.
A. Fiacco, "Stability and Sensitiv
ity Analysis in Nonlinear Programming."
JL. Goffin, "Recent Advances in
NonDifferentiable Optimization."
Y.C. Ho, "Stochastic Optimiza
tion. "
D. Johnson, "Optimization by
Simulated Annealing, "
N. Karmarkar, "Further Develop
ments in the New PolynomialTime
Algorithm for Linear Programming,"
A. Recski, "Applications of Ma
troid Theory. "
A. Rinnooy Kan, "Global Optimiza
tion. "
L. Schrage, "Mathematical Pro
gramming on Personal Computers."
L. Wolsey, "Recent Results in
Mixed Integer Programming Modeling"
In addition to the program of
research presentations, extensive com
puter demonstrations are being organized.
Accommodations for Symposium
participants are available either on the
MIT campus (at $30 to $34 per night) or
at nearby hotels in Cambridge and Boston
($80 to $86 per night, single or double
occupancy).
Among other events on the exciting
social calendar are a reception at the New
England Aquarium, a banquet at one of
Boston area's finest hotels, a New
England clambake dinner, harbor cruises,
historic and scenic tours, and much more.
To receive early registration ma
terials and other information or to
arrange to present a talk in one of the
topic areas, please contact the Sym
posium Secretary, Massachusetts Institute
of Technology, Operations Research
Center, Room E40164, Cambridge, MA
02139; telephone: 617/2533601.
Mathematical Programming
Society Announces Establishment
of the AW. Tucker Prize
The Mathematical Programming
Society has established the A.W. Tucker
Prize for an outstanding paper in mathe
matical programming authored by a
student. It will first be awarded at the
society's Thirteenth International Sym
posium (1988) and at the succeeding
symposia in this triennial series.
Professor Tucker's contributions to
the field have come in the form of out
standing and :.ndi inml research as well
as from his role as teacher, mentor, and
counselor. His students, either literally or
figuratively, have had a remarkably broad
and deep impact on mathematical pro
gramming. The entire field has prospered
from his stimulation and guidance.
Therefore, it is especially appropriate that
this prize be for student research.
All students, graduate or under
graduate, are :liiih1k. Nominations of stu
dents who have not yet received the first
university degree are especially welcome.
The finalists will be invited, but not
required, to give oral presentations at a
special session of the symposium.
The paper may concern any aspect
of mathematical programming; it may be
original research, an exposition or survey,
a report on computer routines and
computing experiments, or a presentation
of a new and ingenious application. The
paper must be solely authored and com
pleted since the beginning of the calendar
year in which the preceding Symposium
was held. The paper and the work on
which it is based should have been under
taken and completed in conjunction with
a degree program.
Nominations must be made in
writing to the chairman of the awards
committee by a faculty member at the
institution where the nominee was
studying for a degree when the paper
to page two
I Ils~ I~ _I I ~E~ ~I~
CONFERENCE NOTES
IFIP
Working Conference
Computational Issues in
Combinatorial Optimization
Capri, Italy
March 2428, 1986
The conference is promoted by the
IASI ( '.. (Institute of Systems \i.' i.
and Computer Science of the National
Research Council of Italy) and the
Department of Statistics and Operations
Research of the Graduate School of
Business Administration of New York
University and is sponsored by IFIP
TC7 (Technical Committee on Modelling
and Optimization). The conference will
be the first ..r,:ii:i.. meeting of a new
proposed IFIP working group on
"Discrete Optimization" and will take
place in the CNR conference center on
the island of Capri in Italy.
During this conference theoretical
and computational progress made to date
in combinatorial problem solving will be
discussed. Topics covered include:
integer and mixedinteger program
ming
algorithmic graph theory
polyhedral approaches to combina
torial optimization
empirical studies in combinatorial
problem solving
computational ..iirp1 .i'. of com
binatorial problems.
The principal speakers at this con
ference will include Egon Balas, Michel
Balinski, Claude Berge, Harlan Crowder,
Giorgio Gallo, Martin Grotschel, Peter
Hammer, Ellis Johnson, Bernhard Korte,
George Nemhauser, Manfred Padberg,
M.R. Rao, Paolo Toth, and Lawrence
Wolsey.
Attendance at the conference is
open, and interested researchers and
practitioners of combinatorial optimiza
tion are ....Ji.ll, invited to submit a
title and an extended abstract for con
sideration, by November 15, 1985
to:
Dr. ANTONIO SASSANO
IASICNR
Viale Manzoni, 30
00185 Rome, Italy
Authors will be notified of accep
tance by February 1, 1986. Due to
limited space at the conference site,
attendance is limited to 100 participants.
It is intended to publish conference
proceedings after due refereeing in a
series or journal of high standing.
A. Sassano
Mathematische Optimierung
Oberwolfach
January 612, 1985
The rapid development in recent
years of mathematical optimization as
part of applied mathematics is also re
:i.. i..l in the Oberwolfach meetings on
mathematical optimization, which have
become almost a tradition by now.
Organized by B. Korte (Bonn) and K.
Ritter (Miinchen), this year's conference
gathered researchers from 12 different
countries in the informal atmosphere of
Oberwolfach to discuss the results and
problems of the current state of the art.
The presentations covered the
whole spectrum of optimization theory.
The central motivation thereby derived
from the need to develop efficient solu
tion methods for nonlinear as well as
combinatorial optimization problems.
(More l1.r ii,.J information may be
obtained from the "Tagungsbericht" of
the Mathematisches Forschungsinstitut
Oi,. ..I,...i, which is available at all
scientific libraries.)
U. Faigle
Callfor Papers:
A Workshop on Global Optimiza
tion will be organized by the Interna
tional Institute for Applied Systems
Analysis (IIASA). It will be held in
Sopron, Hungary, the week of December
9, 1985. Those interested in contributing
should contact Alexander H.G. Rinnooy
Kan, Econometric Institute, P.O. Box
1738, 3000 DR Rotterdam, The Nether
lands, Phone: (10) 525511 ext. 3030.
Mathematical Programming Society Announces Establishment of the A. W. Tucker Prize ...from page one
was completed. Letters of nomination
must be accompanied by four copies
each of: the student's paper; a separate
summary of the paper's contributions,
written by the nominee and no more than
two pages in length; and a brief biograph
ical sketch of the nominee. The awards
committee may request additional in
formation. Nominations and the accom
panying documentation are due seven
months prior to the beginning of the
symposium and must be written in a
language acceptable to the awards com
mittee.
This committee will have four
members, including a chairman, all
appointed by the chairman of the society.
The members will serve staggered terms
covering two successive symposia, with
two members retiring after each sympos
ium.
The awards committee will select
the finalists at least three months prior to
the beginning of the symposium. It will
notify the chairman of the society and
the chairman of the executive committee
at that time. The winner will be selected
by the awards committee, subsequent to
the oral presentations by the finalists.
Selection will be based on the significance
of the contribution, the skillfulness of the
development, and the quality of the
exposition. The winner will be presented
the award prior to the conclusion of the
symposium.
The winner will receive an award of
$750 (U.S.) and a certificate. The other
finalists will also receive certificates. The
society will pay partial travel expenses
for each finalist to attend the symposium.
These reimbursements will be limited in
accordance with the amount of endow
ment income available. A limit in the
range of $500 to $750 (U.S.) is likely.
The institutions from which the nomina
tions originate will be encouraged to
assist any nominee selected as a finalist
with the additional travel expense reim
bursement.
R.G. Bland
Stochastic Programmin
Codes Available
The Adaptation and Optimization
(ADO) project of the Systems and
Decision Sciences program at the Interna
tional Institute for Applied Systems
Analysis is preparing a survey of the tech
niques currently employed to solve
various problems in stochastic linear and
nonlinear programming titled ''NinL l ..Il
Techniques for Stochastic Optimization
Problems," edited by Yu. Ermoliev and
R. Wets. In addition, the project has
assembled a collection of experimental
computer codes that implement several
of the algorithms discussed in the survey.
This collection will be made available on
computer tape to researchers early in
1985. There is a high degree of variation
in the quality of these codes; some are
near productionlevel quality, whereas
others have been built to test the poten
tial of a proposed method or to solve a
specific class of problems. In certain
cases it is assumed that the distribution of
the random variables (which model the
uncertainty) is discrete or has been
discretized. In other cases no assumptions
are made concerning the distribution the
code itself performs the discretization
or simply avoids multidimensional inte
gration.
Ten authors have contributed nine
programs to the ADO collection. These
programs address a number of different
problems and use a variety of tech
niques to solve them. The :l,,! '.i. l!l
authors are :
John Birge, A. Boehme and Kurt
Marti, Alexei Gaivoronsky, Alan King,
Larry Nazareth, Liqun Qi, Andrzej
Ruszczynski, Tamas Szantai, and Stein W.
Wallace.
The ADO tape contains the source
code provided by each author and a
User's Manual for each program. There
are sample input and output files for
most of the codes as well. The tape also
includes a paper outlining a proposal for a
standard input format for routines that
solve stochastic programs with recourse
and a library of utilities to facilitate the
use of the standard format. The tape's
contents total some 4.5 million bytes.
The codes in the collection are
written in various dialects of FORTRAN
and some use subroutines from the IMSL,
MINOS, NAG, or QPSOL libraries. The
User's Manuals and other papers provided
on the tape are intended for use with the
UNIX text processor, troff, although they
can be read as is. Please note that the
majority of the codes in the collection are
still under development and that no
warranty is granted, either expressed or
implied.
The ADO collection may be
obtained from:
Project Secretary
ADO/SDS
IIASA
A2361 Laxenburg
Austria.
Persons who would like a copy of the
collection should send a blank reel of
9track computer tape to the above
address and should include a note indi
cating their preferences for density
and character set (IIASA's computer can
,II..~:~.ic unlabelled tapes at 1600 or 800
bits per inch using either the ASCII or
EBCDIC (C1 ,I t.i. codes.)
BOO K REVIEW V E WS
Optimality and Stability in Mathematical Programming
Mathematical Programming Study 19
Edited by M. Guignard
North Holland, Amsterdam
1982
ISBN 0444864415
During the past 15 years we have seen a number of im
provements and refinements regarding the theory of .t'!ni.!lii;,
in mathematical programming, especially concerning the charac
terization of optimal points for wide classes of optimization
problems. Very sophisticated optimality conditions have been
developed and the types of considered problems became more
general: nonsmooth, nonconvex and :i.'tn .t,.rentiable problems,
to name only a few. This success became possible by a collection
of new tools such as generalized gradients, subgradients, general
ized equations, cones of constancy directions, normal subcones,
etc.
At the same time considerable progress has been made in
the study of the effects of small perturbations of the data in
volved in the nonlinear programming problems on the solution.
Study Nr. 19, a collection of 11 papers by 17 authors (M.S.
Bazaraa, A. BenIsrael, A. BenTal, J.M. Borwein, F. Dubeau, J.
Gauvin, J.J. Goode, J.B. HiriartUrruty, P. Loridan, O.L. Mang
asarian, V. Hien Nguyen, J.P. Penot, S.M. Robison, J.J. Strodiot,
H. Wolkowicz, S. Zlobec, J. Zowe) written between 1979 and
1982, deals with various aspects of the contemporary theory of
optimality and stability mentioned above. The volume, edited by
Monique Guignard, is of invaluable help for the study of the
modern nonlinear mathematical programming theory.
B. Bank
Mathematics for the Analysis of Algorithms
by D.H. Greene and D.E. Knuth
Birkhauser, Basel
1982
ISBN 376433102X
Presenting an algorithm for a particular problem usually
comes in two steps. The first and happy part is the design of the
.l' .'.rjthn A itself, and the proof that A actually works often
provides for exhilarating moments in the researcher's life. But this
joy of discovery is invariably followed up by the piercing and
often uncomfortable question: How good is A? The o, and more
ambitious O, analysis comes into play, familiar to number
theorists and analysts, but not so wellliked in the computer
world.
The book by Greene and Knuth under review addresses the
problems arising in this second part in an admirable way. In no
J
BOOK REVIEWS
more than 80 pages the authors introduce the reader to all the
basic techniques in the analysis of algorithms currently in use 
certainly no small achievement. Chapter I on binomial identities
gives a summary of the combinatorics needed in the sequel. In
chapter II the authors present a beautiful introduction to recur
rence relations. They discuss a usually nontrivial example to
point out the possible attacks, giving the reader the distinctive
flavor of the subject. Chapter III, called operator methods, is not
quite on the same level of generality. It concentrates more or less
on the concept of an "eigenoperator" with applications to
hashing schemes. The final chapter, on asymptotic analysis, is
the heart of the book. It acquaints the reader with such widely
used methods as Euler summation or the use of the residue
calculus. The chapter is written at a brisk pace interspersed with
very interesting examples that are far from easy. The authors
close with a discussion of (on the average very hard) exam prob
lems,
To be sure, the book makes for no easy reading. As men
tioned in the introduction, the reader should have some know
ledge of combinatorics and complex analysis. The format of
the book is very condensed indeed, marking it a reference rather
than an introductory or even advanced text. But as a reference it
should prove (as has proved in the past) invaluable. What about
that second messy step in the design of an algorithm? Armed
with Greene and Knuth the reader will probably find it just as
interesting and enjoyable as the first. What better could be said
about a book?
M. Aigner
Graph Theory
Annals of Discrete Mathematics, 13
Edited by B. Bollobas
NorthHolland, Amsterdam
1982
ISBN 0444864490
i in volume contains a collection of 19 papers presented at
the Cambridge Graph Theory Conference, held at Trinity College
from 11 to 13 March 1981. All contributions are invited and
refereed papers. The authors represent a large variety of nation
alities and interests. Each contributor presents one or two original
research articles from a field in which he is an expert. Survey
articles are not in this volume. Since the theme of the meeting
was not restricted, the papers come from diverse areas of graph
theory. Classical questions as well as recent developments are
considered. The emphasis in this volume is on pure graph theory.
However, a fair amount of the papers deals with applications of
graph theory to related mathematical areas, and one of the papers
(by J.L. Gross) is concerned with an application in social sciences.
The papers cover a broad spectrum of the various branches of
graph theory, including topics such as colouring, connectivity,
cycles, Ramsey theory, line graphs, Hadwiger's number, random
graphs and simplicial decompositions. Some other papers deal
with directed graphs, flows, hypergraphs, latin rectangles, designs,
strongly regular graphs, planarity algorithms, complexity and
games.
Among the many interesting articles in this volume, I would
like to mention the articles of A.J.W. Hilton, A.J.W. Hilton/C.A.
Rodger and A.J. Mansfield/D.J.A. Welsh. The papers of Hilton
and Rodger deal with applications of edgecolouring theorems to
latin rectangles, thus increasing the great number of applications
of graph colouring theorems to other branches of combinatorial
theory. The paper of Mansfield and Welsh is on colouring prob
lems and their complexity; in particular, the relationship between
the complexity conjucture that coNP t NP and a graph theorem
of Haj6s is discussed.
In my opinion, the present volume clearly demonstrates
that graph theory deals with a variety of interesting problems and
that it is still growing in many directions.
T. Andreae
Combinatorial Mathematics
Annals of Discrete Mathematics, Vol. 17
Edited by C. Berge, D. Bresson, P. Camion,
J.F. Maurras and F. Sterboul
NorthHolland, Amsterdam
1983
ISBN 0444865128
This volume of Annals of Discrete Mathematics contains
most of the papers presented at the International Colloquium on
Graph Theory and Combinatorics held in M i,. ll', France, in
June 1981, under the auspices of the National Center for Scienti
fic Research (C.N.R.S.). Different topics in combinatorics are
covered: graph theory, hypergraphs, matroids, coding, and
designs.
About half of the proceedings (almost 40 papers) deals with
questions from graph theory and hypergraphs. Some examples
are: construction of some classes of graphs and hypergraphs,
decomposition of graphs into special subgraphs, on the existence
of some structures in graphs, extension of classical theorems
known for some class of graphs, coloring of the edges of a graph
or a hypergraph, and embedding of a graph.
Coding theory also takes an important place. About 16'
papers discuss the construction of some special codes, the exten
sion of classical codes parameters associated with linear codes,
the ncube as well as the ncode, the application of codes to
designs, etc.
The remaining papers are devoted to designs (at least five),
matroids (five) and to some connections between groups or semi
groups and graphs. The volume ends with 17 problems submitted
during the Colloquium.
The papers of these proceedings represent valuable contri
butions and may be considered as an uptodate reference book
for research and teaching in the fields of graphs, matroids, coding
and designs.
J. Fonlupt and A. Zemirline
An Introduction to Convex Polytopes
Graduate Texts in Mathematics, Vol. 90
by A. Brondsted
Springer, Berlin
1983
ISBN 354090722X
This book treats the "combinatorial" theory of convex
polytopes, in particular the relationships which exist between
the numbers of faces of various dimensions. This book provides
a careful and complete development of this topic leading to
proofs of the DehnSommerville relations, the Upper Bound
Theorem and the Lower Bound Theorem.
There are three chapters plus three appendices which deal
with preliminary material (lattices, graphs, combinatorial identi
ties). In the first chapter the author develops much of the elemen
tary theory of convex polytopes in the more general context of
convex sets. Here such basic notions as convex hull, relative
interior, supporting hyperplanes, faces and polars are defined and
BOOK REVIEWS
their properties are developed. This treatment is careful, concise
and thorough. Moreover, the author makes an obvious effort here
and throughout the book to give the reader an appreciation of the
importance of the various theorems.
The second chapter deals with convex polytopes and, to
some degree, with polyhedral sets. However, this latter topic is
developed only to the extent required for studying polarity of
convex polytopes and so is treated much less extensively than
other topics. For example, cones are not considered explicitly nor
is the result that a general (unbounded) polyhedron is the sum of
a polytope and a cone. Moreover, theorems establishing the
correspondence between facets and essential .i iin:; innequal
ities are considered only in the full dimensional case. This causes
no problems for the intended use in the book, i.e., the study of
certain combinatorial properties of polytopes, but it does restrict
its usefulness to a mathematical programmer. Finally, simple,
simplicial and neighbourly polytopes as well as cyclic polytopes
are introduced in this chapter and are the topics of study in the
final chapter.
In Chapter 3 the author establishes the three main results
mentioned in the first paragraph. This development is carried out
for simple polytopeswhich, by polarity, is equivalent to the
more common line of development for simplicial polytopes. It is
not clear what advantage is gained by taking this "dual" ap
proach. However, it is an advantage to have a unified treatment
of these three main results.
In 1980 proofs of the sufficiency (L. Billera, C. Lee) and
the necessity (R. Stanley) of the socalled McMullin conditions
appeared. These provided a complete characterization of the
number of faces of all dimensions of simple or simplicial poly
topes and implied the results mentioned above. The author des
cribes these general results in the last section and shows that
they do indeed imply the Upper and Lower Bound Theorems but
does not include the proofs of the necessity and sufficiency of
the 'Il. Milirn conditions. (The proofs appearing in the literature
are all presented for simplicial polytopes.)
In conclusion, this book is very carefully and competently
written. The author has prepared a useful introductory mono
graph (with exercises) on convexity in general and convex poly
topes in particular. In the preface he stated that his intent was to
make the book accessible to someone with a background in
standard linear algebra and elementary point set topology. In
this he has succeeded. However, some of the author's decisions
regarding content and point of view may restrict the breadth of
appeal of the book.
W .R. P' lk, 1l.al..
Mathematical Programming and Games
by E.L. Kaplin
John Wiley, New York
1982
ISBN 047103632
The topics considered in the book include various forms of
the simplex method of linear programming, related topics in
linear algebra games, shortestpath algorithms, dynamic program
ming and the transportation problem. A set of exercises with
answers is provided for each of the 74 sections,
By suitably selecting and ordering the material, the book
can be used for a variety of college or university courses of
various lengths and levels. A checklist immediately preceding
chapter 1 illustrates possible selection of topics for courses of
one, two or three terms, and the indicated pages suggest a point
after which the continued study of the topic becomes optional.
In the spirit of mathematical programming itself, one aim
of this book is to try to minimize the effort required of the
reader, subject to nontrivial lower bounds on the amount of
information provided.
Examples and exercises with answers are included in sub
stantial numbers, section by section. Each example is carefully
chosen and organized in a form suitable for the student's own use
in doing exercises. A majority of the exercises are routine applica
tions of the material in the text; the others permit the student to
exercise his or her general mathematical background. A very few
exercises, which are starred, are included for the purpose of
supplementing the theory in the text.
New material and recent developments not available in
other textbooks include the allinteger pivot procedure, new
methods for solving small systems of linear equations, the classi
fication of bimatrix games, the analysis and generalization of
the Shapley and Bauzhag values for games, and the treatment of
mint1;l.' objective linear ].!...r.i,,!,,iiI~ which brings together
several streams of research that have developed rather indepen
dently. One of these is concerned with sheer enumeration of
extreme points, another the .:. ln..i. for efficiency.
C. Fabian
Computer Methods for the Range of Functions
by H. Ratschek and J. Rockne
Ellis Horwood, Chichester
1984
ISBN 0853127034
The calculation of the range of a given function is of great
interest in many areas of numerical analysis, e.g. for finding the
global minimum of a function or for determining Lipschitzian
constants. The aim of the book is to summarize the present state
oftheart of known formulas and methods that could be imple
mented numerically to approximate the range of functions.
The authors start with an introduction into interval arithmetic
and provide the tools used in the subsequent chapters. Some of
the most important concepts to understand the methodology are
the standard centred forms, which are described in detail for
rational functions and which allow development of explicit
inclusion formulas. Extensions to higher order formulas, func
tions in several variables or recursively defined forms are also
discussed. A general definition of centred forms allows the
treatment of nonrational functions and the development of a
quadratic convergence theorem. It is furthermore shown that
these methods can be combined with a subdivision method, and
that standard centred forms for rational functions lead to an
optimal approximation of the range. Finally, the authors discuss
several other inclusion methods for the range of a function, e.g.
methods based on circular complex centred forms, Bernstein
functions or global optimization.
The book represents an excellent introduction into theory
and methodology of the subject and can be recommended for
those people who want to get a comprehensive survey on meth
ods for the range of functions. A lot of examples illustrate
definitions, formulas and methods. Only the term 'computer
methods' in the title might be criticized, since computer pro
grams, algorithmic flow charts or extensive computational tests
are not presented.
K. Schittkowski
JOURNALS & STUDIES
Vol. 31, No. 3
S. Zlobec, "Input Optimization: I. Optimal Realizations of
Mathematical Models. "
Y. Yuan, "On the Superlinear Convergence of a Trust
Region Algorithm for Nonsmooth Optimization."
J.Wang, "Distribution Sensitivity Analysis for Stochastic
Programs with Complete Recourse. "
A. Tamir, "A Finite Algorithm for the Continuous PCenter
Location Problem on a Graph. "
A. Reinoza, "Solving Generalized Equations via Homo
topies. "
M. Preissmann and D. de Werra, "A Note on Strong Perfect
ness of Graphs."
C.D. Ha, "Stability of the Linear Complementarity Problem
at a Solution Point."
S.J. Grotzinger, "Supports and Convex Envelopes."
A.A. Goldstein, "The Complexity of an Qp Method for
Discrete Tchebycheff Approximation in Exact Arithmetic."
R.S. Dembo and J.G. Klincewicz, "Dealing with Degener
acy in Reduced Gradient. ." ..; "
Vol. 32, No. 1
J.B. Orlin and U.G. Rothblum, "Computing Optimal Scal
ings by Parametric Network A .',....'. ', :. ~ "
G.G. Brown, R.D. McBride and R. K. Wood, "Extracting
Embedded Generalized Networks from Linear Programming
Problems."
O.L. Mangasarian and L. McLinden, "Simple Bounds for
Solutions of Monotone Complementarity Problems and Convex
Programs."
D. Le, "A Fast and Robust Unconstrained Optimization
Method Requiring Minimum '. :. ."
R.S. Womersley, "Local Properties of Algorithms for
Minimizing Nonsmooth Composite Functions."
N.I.M. Gould, "On Practical Conditions for the Existence
and Uniqueness of Solutions to the General Equality Quadratic
Programming Problem. "
R. Lazimy, "Improved Algorithm for MixedInteger
Quadratic Programs and a Computational Study.
Vol. 32, No. 2
D.P. Bertsekas, "A Unified Framework for Primaldual
Methods in Minimum Cost Network Flow Problems."
R.G. Jeroslow, "The Polynomial Hierarchy and a Simple
Model for Competitive Analysis. "
U.H. Suhl, "Solving Large Scale MixedInteger Programs
with Fixed Charge Variables. "
A.V. Karzanov, "Metrics and Undirected Cuts."
J.E. Spingarn, "Applications of the Method of Partial
Inverses to Convex Programming: Decomposition."
Y. Yuan, "An Only 2Step QSuperlinear Convergence
Example for some Algorithms that Use Reduced Hessian Approx
imations. "
R.H. Byrd, "An Example of Irregular Convergence in Some
Constrained Optimization Methods that Use the Projected
Hessian. "
G. Morton, R. von Randow and R. Rignwald, "A Greedy
Algorithm for Solving a Class of Convex Programming Problems
and its Connection with Polymatriod Theory."
J. Kyparisis, "On Uniqueness of KuhnTucker Multipliers
in Nonlinear Programming."
Vol. 32, No. 3
T.M. Cavalier and H.D. Sherali, "Sequential Location
Allocation Problems on Chains and Trees with Probabilistic
Demands."
U. Passy and E.Z. Prisman, "A ConvexLike Duality
Scheme for QuasiConvex Programs."
J. Renegar, "On the Complexity of a Piecewise Linear
Algorithm for Approximating Roots of Complex Polynomials."
J. Renegar, "On the Cost of Approximating all Roots of
a Complex Polynominal. "
I.D. Coope and G.A. Watson, "A Projected Lagrangian
.1. .r:' : ; for SemiInfinite Programming. "
U.G. Rothblum, "Ratios ofAffine Functions."
R. EngelbrechtWiggans and D. Granot, "On Market Prices
in Linear Production Games."
Technical Reports & Working Papers
Econometric Institute
Erasmus University Rotterdam
P.O. Box 1738
3000 DR Rotterdam
The Netherlands
B. Bode, "Point Processes and Central Order Statistics,"
8401/S.
J.K. Linstra and A.H.G. Rinnooy Kan, "New Directions in
Scheduling Theory," 8401/0.
J. Bouman, "Testing Nonnested Linear Hypotheses I:
Reduction by Invariance Consideration," 8401/S.
V. Stern, "Nonlinear Network Optimization as a MaxMin
Pro blem, 8405/0.
A. Ster and V. Stern, "An Intelligent Computing System,"
8406/1.
J.L. Geluk, "Abelian and Tauberian Theorems for 0
Regularly Varying Fnctions," 8409/S.
A.S. Louter and G. van der Hoek, "TWOFAS: A 2Phase
Code for Constrained Nonlinear Programming," 8411/I.
i.chn. a Reports & Working Papers
M. Salomon, H.J. Gernaat, G. van der Hoek, "A Financial
Information System for Tendering," 8413/I.
A.C.F. Vorst, "A Stochastic Version of the Urban Retail
Model, 8414/M.
J.B.G. Frenk and A.H.G. Rinnooy Kan, "The Asymptotic
Optimality of the LPT Rule," 8418/0.
A.H.G. Rinnooy Kan and G.T. Timmer, "A Stochastic
Approach to Global Optimization," 8419/0.
A.H.G. Rinnooy Kan, "An Introduction to Approximation
Algorithms," 8420/0.
M. Hazewinkel, "Experimental Mathematics," 8421/M.
M. Hazewinkel, "On Mathematical Control Engineering,"
8422/M.
L. de Haan and E. Verkade, "On Extreme Value Theory in
the Presence of a Trend," 8425/S.
A.W.J. Kolen and A. Tamir, "Covering Problems," 8426/0.
J.B. Orlin, "Some Very Easy 1. . I'.*. Prob
lems," 8427/0.
M. Hazewinkel, "Symmetry in Physics and System
I... .,"8428/M.
A.H.G. Rinnooy Kan, C.G.E. Boender and G.T. Timmer,
"A Stochastic Approach to Global Optimization," 8429/0.
J.L. Geluk, "Tail Probabilities and Moment for a Class of
Random Variables, 8431/S.
J.B. Orlin, "Genuinely Polynomial Simplex and Non
Simplex .1'.. ."' for the Minimum Cost Flow Problem,"
8432/0.
A.W.J. Kolen, A.H.G. Rinnooy Kan and H. Trienekens,
"Vehicle Routing with Time Windows, 8433/0.
J.B.G. Frenk and A.H.G. Rinnooy Kan, "On the Rate of
Convergence to 0''. of the LPT Rule,"8434/0.
M. Meanti, A.H.G. Rinnooy Kan, L. Stougie and C. Ver
cellis, "A Probabilistic Analysis of the Multiknapsack Value
Function, "8435/0.
J.R. de Wit and A. Tramper, "Allocating Men to Jobs,"
8436/0.
J.R. de Wit, "A Note on the Behaviour of the Dirichlet
Prior Distribution in the Absence of Information," 8437/0.
CHR. Michelsen Institute
N5036 Fantoft
Bergen, Norway
S.W. Wallace, T"D. .. .. the Requirement Space of a
Transportation Problem into Polyhedral Cones," CMIreport
no. l.. '. .
S.W. Wallace, "A I .. '.'' Stochastic FacilityLocation
Problem with TimeDependent Supply," CMIreport no.
83255510.
S.W. Wallace, "Pivoting Rules and Redundancy Schemes in
Extreme Point Enumeration," CMIreport no. 83255513.
S.W. Wallace, "On Network Structured Stochastic Optimi
zation Problem, CMIreport no. 8425558.
S.D. Flam and R.JB. Wets, "Existence Results and Finite
Horizon Approximates for Infinite Horizon Optimization Prob
lems, CMIreport no. 84255513.
S.D. Flam and R.JB. Wets, "Infinite Horizon Discrete Time
Stochastic Bolza Type Problems: Existence Results," CMIreport
no. 8426501.
R.JB. Wets, "Algorithmic Procedures for Stochastic Opti
mization, CMIreport no. 84265 02.
S. Story, "On the Relative Ranking of Computer Sys
tems," CMIno. 1984:17.
Department of Pure and Applied Mathematics
Washington State University
Pullman, Washington 991642930
R. '.Iil,,, "A Computational Algorithm for Univariate
Minimization and a Nested Application."
The Johns Hopkins University
Operations Research Group
Baltimore, MD 21218
C. ReVelle, J. Cohon and D. Shobrys, "Multiple Objectives
in Facility Location: A Review," 8101.
A.J. Goldman, "Reflections on Modeling and Model Assess
ment, 8103.
J.A. Filar, "SemiAntagonistic Equilibrium Points and
Action Costs," 8201.
J. Current, C. ReVelle, and J. Cohon, '. .
Design of Transportation Networks," 8202.
R.H. Byrd, A.J. Goldman and M. Heller, "Recognizing
Unbounded Integer Programs, "8203.
S.S. Ting, "A LinearTime .':. ::' for Maxisum Facility
Location on Tree Networks," 8301.
J. '.\1.,F. C. ReVelle and J. Cohon,"A Multiobjective
Integer Programming Model for the Land Acquisition Problem,"
8302.
J.R. Current, C.S. ReVelle andJ.L. Cohon, "The Maximum
Covering/Shortest Path Problem: A Multiobjective Network
Design and Routing Formulation," 8303.
R. D. Parker, "Stability of the Optimum to (. ..., in
Horizon in Certain Linear Control Problems," 8304.
A.J. Goldman and P. Tiwari, "Allowable Processing Orders
in the Cascade Algorithm," 8305.
J.A. Filar and T. A. Schultz, "Interactive Solutions for
the Travelling Inspector Model and Related Problems," 8306.
D. Engberg, J. Cohon and C. ReVelle, "Multiobjective
Modeling for OCS Pipeline Systems, "8397.
S.G. Nash, "Avoiding .11 .'"' Matrix Factorizations in
NewtonLike Methods," 8401.
J. Filar, "Player Aggregation in the Travelling Inspector
Model, 8404.
Brunel University
Department of Mathematics and Statistics
Uxbridge, Middlesex, UB8 3PH
K. DarbyDowman and G. Mitra, "An Investigation of
Algorithms Used in the Restructuring of Linear Programming
Basis Matrices Prior to Inversion," STR/33.
J.J. Judice and G. Mitra, "Reformulation of Mathematical
Programming Problems and Linear Complementarity Problems,"
STR/38.
JJ. Judice and G. Mitra, "An Enumerative Method for the
Solution of Linear Complementarity Problems," TR/04/83.
C. Lucas and G. Mitra, "Modelling of Mathematical Pro
grams. An Analysis of Strategy and Proposal for a Computer
Assisted System, "TR/09/83.
K. DarbyDowman and G. Mitra, "An Extension of Set
Partitioning with Application to Scheduling Problems,"
TR/12/83.
G. Mitra, K. DarbyDowman and C. Lucas, "Computer
Assisted Modelling of Linear, Integer and Separable Programming
Problems, TR/08/84.
 Gallimaufry 
We note with sadness the death of T.C. Koopmans (Yale), a pioneer
in the field and a Senior Editor of the Journal.
The MPS Council has approved a proposal by M. Iri, K. Tone, and
H. Konno that the next Symposium be held in Tokyo in 1988. Specific
dates and a site have yet to be established, but Chuo University is the
likely location....Romesh Saigal reports the founding of SCI Computing,
a consulting firm which also offers mathematical programming soft
ware....Publicity for the upcoming Symposium at MIT emphasizes new
results in areas such as the integration of artificial intelligence, parallel
computation for mathematical programming, and modeling techniques
for spreadsheets on personal computers.
The new OrchardHays Prize for Excellence in Computational
Mathematical Programming is being funded by contributions from CAA,
Inc., Ketron, Inc., ARC, Inc., Optimal Systems, Linus Schrage, Scicon,
Ltd., Linear Programming, Inc. and Haverly Systems, Inc.
Deadline for the next OPTIMA is October 15, 1985.
Donald W. Hearn, Editor
Achim Bachem, Associate Editor
Published by the Mathematical Program
ming Society and Publication Services of
the College of Engineering, University of
Florida. Composition by Lessie McKoy,
Graphics by Lise Drake.
Books for review should be sent to
the Book Review Editor, Prof. Dr.
Achim Bachem, Mathematiches
Institute der Universitlit zu Kiln,
Weyertal 8690, D5000 Kidln,
W. Germany.
Journal contents are subject to
change by the publisher.
MPS Dues Increase Proposed
At the last Executive Committee
meeting the treasurer, A.C. \ iliaum., re
ported that the Society will run a deficit
in 1985, for the second year in a row.
This reverses the trend established in the
mid 1970's toward surpluses in each year.
During that time dues were cut from
US$45.00 to a low of US$32.50, and
proportionately even larger cuts were
made for dues payable in the weaker
European currencies. At the same time,
the number of issues per year of the
Journal were increased. The Optima
Newsletter was established, and the
COAL Newsletter was established as
well.
While the Society's treasury is
projected to stand at a healthy
$60,000.00 at the end of 1985, it is down
from a high of $72,000.00 in 1983, and
projected expenses will exceed income if
nothing is done. Therefore, the Executive
Committee will recommend to Council
that the dues for 1986 be increased and
that COAL begin charging nonmembers
for its Newsletter.
A.C. Williams
I PTI MA
303 Weil Hall
College of Engineering
University of Florida
Gainesville, Florida 32611
FIRST CLASS MAIL
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