September
1984
Number 13
PTI MA
MATHEMATICAL PROGRAMMING SOCIETY NEWSLETTER
Boston Symposium Issues Call For Papers;
Dantzig, Fulkerson Winners to Be Named
Tutorials and MP software demonstrations featured
he XII International
Symposium on Mathe
matical Programming will
be held August 5 to
August 9, 1985, at the
Massachusetts Institute of Tech
nology in Cambridge, Massachusetts.
The organizers are constructing a
program that emphasizes applica
tions and computation, as well as
recent theoretical developments.
A call for papers will be mailed
out in September, 1984. The dead
line for submission of contrib
uted paper titles is April 1, 1985;
paper abstracts are due by June 1,
1985. In addition, invitations to
present papers will be extended to a
number of leading researchers and
practitioners.
The program will be organ
ized around more than a dozen
parallel sessions covering topics on
every aspect of mathematical pro
gramming. It will also contain
approximately 15 tutorials, stateof
theart surveys and minicourses
presented by leading experts in the
field. The following is a partial
list of topics:
* Data Structures
* Simulated Annealing
* Vehicle Routing and Scheduling
* Stateoftheart in Complemen
tarity Theory
* Mathematical Programming on
Microcomputers
* Mathematical Programming and
Economic Theory
* Stochastic Optimization
* New Problems in Graph Theory
* Mathematical Programming and
Expert Systems
* Methods of Model Generation
Arrangements are underway for
extensive software demonstrations at
the Symposium. Several commer
cial linear and mixed integer program
ming systems will be displayed, along
with packages for scheduling and
network optimization, and experi
mental codes of many types. Demon
strations will include microcomputer
as well as mainframe systems. A
minicourse will be offered on linear
programming linked to spread sheet
programs. Participants will be given
"hands on" experience in using these
programs on micros.
The winners of two prestig
ious awards, the George Dantzig Prize
and the Ray Fulkerson Prize, will be
announced at the Symposium's open
ing ceremonies. The Dantzig Prize is
presented jointly with the Society for
Industrial and Applied Mathematics
(SIAM) for original work in the field
of mathematical programming which,
by its breadth and scope, constitutes
an outstanding contribution to the
field. The Fulkerson Prize is presented
jointly with the American Mathe
matical Society (AMS) for an out
standing paper in the area of discrete
mathematics. A new prize, the William
OrchardHays Prize for mathematical
progranimin' computation will be
awarded for the first time at the
Symposium. See Boston, page 2
IBM Prizes Awarded
at TIMES XXVI
At the XXVI International Meeting of
The Institute of Management Sciences
(Copenhagen, June 1984), the S2000 IBM
prize for "the best paper showing the role of
computers in management science and
operations research" was divided between
two papers: one by Martin Gr'tschel,
Michael Jfinger and Gerhard Reinelt on a
polyhedral approach to matrix triangulation
and another by Robert E. Markland and
Shawnee K. Vickery on an integer goal
programming algorithm. Pekka Korhonen
and Jukka Laakso received honorable
mention for their work on interactive
multicriteria decision making.
The prize was made li.l..l. by IBM
See IBM Prizes, page 2
1985 Officers Election;
Call for nominations
In accordance with the Constitution of
the Society, the triennial election of officers
will be held in March, 1985. All offices will
be on the ballot: Chairman, Treasurer, and
four Council membersatlarge. The Nomi
nating Committee (Alex Orden, Chairman)
welcomes suggestions from the membership
for nominees. .jI I.1l.,, before a candidate
is proposed, it should be determined that the
member is in good standing with the Society
and is willing to run.
The Nominating Committee will cir
culate the proposed names among the
Council of the Society, which will choose
the candidates. In addition, any person
nominated in writing by at least six members
of the Society, and who agrees to stand, will
be placed on the ballot.
Suggestions should be sent by Decem
ber 31, 1984. to the Chairman of the
Society, Professor Alex Orden, Graduate
School of Business, University of Chicago,
1101 East 5. il Street, (I1... 1.. i ll. 60637,
U.S.A.
.... Ho ffiff0 wg 10lwll
Boston from page one
The symposium will be held
on the campus of the Massachusetts
Institute of Technology. Dormitory
rooms will be available to Symposium
attendees and their families; blocks of
rooms have also been reserved at
nearby hotels. A range of social
events has been planned including a
reception at the New England Aquar
ium, and a banquet celebrating
George Dantzig's 70th birthday to be
held at one of Boston's leading hotels.
Attendees and their families ill also
be able to choose from an assort
ment of summer activities organized
by the social committee including: a
New England clambake, harbor and
whalewatching cruises, a visit to a
Red Sox baseball game, and walking
tours of historic Boston.
For further iiif. iin ti:.n, con
tact:
Jeremy F. Shapiro
Program Chairman
Operations Research Center
Massachusetts Institu te of
T:' n. ,lo_.',
Room E40164
Cambridge, MA 02139
USA
(6172533601)
NATO ASI on Computational
Mathematical Programming
A highly successful Advanced Study
Institute on Computational Mathematical
Programming was held July 23August 2
in Bad Windsheim, F.R.G., under the spon
sorship of NATO with additional support
from NBS, NSF, and Deutscher
Akademischer Autauschdienst. The meeting
was organized by the MPS Committee on
Algorithms (COAL) with Klaus Schittkowski
as Director, Karla Hoffman and Jan Telgen
as CoDirectors, Jochem Zowe in charge of
arrangements, and Marlis Zowe as secretary.
Over 80 participants from 20 countries
attended the 60 research seminars and the
16 featured lectures by Martin Beale, H.P.
Williams, FA. Lootsma, K. Hoffman, A.
Rinnooy Kan, R.B. Schnabel, M; Rijckaert,
J. Stoer, P.E. Gill, P. T.!!rt, D. Kraft, R.
Wets, and J. Zowe.
Also featured was a "software fair"
in which both commercial software houses
and researchers provided information on the
availability of their mathematical program
ming software.
The tutorial lectures will be published
by Springer within a special NATO ASI
series, and the research papers are being
solicited for a Mathematical Programming
Study to be edited by Karla Hoffman,
Richard H.F. Jackson and Jan Telgen.
Social highlights of the meeting
included excursions to Wurzburg and Roth
enburg and a "Spanferkelessen" in Bad
Windsheim.
D. Hearn
Third Course:
Optimization and Related Fields
September 1730, 1984
Erice,Italy
This course is sponsored by the
European P"., '.. il Society, the Italian
Ministry of Education, the Italian Ministry
for Scientific and Technological Research,
the National RI'tIIiih Council, and the
Sicilian Regional Government.
The aims of this course are to present
both stateoftheart summaries and research
trends of optimization theory and methods.
It will be structured with invited lectures
and some contributed lectures as well.
Special attention will be devoted to inter
actions between infinite and finite dimen
sional theory, method, and applications.
The closing date for application was
June 30, 1984. Requests for information
should be directed to Professor R. Conti,
Institute do Matematica, Universita di
Firenze, Viale Morgagni, 67/A, 50/34
FIRENZE, Italy.
IBM Prizes from page one
World Trade F,ir.pce, NMddle East/Africa
and IBM Denmark. Twentyfour papers
were submitted and considered by a jury
consisting of Laureano F. Escudero (IBM
Spain), Michael Florian (Universit6 de
Montreal), Francesco Maffioli (Politecnico di
hMlan.,), Bent Rosenkrands (IBM Denmark),
and the two program chairmen of TIMS
XXVI, Richard L. Francis (University of
Florida, Gainesville) and Jan Karel Lenstra
(Centre for Mathematics and Computer
Science, Amsterdam). The citations of the
selected papers are quoted below.
"Honorable mention is received by
Pekka Korhonen and Jukka Laakso from the
Helsinki School of Economics for the paper,
A Visual Interactive Method for S hliirn the
Multiple Criteria Problem. They are among
the first ones to explore the combination of
algorithms for multicriteria decision making
and manmachine interaction by means of
computer graphics. The jury feels that this
is a very promising research direction,
completely in the spirit of the prize, and
hopes that this mention will stimulate the
authors' continuing work along these lines.
"One prize is awarded to Robert E.
Markland from the University of South
Carolina and Shawnee K. Vickery from
Michigan State University for the paper,
The Efficient Computer Implementation of
a LargeScale Integer Goal Programming
Model. They have developed a computa
ii..nal m.thl.[.l for a set of production
planning problems that are difficult on three
counts: they are large scale, they have
integer variables, and they are formulated in
terms of ,..1 pr,_i nniniig The method has
been successfully implemented and evalua
ted in a practical context. The jury is
impressed by the achievements reported in
this paper.
"The other prize is awarded to Martin
Grotschel, Michael Jiinger and Gerhard
Reinelt for the paper, A Cutting Plane
Algorithm for the Linear Ordering Problem.
They consider an important optimization
problem that occurs, for example, in the
triangulation of inputoutput matrices, and
that has received insufficient attention so
far. Their solution method is based on their
earlier investigations of the facet structure of
the integer polytope associated with the
problem as ...: 11 as on the use of a standard
LP/ILP package as a subroutine. The re
sulting ..I'rilrhi is very elegant and of
practical relevance in the sense that it is the
first one able to solve problems of the size as
they occur in practical situations."
Jan Karel Lenstra
CONFERENCE NOTES
sF~8~1~91 1 r n* ^s~ Ir~~
BOOK RE V I E W S
Homotopy Methods and Global Convergence
by B. C. Eaves, F. J. Gould, H. 0. Peitgen and M. J. Todd
Plenum, New York, 1983
This book is a collection of papers presented at the NATO
Advanced Research Institute on Homotopy Methods and Global
Convergence held in Porto Cervo, Sardinia, in 1981. Two papers
should be of particular value to practitioners in that they present
much useful material that, up to now, has circulated as part of
the folklore of the subject. One of these is the paper by John B.
Shoven discussing the interplay of mathematical and economic
reasoning involved in applying homotopy and fixed point meth
ods to general equilibrium modeling. The other is Layne T.
Watson's paper in which he tells about his experiences in applying
the ChowYorke algorithm to a variety of engineering problems.
The remaining papers are more theoretical in nature and
present many new ideas that are only now beginning to be fully
appreciated and exploited by workers in the field. Some of these
are piecewise smooth homotopies, global Newton methods for
stationary point problems, exploiting structure in large homotopy
problems, and probabilistic analysis.
A final interesting feature of the collection is an appendix
that presents descriptions of several current implementations of
fixed point and homotopy procedures. I was, however, disap
pointed that no complementarity codes were included, i11h..i i.
several excellent implementations are available.
The index to the collection is also disappointing. It lists,
for example, only one reference to linear complementarity,
although references to linear complementarity abound through
out the collection. Additionally, it would have been interesting if
the editors had provided an introductory preface, giving their
view of the field and placing the collection in context.
The papers contained in this collection represent valuable
contributions and are interesting to read. Researchers and
practitioners will both find this book a worthwhile investment.
Philip C. Jones
Discrete Optimization Algorithms with Pascal Programs
By M. M. Syslo, N. Deo and J. S. Kowalik
PrenticeHall, Englewood Cliffs, New Jersey, 1983
The purpose of this book on discrete optimization is to
offer "a collection of readytouse computer programs together
with their derivation and performance characteristics." The
authors recommend its use as a supporting textbook in advanced
undergraduate or graduate courses and as a software handbook.
There are four chapters. The first one deals with linear and
integer programming, including the transportation problem.
Chapter 2 discusses knapsack, set partitioning and set covering
problems. Chapter 3 covers network optimization problems:
paths and trees, maximum and minimumcost flow, cardinality
matching, and the traveling salesman problem. The final chapter
presents a selection of coloring and scheduling algorithms.
The book would be quite useful as a supplementary text in
courses on discrete optimization. It contains a lot of informa
tion, and the 28 Pascal codes are suitable for a quick and inci
dental use by students. We would hesitate, however, to describe
the text as a software handbook. This is not because of the
incomplete coverage of the area (excluded are topics like loca
tion, network design and matroid optimization), but because the
selection criteria for the il: _.. l;I, to be coded are not clear and
because the codes themselves are not up to the current standards
for production purposes. The choice of algorithms as well as the
style of implementation seems to have been determined by the
availability of .,i 1. material and by educational requirements
of clarity and simplicity rather than by considerations of time
and space efficiency. For example, Dinic's maximum flow
.,r..rirtm in the version of "the three Indians" is conceptually
very simple indeed but probably not the most efficient one 
even if the authors' implementation would be modified so as to
attain the claimed cubic time bound. But let us repeat that the
book could prove its value in supplying supporting material in
courses based on the unified expositions by, e.g., Lawler and
Papadimitriou and Steiglitz.
B.J. Lageweg,J. K. Lenstra
Direct Methods for Sparse Matrices
By 0. Osterby and Z. Zlatev
Springer, Berlin, 1983
This book is on the algorithmic solution of large sparse
systems of linear equations. It explains the strategies imple
mented in a software package called Y12M, which is available at
the Regional Computing Centre of the University of Copenhagen
(RECKU).
Let L U be a triangular decomposition of the square
matrix A and x0 an approximate solution of A x = b. Then,
if convergent, the process of iterative refinement
di : = U1 L1 (bAx);
x i+: = xi + di
yields a very exact solution of the original problem, even if
the decomposition A = L U is fairly inexact.
The authors use sparse representations of the matrices
involved. A large drop tolerance reduces fillin during the process
of Gaussian elimination and yields a crude but very sparse LU
decomposition. Subsequently, accuracy is retrieved by iterative
refinement. Compared to direct solution methods, this approach
results (for sparse problems) in a considerable reduction of
computing time and storage requirements as well as in improved
accuracy.
Chapter 1 gives an introduction and explains the classes of
test matrices used in computational comparisons. Data structures
for storing and manipulating sparse matrices are discussed in
Chapter 2, and Chapter 3 covers (modified Markowitz) pivotal
strategies to keep balance between sparsity and accuracy. Con
vergence results for the process of iterative refinement, considera
tions on the choice of the drop tolerance and computational
comparisons are given in Chapter 4. Finally, Chapter 5 intro
duces a general computational scheme which extends these ideas
to overdetermined systems and contains many wellknown direct
methods as special cases.
The book contains many tables with computational results
and is clearly written. It can be recommended to everyone
interested in efficient solution procedures for sparse linear
systems.
M. Bastian
Technical University, Aachen
BOOK REVIEWS
Probability Theory and Computer Science
By G. Louchard and G. Latouche
Academic Press, London, 1982
This book presents lectures given at the "Universite Libre
de Bruxelles" during 1980/81 by D. P. Gaver, H. Kobayashi and
R. Sedgewick. These lectures are intended as variations on the
theme "Probability Theory and Computer Science."
Chapter I, written by D. P. Gaver, describes "Stochastic
modeling: Ideas and Techniques" in detail. First, a review of
probabilistic concepts is given; after this, e.g., Bernoulli trials,
Poisson processes, Markov processes and renewaltheoretic
modeling are presented. This chapter closes with some additional
modeling topics.
Chapter II, written by H. Kobayashi, deals with "Stochastic
modeling: Queueing models." First, discrete time queueing
systems are investigated. Several models are described. Then
diffusion approximations in queueing analysis is investigated, and,
finally, computational algorithms for Markovian queueing net
works are given.
Chapter III, written by R. Sedgewick, deals with "Mathe
matical analysis of combinatorial algorithms." Trees are con
sidered; asymptotic approximations, asymtotics in the complex
plane and probabilistic models are discussed.
D. Kalin
Universitat Ulm
Complementary Pivoting on a Pseudomanifold
Structure with Applications in the Decision Sciences
By F. J. Gould and J. W. Tolle
Heldermann Verlag, Berlin, 1983
A unified framework is presented in the book in which the
socalled complementary pivoting algorithms can fit. Contrary to
the standard analytical algorithms, such as the simplex algorithm
or a gradient .jil.lrIli, r. a complementary pivoting algorithm is a
combinatorial method which does not proceed by generating a
monotone sequence of approximate solutions to the underlying
problem. Instead of that, a complementary pivoting algorithm
labels each element in a collection of sets of n elements, e.g.
indices or vertices of simplices of a triangulation (so that each
subset of n1 elements of a set is contained in at most one other
set of n elements) with an integer out of the set [ 1,...,n ] s.t. a
completely labelled set whose n elements are differently labelled
yields an approximate solution to the underlying problem.
Starting from an a priori known subset of nI differently
labelled elements contained in only one set of n elements or from
an artificial completely labelled set of n elements the algorithm
generates in general by complementary pivoting a unique path of
adjacent sets of which the common elements are differently
labelled until a completely labelled set of n elements is found.
Conditions on the underlying problem must guarantee the finite
termination of the algorithm. The description of the several
possibilities of a path is given in a very clear way.
The complementary pivoting algorithm is applied to solve
the linear complementarity problem (LCP) to approximate fixed
points of continuous functions and of upper semicontinuous
pointtoset mappings, and to find approximate solutions for
unconstrained nondifferentiable minimization and nondiffer
entiable programming. In almost all applications the problem is
piecewise linearized with respect to a triangulation and the
corresponding problem is solved by the complementary pivot
J..,! li h. When the accuracy of the approximating solution
found by the algorithm is not sufficient, the algorithm is re
started in the approximate solution with a triangulation having a
smaller mesh in order to increase the accuracy. The accuracy of
an approximate solution is discussed in detail.
The authors succeed in presenting in clear and simple terms
a unifying exposition of complementary pivot theory. Moreover,
the reader gets a good idea how this theory can be applied to
solve many highly nonlinear problems arising in the decision
sciences. Extensive references to earlier work on these problems
are given and each chapter is concluded with interesting exercises.
A. J. J.Talman
Sill.il! University
Convex Analysis: An Introductory Text
By Jan van Tiel
John Wiley, Chichester, 1983
This book gives a nice introduction into the theory of
convex sets and convex functions in finite and in infinite
dimensional spaces. It is suitable for either selfstudy or for
classroom work at the undergraduate level for students whose
mathematical background includes the basic facts of calculus,
linear algebra, and some basic material from general topology and
functional analysis.
The book is written in a clear, easily readable style. The
basic concepts and the characteristic methods of classical convex
analysis (such as separation, ,il.,...il.l',. conjugate function,
convex optimization) are developed step by step and presented in
a selfcontained approach. A large number of exercises at the
end of each chapter (with hints and answers at the end of the
book) helps understand the concepts employed. Some historical
remarks and additional material related to that covered in the
text are collected in bibliographical notes. These notes should be
useful to the interested reader for further study. The book is
organized as follows: Chapter 1 summarizes the essentials of the
theory of convex functions on the real line. Algebraic properties
of convex sets in a linear space are studied in chapter 2. Chapters
3 and 4 develop the theory of separation in a linear space and in
Rn, respectively. Chapter 5 studies convex functions on a linear
space. The concept of duality for convex functions is introduced
in chapter 6, and chapter 7 presents some basic facts from convex
optimization (such as KuhnTucker conditions and Fenchel's
duality theorem).
J. Zowe
Universitat Bayreuth
Nonlinear Programming 
Theory, Algorithms and Applications
By G.P. McCormick
John Wiley, New York, 1983
As a rule the books on optimization in finite dimensional
spaces concentrate either on theory or on algorithms and rarely
treat adequately the construction of optimization models. A
distinguishing feature of McCormick's book consists of harmo
nizing theoretical and numerical aspects with mathematical
The book provides a rigorous development of first and
second order optimality conditions, uptodate treatment of
algorithms for singlevariable, unconstrained nvariable, linearly
constrained and nonlinearly constrained problems together with
carefully chosen and elaborated mathematical models of real
world problems that can be solved by nonlinear programming
BOOK REVIEWS
methodology. It contains several topics not usually covered in
books on nonlinear programming. The most notable example is a
chapter on a computationallyoriented way of representing non
linear functions of several variables intended to provide the inter
face between computercoded algorithms and the algebraic
representation of nonlinear programming problems.
To summarize, the book gives a balanced uptodate treat
ment of various aspects of optimization in finite dimensional
spaces with a certain emphasis on the numerical aspects. It
represents a valuable addition to the existing literature on the
subject.
M. Vlach
Charles University, Prague
Nonlinear Optimization in Rn
By H. Th. Jongen, P. Jonker and F. Twilt
Peter Lang, Frankfurt Bern New York, 1983
Among various approaches to the theory of nonlinear
optimization this seems to be the first textbook attempt of a
systematical use of topological methods. In particular, Morse
theory is applied in order to study critical points of differentiable
functions on differentiable manifolds in Rn.
After an introduction into the basic concepts of optimiza
tion, Morse theory, and some notions of general topology and
matrix theory, real valued Crfunctions f on Rn are studied, the
focus being on the connection between the existence and
number of critical points and the behavior of the lower level sets
of f.
In Chapter 3 differentiable functions on differentiable
manifolds with generalized boundaries are studied under the same
aspects. An important class of such manifolds are socalled
regular constraint sets. So the theory being developed in this
chapter can be applied immediately to nonlinear optimization
problems and gives a considerable insight into their topology
features.
In Chapter 4 an application of Morse theory is made to
certain Chebychev approximation problems.
The final chapter of the book is devoted to the description
of a singular homology theory and its application to the study of
critical points of differentiable functions on differentiable mani
folds. The primary aim of the authors as expressed in the preface
is to give a good insight into nonlinear phenomena of optimiza
tion. This aim has been achieved by a very clear and concise
representation of the subject and by various geometrical illustra
tions which help to understand better the underlying ideas.
W. Krabs
Technical University, Darmstadt
Advances in Data Base Theory, Volume 2
By H. Gallaire, J. Mincker and J. M. Nicolas
Plenum Press, New York, 1984
This book includes 13 of the most interesting and reviewed
papers of the 27 talks given at the 3rd 'Workshop on Logical
Bases for Data Bases' held in Toulouse (France), December 14 
17, 1982. The papers cover different topics in database theory
reflected in the several chapters of the proceedings: database
scheme design, integrity constraints, incomplete information,
abstract datatypes for formal specifications and views, and query
language theory. These papers are discussed briefly below in the
same sequence as in the proceedings.
The major part of the proceedings is the section on data
base scheme design which deals mainly with acyclic database
schemes that form one of the most interesting aspects in design
theory.
Biskup and Bruggemam give a method to design acyclic,
synthesized 3NFdatabase schemes that join the desirable proper
ties of synthesized and acyclic database schemes.
Ausiello, D'Atri, and Moscarini define three different
concepts of minimal coverings in a given hypergraph and study
the degrees of acyclicity of the associated database schemes as
well as the complexity of their determination. Hanatani shows
that database schemes described by a single cyclic join depen
dency are useful, if the database schemes are simple, i.e. there
exists an acyclic database scheme satisfying the same multivalued
dependencies.
Gyssens and Paredaens introduce a methodology to decom
pose every decomposable, acyclic and cyclic join dependency into
a nonredundant set of smaller cyclic and acyclic join depend
encies.
The only paper not dealing with acyclic database schemes is
the paper of De Bra and Paredaens. They introduce the concept
of horizontical decomposition of relations in contrast to the
wellknown vertical decomposition of a relation into its projec
tions. Horizontical decompositions are useful to treat exceptions
of constraints. This is formalized by d. f;i; L functional depend
encies and two related normal forms.
The second chapter of this book deals with integrity
constraints. Henschen et al. propose and justify a method for
translating semantical constraints expressed in first order logic
into programs for testing a priori the validity of database updates.
These programs are generated at design time and they are applied
before updating the database.
Paige presents a new approach to improve the enforcement
of integrity constraints by finite differencing. He defines a
special class of predicates that can be monitored efficiently by
differencing.
Casanova and Furtado introduce transition constraints
restricting sequences of database states. Several classes of langu
ages based on temperal logic are defined to describe transi
tion constraints, and various results on related decision problems
are given.
The third chapter deals with incomplete information.
Bossu and Siegel introduce a system of nonmonotonic reasoning
in order to check the validity of database transactions. It in
cludes integrity rules as well as transaction rules, and it is shown
that the presented proof procedure is complete and correct with
respect to incomplete information.
Imielinsky favours the bottomup 'algebraic' method in
contrast to the topdown proof theoretic strategy for answering
queries in databases with incomplete information. Theorem
proving methods are only used for a required refinement of
queries, where the extended relational algebra methods yield
to an approximation answer. This yields to a twophase tech
nique for query evaluations.
The fourth chapter deals with abstract data types for
formal specifications and views in database system. Veloso and
Furtado present a multistep methodology for the formal speci
fication of databases based on the algebraic approach of abstract
data structures. The proposed strategy realises a stepwise refine
ment method, where each step is within a single algebraic forma
lism itself.
Paolini and Zicary give a precise algebraic model to forma
lize the relationship of databases and views. Databases as well as
views are modeled as algebras, i.e. sets of possible valid states and
possible operations. The relationship between databases and
_~~
BOOK REVIEWS
views are expressed by morphisms between both of these classes
of abstractions. This provided formalism is used to classify views.
The last chapter on query language theory consists of a
single paper of Imielinsky and Lipsky on undecidable equivalence
problems for relational expressions. Two versions of relational
algebras are considered, and the undecidability of the equivalence
and finite equivalence problem for various restricted expressions
are shown. These results are minimal in the sense that further
restrictions yield to the decidability of the mentioned problems.
H. Noltemeier, D. Ruland
Universitat Wirzburg
Matrix Computations
By G. Golub and C. F. van Loan
North Oxford Academic Publishing Company
Oxford, 1984
This book provides a comprehensive, advanced survey of
the field of numerical linear algebra as needed by scientists and
engineers working in many different areas. Although modern
developments of the lively field are discussed in survey articles
and some specializing books are available, the broad and neverthe
less indepthtreatment given will be highly appreciated.
After three short introductory chapters on the necessary
background from linear algebra, chapter 4 discusses Gaussian
elimination including roundoff error analysis. Chapter 5 on
special linear systems is devoted to the question of how to exploit
inherent special structures, e.g., positive definitness, bounded
systems, block triagonal structure, Vandermonde and Toeplitz
systems. Chapter 6 discusses orthogonalization and least squares
with special attention to rank deficiency. Chapter 7 addresses
the unsymmetric eigenvalue problem and develops in detail the
QR algorithm followed by invariant subspace calculations.
Further, the QZ algorithm for generalized eigenvalue problems is
considered. Chapter 8 covers the symmetric eigenvalue problem.
Besides the QR algorithm and its variant for singular value decom
position, some special procedures are described. In view of
parallel computing, the Jacobi method is discussed too. Chapters
9 and 10 are devoted to the treatment of large, sparse, symmetric
systems. The lanczos method and the conjugate gradient method
are presented with applications to linear equations and least
squares. Chapters 11 and 12 discuss special problems/applica
tions which can be solved using algorithms froni previous
chapters. Chapter 11 on functions of matrices discusses eigen
values, approximation and the matrix exponential. Chapter 12
contains mainly applications of the singular decomposition
technique.
Every section of a chapter closes with some exercises and
annotated references. A '.;1.11.. i pl.. with more than 400 papers
is included.
The book may serve as an advanced text book for preparing
courses in numerical linear algebra as well as an uptodate refer
ence book for research and teaching in areas using matrix compu
tations, e.g., mathematical programming or computational
engineering. We highly recommend the book for everyone
working on related subjects.
U. Zimmermann
University of Cologne
Books for review should be sent to the Book Review Editor, Prof. Dr.
Achim Bachem, Mathematiches Institute der Universitit zu K61n,
Weyertal 8690, D5000 Kiln, W. Germany.
JOURNALS & STUDIES
Vol. 30 No. 1
E. Balas and J. B. Mazzola, "Nonlinear 01 Programming: I.
Linearization Techniques. "
E. Balas and J. B. Mazzola, "Nonlinear 0I Programming:
II. Dominance Relations and Algorithms. "
A. Hordijk and L. C. M. Kallenberg, "Transient Policies in
Discrete Dynamic Programming: Linear Programming Including
Suboptimality Tests and Additional Constraints. "
M. J. Best, "Equivalence of Some Quadratic Programming
A '. ; ... "
J. Beck and J. Spencer, "Integral Approximation Se
quences. "
L. Nazareth, "An Alternative Variational Principle for
Variable Metric U. '.. .. "
P. T. Harker, "A Variational Inequality Approach for the
Determination of '' ;. ' Market Equilibrium."
Mustafa AkgIl, "On Polyhedral Extension of Some LP
Theorems. "
Vol. 30 No. 2
U. Passy and E. Z. Prisman, "Conjugacy in QuasiConvex
Programming."
J.L. Goffin, "Variable Metric Relaxation Methods, Part II:
The Ellipsoid Method."
M. Fukushima, "A Descent Algorithm for NonSmooth
Convex Optimization."
P. E. Gill, N. I. M. Gould, W. Murray, M. A. Saunders, and
M. H. Wright, "Weighted GramSchmidt Method for Convex
Quadratic P.. ;. .."
G. van der Laan and L. P. Seelen, "Efficiency and Imple
mentation of Simplicial Zero Point Algorithms. "
J. Mandel, "Convergence of the Cyclical Relaxation Method
for Linear Inequalities. "
D. M. Topkis, "Adjacency in Polymatroids."
J.Ch. Pomerol, "A Note on I' '' Infisup Theorems."
Technical Reports & Working Papers
Stichting Mathematisch Centrum
Kruislaan 413 1098 SJ Amsterdam
PothuI 4079 1009 AB Amsterdam
THE NETHERLAXNDS
E. A. van Doom, "On Orthogonal Polynomials on a Half
Line and the Associated KernelPolynomials, BW 182.
E. A. van Doom, "Some Analytical Aspects of the Peaked
ness Concept," BW 183.
G. Picci and J. H. van Schuppen, "On the Weak Finite
Stochastic Realization Problem," BW 184.
H. Hazewinkel, J. H. Lewis and C. Martin, "Symmetric
Systems with SemiSimple Structure Algebra: The Quarternionic
Case, BW 185.
E. A. van Doorn, "Connectivity of Circulant Digraphs, BW
186.
P. S. Krishnaprasad, S. I. Marcus and M. Hazewinkel,
"Current Algebras and the Identification Problem," BW 187.
J. K. Lenstra and A. H. G. Rinnooy Kan, "Scheduling
Theory Since 1981: An Annotated Bibligraphy," BW 188.
G. A. P, Kindervater andJ. K. Lenstra, "Parallel. I Ur..rl,.. r
Optimization: An Annotated ;Jl.i.l.;p't, BW 189.
E. A. van Doom, "A Note on Delbrouck's Approximate
Solution to the Heterogeneous Blocking Problem," BW 190.
J. H. van Schuppen, "The Weak Stochastic Realization
Problem for DiscreteTime Counting Processes, BW 191.
J. P. C. Blanc, "The Relaxation Time of Two Queueing
Systems in Series, BW 192.
C. van Putten and J. H. van Schuppen, "Invariance Proper
ties of the Conditional Independence Relation, BW 193.
A. Bensoussan and J. H. van Schuppen, "Optimal Control
of Partially Observable Stochastic Systems with an Exponential
ofIntegral Performance Index, BW 194.
University of Bonn
Department of Operations Research
Nassestr. 2
D5300 Bonn 1, West Germany
M. Skowronska, M. M. Syslo and C. Zamfirescu, "An
,A ..: . : Characterization of Total Digraphs, WP 83302OR.
U. Faigle and R. Schrader, "Minimizing Completion Time
for a Class of Scheduling Problems, WP 83303OR,
B. Korte and L. Lovasz, "Relations Between Subclasses of
Greedoids, WP 83304OR.
U. Derigs, "Uber eine Anwendung statistischer Schranken
in der kombinatorischen Optimierung, WP 83305OR.
U. Faigle and R. Schrader, "Zur Maschinenbelegungs
planung unter TNIgeordneten Restriktionen," WP 83306OR.
S. Holm, "Dual Price Function v. Dual Prices for the
Capital Budgeting Problem, WP 83307OR.
U. Faigle and R. Schrader, "Comparability Graphs and
Order Invariants," WP 83308OR.
M. A. Gurgel and Y. Wakabayaschi, "A Result on
HamiltonConnected Graphs," WP 83309OR.
G. Cornuejols and W. H. Cunningham, "Compositions for
Perfect Graphs, "WP 83310OR.
A. Bachem and W. Kern, "Adjoints of Oriented Matroids,"
WP 83311OR.
M. Vlach, "On the ThreePlanar Sums Transportation
Polytope, WP 83312OR.
U. Derigs, "Exchange Properties and Kbest Strategies in
Combinatorial Optimization," WP 83313OR.
G. Turn, "On the Greedy Algorithm for an Edge
Partitioning Problem," WP 83314OR.
Technical University Graz
Institute fiir Mathematik
Kopernikusgasse 24
A8olo Graz
AUSTRIA
R. E. Burkard and F. Rendl, "A Thermodynamically
Motivated Simulation Procedure for Combinatorial Optimization
Problems," 8312.
R. E. Burkard, J. Krarup and P. M. Pruzan, "Some Rela
tionships Between Multicriteria and Parametric Discrete Optimi
zation Problems with Bottleneck Objectives, 8313.
R. E. Burkard, "Quadratic Assignment Problems," 8320.
R. A. CuninghameGreen and R. E. Burkard, "Eigenfunc
tions and Optimal Orbits, 8330.
R. E. Burkard, "Locations with Spatial Interactions 
Quadratic Assignment Problems, 8331.
R. E. Burkard, H. W. Hamacher and J. Tind, "On General
Decomposition Schemes in Mathematical Programming,"
University' di Pisa
Dipartimento di Ricerca Operativa
e Scienze Statistiche
Pisa, ITALY
A. Maugeri, "Applicazioni delle disequazioni variazionali a
problem di traffic su reti, 1983, No. 96.
A. Volpentesta, "Row Circular Matrices and Related
Polyedra," 1983, No. 97.
A. Cambini, "Sulla regolarira nei problem di estremo
vettoriale, 1983, No. 98.
P. Favati and M. Pappalardo, "Sulla reciprocity nei prob
lemi di estremo vettoriale, 1983, No. 99.
L. Pellegrini, "Scomposizione di problem di estremo
vincolato mediante la teoria della duality," 1983, No. 100.
O. Ferrero, "Sulla convessita" della restrizione di una forma
quadratica su un poliedro ed alcune applicazioni," 1983, No. 101.
G. Giorgi and S. Mititelu, "Extremum Conditions in Quasi
Convex Programming," 1983, No. 102.
 ~ ~I~s~~ ~ ~~~
(ALLIMAUFRY
Alexander H.G. Rinnooy Kan will be spending the fall semester of
1984 at the Sloan School of Management (M.I.T.) and the i 'ni, semester
of 1985 at the Department of Industrial Friii..n..liii. and Operations
Research at the School of Business Administration of the University of
California at Berkeley...H.P. (Paul) Williams has moved from the Chair of
Management Science at Edinburgh University to the ( h.iI of Operational
Research at Southhampton University .The MP Study based on research
papers at the recent NATO ASI (see article, page 2) has a submission
deadline of November 15, 1984. Submission is not limited to papers from
the meeting, but is open to everyone. Title of the Study will be Computa
tional Mathematical Programming. .Ralph E. Gomory, Vice President
and Director of Research at IBM, was awarded the John von Neumann
Theory Prize by ORSA/TIMS at the May meeting in San Francisco. Dr.
Gomory was cited for his contributions in in I. .,. r Programming, especial
ly the cutting plane methods and papers on special problems such as the
knapsack, traveling salesman, and cutting stock problems.
Deadline for the next OPTIMA is December 1, 1984.
New Superfast LP Method?
The September, 1984 issue of Science
contains an article by Gina Kolata on a new
method for linear programming developed
at AT&T Bell Laboratories. According to the
article, Narendra Karmarkar has developed a
polynominal time algorithm which
approaches the optimal vertex by creating a
sequence of spheres inside the feasible
region. Pi. linriir.. computational results
show the method to be 50 times faster than
an IBM code of the simplex method on
problems with 5000 viariables.
D. Hearn
This public document was promulgated at a
cost of $426.15 or $0.61 per copy to inform
researchers in mathematical programming of
recent research results.
OPTIMA
303 Weil Hall
College of Engineering
University of Florida
Gainesville, Florida 32611
%i~dC~ ~
FIRST CLASS MAIL
C ALE N DAR
This Calendar lists noncommercial meetings specializing in mathematical programming 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'.) Any one knowing of a meeting that should be listed here is
urged to inform Dr. Philip Wolfe, IBM Research 332, POB 218, Yorktown Heights, NY 10598, U.S.A;
Telephone 9149451642, Telex 137456.
Some of these meetings are sponsored by the Society as part of its worldwide 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.
1984
August 2729: 9th Symposium on Operations Research, Osnabrtck, Federal Republic of Germany.
Contact: Professor Dr. P. Brucker, Universitat Osnabriick, Fachbereich Mathematik, Postfach
4469, D4500 Osnabrtick, F.R.G. Telephone 0541 608 2564. Sponsored by the German
Society for Mathematics, Economics, and Operations Research.
September 1017: 'International Symposium on Stochastic Optimization', Kiev, U.S.S.R. Contact:
Professor Andrzej Wierzbicki, International Institute for Applied Systems Analysis, A2361
Laxenburg, Austria. Telephone 02236 71521, Telex 079137 iiasa a. Cosponsored by the
Society through the Committee on Stochastic Programming.
October 1012: Symposium on Multiobjective Optimization, University of NebraskaLincoln, Nebraska,
U.S.A. Contact: Ann Bleed, 310 Agricultural Hall, University of Nebraska, Lincoln, NE
68583. Telephone 4024723305.
October 1112: Fifth Mathematical Programming Symposium Japan, Fukuoka, Kyushu, Japan. Recent
Topics in Mathematical Programming, Stochastic Programming, and Applications. Contact:
Professor Masao Iri (General Chairman), Faculty of Engineering, University of Tokyo,
Bunkyoku, Tokyo 113, or Professor Nasata Furukawa (Program Chairman), Department of
Mathematics, Kyushu University, Fukuoka 812, Japan.
December 1214: 23d IEEE Conference on Decision and Control, Las Vegas, Nevada, U.S.A. Contact:
Abraham Haddad, School of Electrical Engineering, Georgia Institute of Technology, Atlanta,
GA 30332, U.S.A. Telephone 4048943930.
1985
June 1114: 5th IFAC Workshop on Control Applications of Nonlinear Programming and Optimization,
Capri, Italy. Contact: Professor G. Di Pillo, Dipartimento di Informatica e Sistemistica,
UniversitA degli Studi di Roma 'La Sapienza', Via Eudossiana 18, 00184 Roma, Italy. Tele
phone (39) 6484441.
August 59: Twelfth International Symposium on Mathematical Programming in Cambridge, Massachu
setts, U.S.A. Contact: Professor Jeremy Shapiro, Sloan School of Management, Massachusetts
Institute of Technology, Cambridge, MA 02139, U.S.A. Telephone 6172537165. Official
triennial meeting of the MPS.
Application for membership
Mail to: MATHEMATICAL PROGRAM i'l\l G SOCIETY, INC.
c/o International Statistical Institute
428 Prinses Beatrixlaan
2270 AZ Voorburg, The Netherlands
(I. i'.;: or money orders should be made payable to The Mathe
matical Programming Society, Inc. in one of the currencies
indicated below.
lj I wish to enroll as a member of the Society. My dues payment
for 1984, which covers subscription to volumes 2830 of
MATHEMATICAL PROGR MMI!NG is enclosed: Dfl. 94.00
(or $32.00 or 20.00 or Sw.Fr. 68.00 or FF 250.00 or DM
81.00).
1 As a member of the Society I wish to subscribe to the serial
edition of MATHEMATICAL PROGRA.MMING STUDIES,
volumes 23, 24. Payment is enclosed: Dfl. 20.00 (or
$10.00 or 6.25 or Sw.Fr. 22.25 or FF 77.00 or DM 26.00).
My subscriptions) is (are) for my personal use and not for the
benefit of any library or other institution.
Name (printed): ...................................... .......Signature: ...........................
Mailing address (.'. print): ....................................................................
Student Applications: Dues are onehalf the above rates. Have a faculty member verify your student status below and send
application with dues to the above address.
F j. .!t. verifying status ........................................ .Institution ...........................
__
