Title: Optima
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Permanent Link: http://ufdc.ufl.edu/UF00090046/00018
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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: May 1986
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Number 18
May 1986

Some Observations on

Mathematical Programming

by Alex Orden
(From the Opening Session Address at the
Boston Symposium, Ed.)

D he Constitution of the MP
Society calls upon the Chairman
of the Council to give a report
on the state of affairs of the
Society at the end of his term of office.
It seems a bit odd for that to be included
in the Constitution, but so be it. The
Constitution also specifies that the
Chairman's term of office runs until one
year after each of the triennial interna-
tional symposia, at which time the
Chairman-elect becomes Chairman. So at
this point a year from now, Michel
Balinski will become Chairman, and I
will then perhaps, heeding the Constitu-
tion, prepare a final report. The time of a
symposium seems then to be a time for
an interim report, or more accurately in
this case, for some general observations.
It is appropriate here to examine broad
matters which surround our scientific
domain. Let us look at matters for which
a much wider time frame than that of
scientific developments of the last two or
three years is appropriate. I will sweep
from 1950 to 2072, from 35 years ago to
nearly 100 years into the future.
1950 is a nice round mid-century year
back around the time when Mathematical
Programming was getting started. No
computer program for the simplex method
had yet been written; in fact I think no
suitable computer had yet been success-
fully built and put into operation. In the
timetable which the MP community
devised in about 1965, "Symposium
Zero" took place in 1948 as part of a
meeting of Econometricians at the
University of Chicago at which George
Dantzig first formally presented the
foundations of linear programming.

Tjalling Koopmans subsequently produced
the famous conference proceedings on
"Activity Analysis." In 1950 Sym-
posium 1, the first devoted entirely to
linear programming, had not yet occurred.
That took place in 1951, and as you
know, Symposium 12 in 1985.
(With June 1950 in mind, I can't resist
reminiscing that about 75 yards from this
podium, there is a gymnasium which was
used at that time for commencement cere-
monies. That was where MIT granted me
a diploma which confirmed that I had
taken enough courses in mathematics and
written a suitable dissertation so that I
could go on to other things. I expected to
engage in mathematical applications of
the about-to-explode field of electronic
digital computers. And so a couple of
months later, totally unaware that the big-
bang called the simplex method had been
invented, I found myself working with
George Dantzig in the Pentagon on the
mathematics of linear programming and
on initial computer programs for solving
LP problems.)
As for the other reference year in this
discussion 2072 that will be the 100th
anniversary of the founding of the
Mathematical Programming Society.
Everyone here knows, I suppose, that the
MP Society is a world-wide organization
for fostering research and other activities
in its field. In offering some thoughts on
the place of the Society in the field along
broad lines which we don't usually dis-
cuss, I will look first at the professions
which have participated in research in
mathematical programming during the
past 35 years, and then briefly at the role
of MP in the world at large, looking
speculatively at the far future.
First, a digression about international
societies: In the political, economic, and
social arenas world-wide organizations
Continued on page 2

M martin Beale (1928-1985)

Sartin died at his home in
Cornwall on December
23rd, 1985, having been
seriously ill for several
months. Participants at
the Mathematical Programming
Symposium in Boston last summer
witnessed his courage and selflessness, and
there seemed to be no end to his enthu-
siasm for the successful development of
our subject. We can remember him
sitting at the front of a lecture room, both
figuratively and literally, in order to take a
close interest in events and to contribute
his views to discussions. Occasionally he
found himself at centre-stage; the Mathe-
matical Programming Society (MPS) as
well as mathematical programming re-
search and applications have gained greatly
from his leadership.
He was educated at Winchester and at
Trinity College, Cambridge, graduating in
Mathematics in 1949 and gaining a
diploma in Mathematical Statistics in
1950. He then joined the Mathematics
Group of the Admiralty Research Lab-
oratory in Teddington, England, where he
worked for 11 years with Stephen Vajda,
except for a leave of absence in 1958 at
the Statistical Techniques Research Group
of Princeton University. In 1961 he
moved to become Manager of Mathe-
matical Statistics at CEIR (now Scicon)
in London, where he was promoted to
Technical Director in 1968. Further, he
accepted a visiting Professorship in the
Mathematics Department, Imperial
College, University of London, in 1967.
Thus he was both an academic and an
industrial applied mathematician for the
last 18 years.
Since the MPS grew from the
sequence of mathematical programming
symposia, his part in the organisation of
the London symposium in 1964 can be
Continued on page 3


- -- ~

2J Some Observations from page 1

strive with little visible progress to find
paths to harmony in a world of terrifying
discord. The United Nations is the
clearest example. In the "scientific
world" things are much better, but the
discord and disorganization of mankind
penetrates. Those who undertook in 1972
to establish the MP Society soon learned
that they were forming an entity which
would have no legal status. We live in a
world in which the laws, all laws, are the
laws of nations. There are no interna-
tional laws, only some treaties and other
agreements for which there are no enforce-
ment mechanisms. We learned back in
1972 that in setting itself up to be truly
international, the MP Society would be
born in a legal vacuum, stateless, like a
stateless person.
But in a legal vacuum or not, inter-
national scientific organizations do exist,
and in contrast to political organizations
they commonly operate in a fairly good
state of harmony. At times one senses a
wistful feeling in the international wilder-
ness about how nice the world would be if
only international political, economic, and
social organizations were as harmonious
as scientific organizations. What a
utopian thought! Since international sci-
entific organizations operate harmoniously
in a legal vacuum, it seems we should
aspire to world conditions so benign that
laws are unnecessary.
While the MP Society, like many
international scientific societies, operates
largely in harmony, it does contain
factions. I suggest that the professions
which participate in MP research be the
identifiers of the factions.
There are in the first place many
specialists in MP who, when among their
colleagues, comfortably indicate that
professionally they are "mathematical pro-
grammers," thereby giving a clearer
indication of the nature of their work than
saying that they are mathematicians,
engineers, economists, or the like. In
other words, a considerable number of
those here would be glad to be known as
"mathematical programmers" if the world
at large knew what that meant. But there
the phrase is unknown, or worse yet, is
understood erroneously. In that renowned
vehicle-of-record, the New York Times, in
which we have been glad (or I could say
proud) to see items on new developments
in MP appear occasionally on the very
front page, I doubt that there is even one
editor or reporter who knows that there are
people who identify themselves pro-
fessionally as "mathematical program-
mers." And now coming to the worse-
yet part, I doubt that anyone connected

with the NY Times knows that the word
programming in the term, mathematical
programming, refers to the planning of
activities, not to the programming of
computing machines.
Now, while there are, I believe, many
at this symposium and elsewhere for
whom what I have just said applies, there
are in the MP society and in the field
overall, other important constituencies.
The largest, described in ways with which
you may not fully agree, are:
1. Mathematicians: Those who view
themselves as mathematicians whose
strongest interests happen to lie in the-
orems and algorithms for extremal
problems, or more specifically, con-
strained optimization. The mathe-
maticians in the MP field are interested in
developing appropriate theorems and
mathematical properties of algorithms
while the "math programmers" are not
content unless the results of their work on
the mathematics, algorithms, and compu-
tation contribute to solution of real-world
2. Operations Researchers: Those who
consider their professional field to be
technical support of planning and decision
making by means of all formalizable
methods ranging across mathematical
modeling, statistics, computer-based
heuristic simulation and, nowadays, pro-
spectively the computerization of complex
logic which goes under the rubric, "expert
3. Computer Scientists: Those whose
view of their profession is that in
conjunction with the mammoth phenom-
enon known as "the computer" there has
come to be an underlying scientific field
which, for lack of a better-sounding term,
is called Computer Science, and within
that discipline happen to specialize in
optimization and combinatorics algo-
rithms and in related matters involving
computational complexity, software for
model generation, prospective advances in
parallel computing, and possibly the link-
age of artificial intelligence to mathe-
matical programming.
There are still other professional
constituencies in MP, particularly engi-
neers and economists, but the influence of
those disciplines on MP research is
currently smaller than those which I have
previously listed. Back in 1950, econ-
omists were probably the largest group,
but the participation of economists in
recent symposia in MP has been quite
Over a recent time span, say the last
10 years, what has been happening, I
believe, is that the proportion of two of

the constituencies, those who think of
themselves professionally as math pro-
grammers and those who view them-
selves as mathematicians (with strong
interest in MP) have not changed. The
proportion of operations researchers seems
to have declined somewhat, and that of
computer scientists has clearly grown.
Certainly if you look over the program of
this symposium, you will see a signi-
ficant number of papers which would be
equally appropriate at a meeting of com-
puter scientists.
Clearly the presence of several types
of researchers invigorates this sympo-
sium. Much will be gained from the flow
of ideas between the math programmers,
the mathematicians, the operations re-
searchers, the computer scientists, and
others. It is pertinent at the same time to
ask whether the constituencies are factions
which, as in international political or
economic or social organizations, have
conflicting interests. In some ways I
believe they do.

although I've laid some groundwork,
I'm not inclined on this occasion to
probe those issues. In the
operations research societies there are
heated controversies be- tween
theoreticians and practitioners, but that is
not the heart of the matter in the MP
Society. For us it is important in the
first place to assess which kinds of
research in MP have the best prospects of
high and lasting significance, and
secondly, in my opinion, to identify and
practice the scientific paradigms which are
best for our kind of science.
To do that calls for a "vision" of the
field. Allow me to go beyond vision to
visionary. I raise two questions:
1. In a far reaching (perhaps utopian)
sense, what are the broad aims of MP,
expressed in terms which can be easily
understood by the world at large?
2. How important is the MP field to
that world at large, not only now, but
quite far off in the future?
In order to address these questions, I
ask first that you distinguish between
modeling for optimization in engineering
and MP-type modeling in matters of
human organization and business affairs.
Engineering models are based on princi-
ples of physical science and engineering,
and what sometimes comes up is a need
for optimization algorithms to solve
given problems. But in organizational
and business matters, and so to speak in
human affairs in general, math pro-
gramming developments involve not only
(continued on next page)

-----~-------~e ~----- ~ I

Martin Bealefrom page 1

regarded as his first major contribution of
the activities of the Society. In 1971 the
original Founding Committee of the MPS
(J. Abadie, M.L. Balinski, A. Orden,
A.W. Tucker, P. Wolfe and G.
Zoutendijk) was extended to an Organising
Committee that included Martin. The
members of the newly-formed society then
chose him as their first "Chairman-Elect,"
so in 1974 he succeeded George Dantzig
as Chairman of the MPS. During his
chairmanship the first issue of Mathe-
matical Programming Studies appeared
and the Working Committee on Algo-
rithms was established, but his two years
of leadership seemed to pass in a flash, for
Al Tucker replaced him at the Budapest
symposium in 1976. However, he was
elected again to Council in 1982.
Further, he served as a Senior Editor of
Mathematical Programming and of Mathe-
matical Programming Studies after these
journals were founded. These appoint-
ments give some indication of his
contributions to the Society, and we are
indebted to him.
His range of professional interests and
his participation in many fields are
remarkable. In addition to his activities in
the MPS, he was a member of the
International Statistical Institute, a Fellow
of the British Computer Society, a Vice
President of the Institute of Mathematics
and its Applications, and both an
Honorary Secretary and a Vice President of
the Royal Statistical Society. He was
awarded the Silver Medal of the Opera-
tional Research Society and was elected a
Fellow of the Royal Society of London in
1979 "for his applications of mathe-
matical and statistical techniques to
industrial problems, and for his contribu-
tions to the theory of mathematical
programming." Further, he became a
member of Council of the Royal Society
in 1984.
The intersection of his research
interests with mine include quadratic pro-
gramming and the conjugate gradient
method for nonlinear optimization. In
both of these fields his work is of central
importance. Further, I believe that his
contributions to discrete optimization
have had a greater impact and that his
research in statistics was just as strong.
Further, he applied mathematical
programming and statistical techniques

very successfully for the modeling and
solution of many serious real problems.
This extraordinary range of skills was
surely far more than a consequence of the
needs of customers of Scicon. Indeed, he
was the most assiduous listener to papers
at conferences that I have known, his
thirst for professional knowledge was
unquenchable, and he communicated his
expertise very readily. Discussions with
Martin helped my own work directly, and
I am sure that the indirect benefits are far
greater. Here I have in mind not only his
contributions to knowledge and their part
in further research, but also his influence
at the interface between the development
of algorithms and real-world computing.
It is of vital importance to our subject
that much of our work is actually useful,
but most computer users find published

algorithms indigestible. Therefore,
Martin's achievements in bridging this
gap are of outstanding value to the global
standing of mathematical programming.
The mathematical programming
community abounds with affectionate and
lively memories of Martin. We can recall
his self-effacement, his gentleness, his
delightful humor, his dislike of unnec-
essary mystification in mathematics, and
his intellectual honesty. Let me leave
you with your personal memories of
Martin, as George Dantzig and John
Tomlin are compiling a biographical
portrait of him. We are thoroughly
grateful for his warm friendship and for
his illustrious career in mathematical
MJ.D. Powell
March 20, 1986

Some Observations continued

algorithms but mathematical structures
which people may sooner or later choose
as the best way to organize how to think
about various problems. There is a
profound difference between the latter and
the computation of solutions to given
engineering problems. We should not
carry lightly views and paradigms from
engineering and physical science into
math programming for human affairs.
With this in mind my (visionary) answer
to question 1 above is:
All human beings, in most aspects of
their lives and particularly in the
organization and economic aspects, seek
constantly, sort of minute by minute, to
attain objectives. Math programming is
the science of expressing those human
efforts in mathematical form and finding
solutions to the mathematical formula-
It is conceivable that the devel-
opment and introduction of ways to think
in math programming terms about
common organizational and business
problems are at present in their relative
infancy, with a current role in human
affairs which is analogous, say, to that of
air transportation in about 1920. Such an
analogy has, of course, no predictive
value, but the view that a time may come
when the role of mathematical optimiza-
tion in society is a great deal larger than it
is today is, for researchers in our field, at
least a fond hope. The question of

whether MP will come to have an
extensive role in the world at large may be
phrased: will such a time ever come, and
if so, how far off is it?
Any attempt to answer this question is
wildly speculative. I will go only so far
as another, perhaps better, analogy:
The MP Society is an organizational
symbol of math programming as a field of
knowledge. In 1972 when the Society
was established, we made a deal with the
International Statistical Institute's head-
quarters in The Hague to provide us with a
secretariat, that is with a place for keeping
our membership records, for issuing and
tallying election ballots, and the like. It
was comforting that the ISI was a
distinguished international organization of
the kind that we aspired to become. ISI
was founded in 1885 and is celebrating its
100th anniversary. The growth of know-
ledge of statistical concepts and methods
and the spread of the scientific use of
statistics in innumerable human activities
since 1885 has been phenomenal. Will
the growth of math programming from
1972 to 2072 be comparable? Will MP
or related models and solutions for many
everyday problems in human planning be
as ordinary on the 100th anniversary of
the founding of the MP Society as use of
at least the basic techniques of statistics is
today, 100 years after the founding of the
ISI? Perhaps so. If so, our work is
paving the way.

-- -- -~II----~-I-- ~- "-- -~-~ -~- P---- -----


Global Optimization
Computational Study
A computational study of algo-
rithms for global optimization
will be carried out in accordance
with guidelines discussed during a
recent SDS-IIASA workshop in
this area.
As a first step, appropriate test
prob- lems are being assembled
featuring arbitrary objective
functions and con- straints. (Test
problems for the special case of
concave functions subject to linear
constraints are available from J.B.
Rosen, 136 Lind Hall,
Minneapolis, MN 55455, U.S.A.)
Those interested in contributing
to the computational study are
invited to contact C.G.E. Boender
and A.H.G. Rinnooy Kan,
Econometric Institute, Erasmus
University Rotterdam, P.O. Box
1738, 3000 DR Rotterdam, The
-A.H.G. Rinnooy Kan


April 6-8, 1987
Southampton, U.K.

A conference on the theory and
application of Combinatorial Op-
timization in Operational Research,
Management Science, Computer
Science and Statistics will be held at
the University of Southampton,
U.K., from April 6 to April 8,
The topics include integer
program- ming, complexity theory,
analysis of algorithms, polyhedral
combinatorics, applications to
coding theory and cryptography,
parallel and sequential computing,
Abstracts of contributed papers
should be sent before January 5,
1987 to
The Secretary, CO'87
Department of Mathematics
University of Southampton
Southampton S02 5NH, U.K.

.1. ..

The Seventh Mathematical Programming
Nagoya, Japan
November 6-7, 1986
This annual symposium will be held November 6-7, 1986, at
Nagoya International Center, Nagoya, Japan. It will consist of
the following three sessions:
1.Mathematical Programming, General. Chairman: S.
2. Scheduling and Production Control. Chairman: T. Ibaragi.
3.Applications. Chairman: S. Enomoto.
The first two sessions will consist of three or four talks of an
expository nature and those presenting original development.
There will be no call for contributed papers; only invited papers
will be presented.
Participation from abroad will be welcomed. The conference
language is Japanese, but non-Japanese participants may use
For further information contact Organizing Chairman,
Professor Masao Iri, Faculty of Engineering, University of
Tokyo, Bunkyo-ku, Tokyo 113, Japan, or Program Chairman,
Professor K. Sawaki, Faculty of Business Administration,
Nanzan University, Nagoya 466, Japan.

------1 "1 _2

Call for Papers

International Conference on
Vector Optimization

This conference will be held August
4-7, 1986, at the Technical University
of Darmstadt, F.R. Germany. Par-
ticipation is open. Authors are invited
to submit abstracts by May 1, 1986. A
proceedings will be published. For
further information write Vector
Optimization, Tech. University of
Darmstadt, FB4-AG10, 6100 Darm-
stadt, F.R.G.

-- -- -- ----- ---

George Mason University
Systems Engineering Department

Applications are sought to fill a
tenure-track opening at the
assistant, associate, or full
professor level. Candidates should
have a Ph.D. in operations
research, systems engineering,
applied mathematics, etc., with
strong interest in computational
issues in mathematical program-
ming. Applicants must demonstrate
outstanding achievement or poten-
tial for research and a commitment
to graduate and undergraduate
Application letter, vita, and three
reference letters should be sent to:
Carl Harris, Chairman, Department
of Systems Engineering, 4400
University Drive, George Mason
University, Fairfax, VA 22030.

1 II

A Model-Management Framework for
Mathematical Programming
By Kenneth H. Palmer
John Wiley, New York, 1984
ISBN 0-471-80472-X
This book covers one aspect of the application of linear
programming to real problems in real industries, namely the care
and feeding of large formulations. It gives a description of the
software system PLATOFORM (Planning Tool written in
DATAFORM), a support system for mathematical pr. grarmning
applications. PLATOFORM was developed using the Enhanced
Mathematical Programming System (EMPS) and its associated
language, DATAFORM. The products are currently marketed as
MPS III by Ketron, Inc. All six of its authors have been closely
involved with the basic design and subsequent growth of this
system which, since 1972, has been an indispensable tool used
throughout Exxon, one of the largest international corporations.
Thus, most of the examples used to illustrate the text are based on
an oil-refining application. The main feature of PLATOFORM is
the possibility of adapting to any application. PLATOFORM has
proven useful in the field of nonlinear models as well.
This book contains 12 chapters. The first two deal with his-
torical development within Exxon. Chapter 3 provides sufficient
details of the DATAFORM language. The detailed structure of
PLATOFORM is described in chapters 4 through 11: Data and File
Structure, System Structure, Input Syntax, Data Management, File
Management, Matrix Generation, Optimization, and Report
Writing. By the end of Chapter 11, the reader will have been
exposed to internal construction of quite a complex system. The
purpose of the final chapter is to look at this system from the
user's point of view. The authors have taken a simplified oil-
refining problem to show how PLATOFORM would be used to set
up, solve and report on such a model.
The book is easy to read and well-illustrated. Each chapter
concludes with a summary and has many links to other sections.
The pros and cons of conception and solution are considered in
full detail from a practical point of view. Thus, it is not a big
surprise that literature references are not given!
The material presented will be of use and interest to:
Practitioners of LP who need to know the problems that arise
in its application and ways to solve them.
Developers of LP-software so that their products match the
requirements of actual business problems.
* Those in academia who teach and study these topics.
-K.-P Schuster

Stochastic Models in Operations Research
Vol. I, II
By D.P. Heyman and MJ. Sobel
McGraw-Hill, Hamburg, 1982/84
ISBN 0-07-028631-0
ISBN 0-07-028632-9
These books are divided into three parts. In Part A the basic
theory of stochastic processes is presented with its illustrations in
Operations Research and other fields. In Part B operating
characteristics of a wide variety of models, primarily of conges-

tion and storage type, are investigated. These two parts form
Volume I. Part C, in Volume II, handles optimal control problems
of stochastic processes.
Part A, a short and revealing chapter, introduces the reader to
the areas of application of stochastic processes. Then a few pages
are devoted to definitions which are followed by seven chapters
entitled: Birth-and Death Processes, Renewal Theory, Renewal-
Reward and Regenerative Processes, Markov Chains, Continuous-
Time Markov Chains, Markov Processes, and Stationary Processes
and Ergodic Theory.
In Part B there are three chapters. The first has the title
System Properties and deals with problems such as reservoir
operation, inventory control, and effects of order of service
priorities on waiting times concerning queuing models. The
second chapter deals with networks of queues. In the third
chapter, Bounds and Approximations, primarily queuing and
diffusion processes are investigated. Volume I ends with
background material on Probability Theory.
In Part C, elementary models of stochastic optimization are
mentioned. Then the expected utility criterion is discussed in
detail. The next chapter, Myopic Optimal Policies, handles
control of finite and infinite horizon decision processes with one
and more-than-one decision variable. The following three
chapters are devoted to Markov decision processes. The authors
always start with nice elementary problems and turn to the more
general theory when the practical importance of the processes
involved is well understood. Many methods, including linear
programming, are mentioned to find optimal policy. The next
two chapters analyze classes of models, primarily of production
and inventory type, with specially structured optimal policies.
Finally, there is a chapter on sequential games which generalizes
Markov decision processes. This volume closes with some
background material on Probability Theory and Mathematical
These books are very well written and can be recommended for
teaching in graduate schools. While primarily textbooks, they
can be used by practitioners too for the solution of classes of
control problems of stochastic processes. The only critical
remark of the reviewer is that the very powerful and very practical
branch of science, stochastic programming, is entirely left out.
Thus the books, with all their merits, handle only part of the
stochastic models in Operations Research.
-A. Prekopa

Progress in Combinatorial Optimization
by W.R. Pulleyblank
Academic Press, London, 1984
ISBN 0-12-566780-9
This volume contains 21 papers presented at a Conference on
Combinatorics held at the University of Waterloo in the summer
of 1982. Included are five papers on matroid theory, two on
perfect graphs, two on total dual integrality and two on sched-
uling. The remaining subjects are: facets of polyhedra, finite
interval orders, submodular flows, submodular functions, the
ellipsoid method, combinatorial problems on matrices, greedoids,
problems in dynamic periodic graphs, heuristics for graph parti-

sr~ W,

~-s~--~-----~-~ ---~s~ ---- II

Book Reviews

tioning and integer programming.
All the material has been reviewed, and it may be considered
as an up-to-date reference for graduate students and researchers on
Combinatorial Optimization.
-F. Barahona

Algorithms & Software (Special
Fachinformationszentrum Energie, Physik,
Mathematik GmbH
Karlsruhe, 1985
This bibliography is a loose-leaf edition containing
information about both software and mathematical solution
algorithms published in scientific literature. More than 4000
documents dating to 1984 and concerning mathematical problems
as well as problems of computer science, physics, operations
research, etc., are collected in five files. A sixth file containing
an introduction and three indices (an author's index, a cross-
reference list and a KWIC-index based upon keywords) is added.
The entries are classified according to the "Mathematics
Subject Classification Scheme." The information given to each
entry is divided into three blocks. First, bibliographical data are
listed, such as the name of the algorithm, its author and its
source. The second block yields information about the documen-
tation, especially concerning the programming language, the
complexity of the algorithm, the implementation, availability,
etc. Finally, the purpose of the algorithm is described.
It is worth mentioning that no control of quality or proof of
correctness of the documents has been carried out. However,
corrections, counterexamples or a proof to the contrary, if known,
are mentioned.
-M. After and K. Mattar

Matrices and Simplex Algorithms
by A.R.G. Heesterman
Reidel, Dordrecht, 1983
ISBN 90-277-1514-9
The book is devoted to mathematical programming algorithms
and is to serve as a textbook. It consists of five chapters, all
quite long.
The first chapter deals with the fundamental tools of linear
algebra which are used in linear programming. This undergraduate
material describes the uses of matrices, systems of equations and
determinants. In the second chapter, dealing with linear
programming, the author gives the basic theory of the Simplex
Method augmented by a number of valuable hints and proposals
for the numerical treatment of problems. The third chapter
introduces mathematical programming problems under more
general circumstances. Here we find many interesting results on
optimality conditions and feasible sets. In chapter four quadratic
programming and efficient algorithms for solving quadratic
problems are discussed. The author starts with linear restrictions
and then explains the general quadratic case. The last chapter
introduces the concept of integer programming. Here the
branching method and the use of cutting planes are described. A
main feature of the book is the great number of examples,
graphical illustrations and the extensive and valuable offer of code

listings for the algorithms under discussion. These code listings
are written in a readable manner with many comments such that
they are instructive for the reader. Most of the theoretical results
are explained with numerical examples which are discussed in
But here I see a certain danger of the presentation. It is not
easy to see the theoretical and general background clearly because
one is concentrating on the example under discussion. An
additional difficulty results from a number of non-standard
definitions, such as interior point or convex function, etc. Also
the derivation of the results and algorithms is long due to the less-
formalized language.
As I see it, the main value and purpose of the book (agreeing
with the author's intention) is as a textbook for readers with
knowledge of mathematical programming rather than as an
instruction book for undergraduate students. The textbook will be
very helpful to the reader acquainted with the basic concepts of
mathematical programming and interested in numerical details as
well as in efficient codes. It will also benefit students as a
resource for numerical examples and code details.
-K.H. Borgwardt

Linear Programming
by Katta G. Murty
John Wiley, New York, 1983
ISBN 0-471-09725-X
This book is the first of a "trilogy" consisting of textbooks
on linear programming, combinatorial programming and linear
complementarity. This series is meant to extend the contents of
the book, Linear and Combinatorial Programming (1976), by the
same author. It is the aim of this first book to cover all
theoretical, practical and computational aspects of linear pro-
The first chapter discusses the methods for obtaining a linear
programming (LP) model for a given practical problem (including
e.g. piecewise linear approximation and multiobjective LPs).
Chapter 2 presents the original version of the simplex method of
G.B. Dantzig. Chapter 3 deals with the mathematical background.
All the material of linear algebra needed to understand the
mathematical theory of LP is presented. In the next chapter
duality, especially the economical aspects, is discussed in detail.
This chapter contains the various theorems of stability in the LP
models and conditions for unique solutions. Computational and
numerical aspects of linear programming (which are often omitted
in textbooks) are extensively discussed in Chapters 5-7. Guide-
lines for designing computationally efficient implementations of
the simplex method are given; column-generation techniques, dual
simplex methods and the various factorization methods are
Chapters 8 and 9 deal with the postoptimal analysis of a
linear programming problem. In Chapter 8 we can find the
parametric linear programs in detail while Chapter 9 presents the
sensitivity analysis. Degeneracy problems are considered in
Chapter 10. Here Lexico-Simplex algorithms, both in the primal
and dual case, are presented. Chapter 11 considers the bounded
variable LPs, and Chapter 12 discusses the methods for large-scale
LPs. Transportation problems are the focus of Chapter 13.

---~ I---~ I

Book Reviews

Chapter 14 discusses worst-case and average-case behaviour of the
simplex algorithm. The last three chapters extend the 1976 book.
They contain the ellipsoid method, iterative methods for LPs and
vector minima.
The book does not contain new results (of course, this was not
intended). It provides an introductory course in linear
programming as well as a basic reference for the experienced
reader since it covers all important aspects of linear program-
ming. A main advantage of the book is its clear and
understandable style. The chapters are constructed to require a
minimal mathematical background; numerous examples and
exercises are given. At the end of each chapter a brief reference
list can be found. Unfortunately, no solutions to at least a subset
of the exercises are given. This would have helped control the
reader's knowledge.
In summary, Murty's book can be rated as a valuable textbook
for the inexperienced as well as for the advanced reader.
-G. Galambos

Selected Topics in Graph Theory 2
Edited by Lowell W. Beineke and Robin J. Wilson
Academic Press, New York, 1983
Four years after the success of Selected Topics in Graph
Theory 1, which is considered one of the top six mathematical
books for 1979, Beineke and Wilson have published the second
The exceptionally favorable critique of the first volume was
well merited, and those who have read it would be as pleased with
the second. It is indeed as good as the first. This second book,
although dealing with different topics from the first one, has kept
the same spirit and style. Each chapter, written by an expert in
the field, gives a survey of that field of graph theory. The
chapters are titled as follows: Eulerian Graphs, Perfect Graphs,
Automorphism Groups of Graphs, Infinite Graphs, Extremal Graph
Theory, Random Graphs, Graphs and Partially Ordered Sets and
Graphs and Games.
The list presents a large and diversified panorama of graph
theory. The chosen topics are still the field of interest of a large
number of researchers. The choice of the topics was guided by the
need for surveys on particular topics, the timeliness of certain
areas, suggestions from colleagues and friends, and the editors'
own preferences.
In the introduction we find the same notations used by all the
authors as well as certain definitions necessary for the
understanding of any part of the book. From one chapter to
another we find a great resemblance in style, manner of
presentation, and degree of difficulty. This facilitates the
transition from one chapter to another, making it one of the more
interesting aspects of the book. Each author presents a complete
survey of his topic. Moreover, the absence of superfluous
technical details lightens the task of the reader. Most proofs are
voluntarily omitted or simply replaced by sketches of proofs or
outlines of proofs. Thus, the reader is always in touch with the
main ideas. Each author knows how to present the motivations
and the important results of the topic. Even more recent results
are given. Each chapter is 30 to 40 pages and gives a quick and
comprehensive overview of the subject. Furthermore, many (50 to

120) references are given, including the most recent. This is
important in a discipline which progresses very rapidly. This
book will interest specialists as well as advanced beginners who
are interested in a particular topic.
However, we regret the absence of the algorithmic aspect of a
large majority of the topics. Specifically, the application of the
complexity theory in graph theory should not be omitted. This
probably could be explained by the emphasis given to the pure
aspects of graph theory. Note that the graph isomorphism
problem has not been proven NP-complete yet (if it has been
proven, please give a reference) and that a line graph is not a
perfect graph. It is up to the reader to verify the rectification of
these mistakes elsewhere in the book. Note also that it would be
useful to mention the topics treated in the first volume.
Nevertheless, this is an excellent collection and is indeed
useful for professional graph theorists, for newcomers in the field,
and for experts in other fields who may want to learn about
specific topics. This book should definitely be in libraries
accessible to researchers in combinatorics. Note that Selected
Topics in Graph Theory 1 and 2 are already accompanied by a
volume which is a bit more applied, Applications of Graph
Theory, also edited by Beineke and Wilson. We would like to
inform the reader that the third volume of Selected Topics in
Graph Theory is in its gestation period.
-M. Burlet

Handbook of Algorithms and Data Structures
by G.H. Gonnet
Addison Wesley, London, 1984
Although a lot of books on data structures and algorithms
have been written, this book is outstanding and new in its field.
It is a real "handbook." A great number of useful data structures
and algorithms are listed and analysed in a compact and
convenient form.
The major advantage of this book is its extensive average case
analysis of the algorithms considered which is outstanding and
state of the art. However, I feel that the description of
multidimensional searching algorithms falls short in comparison
to the extensive treatment of hashing. This might be because the
author himself has been very active in the latter area, but such
considerations are inappropriate for a handbook.
The structure of the book and partitioning of the algorithms
into searching, sorting, selection and arithmetic algorithms are
useful for programmers and computer scientists who wish to find a
suitable data structure for a given problem. The author intends to
contribute to a change of computer science from an art to a
science and describes all his algorithms in PASCAL and C
directly. Thus, a programmer has something "to stand on."
However, some doubts remain about its ability to make available
the wealth of information in one book which this field has
generated in the last 20 years, as claimed by the author.
In summary, this is an outstanding book with a highly
condensed description and analysis of a great number of
algorithms. Especially the extensive average case analysis makes
this book very interesting for the programmer as well as for the
computer scientist.
-H. Noltemeier

I -~ -~ -~- II

"I I

The New York Times recently reported that Professor L.V.
Kantorovich died on April 7, 1986. Professor Kantorovich was a
Nobel laureate and a senior editor of Mathematical Programming...
Georgia Institute of Technology announces the appointment of George
L. Nemhauser to the A. Russell Chandler m Chair. .IFORS reports
that its new officers are J. Lesbourne (Paris) as President and S.
Bonder (USA), B. Kavanagh (Australia) and F. Ridgway (Ireland)
as Vice-Presidents with J.R. Borsting continuing as Treasurer .Carl-
Louis Sandblom, formerly of Concordia University, has been
appointed as Professor of Industrial Engineering at the Technical
University of Nova Scotia. .The IFORS '87 conference will be held
August 10-14 in Buenos Aires.
OPTIMA No. 17 contained a Dantzig prize article which should have
been attributed to George Nemhauser and Mike Powell as well as
M. Balinski and R. Wets.
Deadline for the next OPTIMA is August 15, 1986.

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

Journal contents are subject to change
by the publisher.

Donald W. Heam, 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.


Prize winners at Boston:
Michael Saunders (top), winner of
Orchard-Hays Prize and Jozsef Beck,
a Fulkerson Award Winner.


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


~ I I~

------- -- ---

~ ~_


15 April 1986 Maintained by the Mathematical Programming Society (MPS)

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

April 30-MAy 2: "Optimization Days" at Ecole
des Hautes Etudes Commerciales, Montrdal,
(Submission deadline January 31.) Contact: Prof.
Alain Haurie, GERAD, Ecole des H.E.C., 5255
avenue Decelles, Montrial, Quebec, Canada
H3T 1V6; telephone 514-340-6042.
May 14-16: Third SIAM Conference on Discrete
Mathematics, Clemson, South Carolina, USA.
Contact: SIAM Conference Coordinator, 117
South 17 Street-14th Floor, Philadelphia, PA
19103. Telephone 215-564-2929.
May 22-23: 'Eighth Symposium on Mathemat-
ical Programming with Data Perturbations', The
George Washington University, Washington, DC,
USA. Contact: Professor Anthony V. Fiacco,
Department of Operations Research, School of
Engineering and Applied Science, The George
Washington University, Washington, DC 20052,
USA; Telephone 202-676-7511. Deadline for
abstracts, 10 March 1986.
June 16-19: The International Conference on
Numerical Optimization and Applications, Xi'an,
Shaanxi, China. Contact: Professor You Zhao-
Yong, Department of Mathematics, Xi'an Jiaotong
University, Xi'an, Shaanxi, China. Telex 70123

July 29-August 1: Conference on Continuous
Time, Fractional and Multiobjective Programming,
Canton, New York, USA. Contact: Professor
Chanchal Singh, Department of Mathematics, St.
Lawrence Umversity, Canton, NY 13617, USA.
Telephone 315-379-5293.
August 12-14: SIAM Conference on Linear
Algebra in Signals, Systems, and Control; Boston,
Massachusetts, USA. Contact: SIAM Conference
Coordinator, Suite 1400, 117 South 17 Street,
Philadelphia, PA 19103.
Telephone 215-564- 2929.
September 15-19: International Conference on
Stochastic Programming, Prague, Czechoslovakia.
Contact: Dr. Tomas Cipra, Dept. of Statistics,
Charles University, Sokolowska 83, 18600
Prague 8, Czechoslovakia. Cosponsored by the
Committee for Stochastic Programming of the
Mathematical Programming Society.

August 29-September 2: Thirteenth Interna-
tional 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.

s ~

Technical Reports & 1Working Papers

Universitdit zu K6ln
Mathematisches Institut
Preprints in Optimization
Weyertal 86-90
D-5000 K61n 41

U. Zimmermann, "Submodulare Flusse: Verfahren zur
Minimierung Linearer Zielfunktionen," WP 84.11.
A. Bachem, "Dualitat und Polaritat in Diskreten Strukturen,"
WP 84.12.
R. Euler and A.R. Mahjouk, "On a Composition of
Independence Systems by Circuit-Identification," WP 85.13.
A. Bachem and H. Hamacher, "Joint US/FRG Seminar:
Applications of Combinatorial Methods in Mathematical
Programming Abstracts and Open Problems," WP 85.14.
W. Kern, "Verbandstheoretische Dualitat in Kombinatorischen
Geometrien und Orientierten Matroiden," WP 85.15.
W.Kern, "An Efficient Algorithm for Solving a Special Class
ofLPs," WP 85.16.
A. Bachem and A. Wanka, "On Intersection Properties of
(Oriented) Matroids (Extended Abstract)," WP 85.17.
A. Bachem and W. Kern, "On Sticky Matroids," WP 85.18.
A. Bachem and A. Wanka, "Separation Theorems for Oriented
Matroids," WP 85.19.
W. Kern, "On the Existence of Modular Embeddings of the
Lattice of a Matroid (Extended Abstract)," WP 85.20.
J. Bokowski and B. Sturmfels, "Coordination of Oriented
Matroids," WP 85.21.
J. Bokowski and B. Sturmfels, "Programmsystem zur
Realisierung Orientierter Matroide," WP 85.22.
W. Kern, "On Finite Locally Projective Planar Spaces," WP


Vol. 34, No. 3

W. Cook, A.M.H. Gerards, A. Schriver, and E. Tardos,
"Sensitivity Theorems in Integer Linear Programming."
R.E. Stone, "Linear Complementarity Problems with an
Invariant Number of Solutions."
Y. Fathi and C. Tovey, "Affirmative Action Algorithms."
J. Boucher and Y. Smeers, 'The Manne-Chao-Wilson
Algorithm for Computing Competitive Equilibria: A Modified
Version and its Implementation."
J.L. Nazareth, 'The Method of Successive Affine Reduction for
Nonlinear Minimization."
R. Hettich, "An Implementation of a Discretization Method for
Semi-Infinite Programming."
J. Semple and S. Zlobec, "On the Continuity of a Lagrangian
Multiplier Function in Input Optimization."

The Johns Hopkins University
Department of Electrical Engineering
and Computer Science
Baltimore, Maryland 21218

N. Adlai and A. DePano, "On k-Envelopes and Shared Edges,"
N. Adlai and A. DePano, "Efficient Polygonal Enclosures That
Cover the Plane," 85/04.
J. O'Rourke and S.R. Kosaraju, "Computing Circular
Separability," 85/05.
WJ. Rugh, "An Extended Linearization Approach to Nonlinear
System Inversion," 85/06.
W.T. Baumann and WJ. Rugh, "Feedback Control of
Nonlinear Systems by Extended Linearization: The Multi-Input
Case," 85/07.
S. Suri and J. O'Rourke, "Finding Minimal Nested Polygons,"
M. McKenna, J. O'Rourke, and S. Suri, "Finding the Largest
Rectangle in an Orthogonal Polygon," 85/09.
S. Suri, "A Linear Time Algorithm for Minimum Link Paths
Inside a Simple Polygon," 85/11.
S. Suri and J. O'Rourke, "Worst-Case Optimal Algorithms for
Constructing Visibility Polygons with Holes," 85/12.
J. O'Rourke, "Reconstruction of Orthogonal Polygons from
Vertices," 85/13.
N. Adlai and A. DePano, "Finding Smallest Perimeter
Rectangles for a Given Convex Polygon, Or Cropping for the
Cheapest Frame," 85/14.
J. O'Rourke, "A Lower Bound on Moving a Ladder," 85/20.


Vol. 35, No. 1

M.E. Dyer, A.M. Frieze, and C.J.H. McDiarmid, "On Linear
Programs with Random Costs."
J.T. Fredricksen, L.T. Watson, and K.G. Murty, "A Finite
Characterization of K-Matrices in Dimensions Less than Four."
R.H. Byrd and R.B. Schnabel, "Continuity of the Null Space
Basis and Constrained Optimization."
J.-P. Crouzeix and P.O. Lindberg, "Additively Decomposed
Quasiconvex Functions."
M. Fukushima, "A Relaxed Projection Method for Variational
E.W. Sachs, "Broyden's Method in Hilbert Space."
J.M. Borwein and H. Wolkowicz, "A Simple Constraint
Qualification in Infinite Dimensional Programming."
J.L. Nazareth, 'The Method of Successive Affine Reduction for
Nonlinear Minimization."
J. Guelat and P. Marcotte, "Some Comments on Wolfe's
'Away Step.'"

1~------1----- .~---011-`---33~-~I~---CIIIIC-


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