Title: Optima
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Title: Optima
Series Title: Optima
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Place of Publication: Gainesville, Fla.
Publication Date: August 1983
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Testing the Theory of Evolution

An Application of Combinatorial Optimization

L. R. Foulds
University of Florida

Implications of C ,. I. Darwin's
theory of evolution have recently been
rigorously tested using combinatorial opti-
mization techniques. It 11 come as no
surprise to many academics that the results
of the test in no way invalidate the theory.
Dr. David I'. uI, and Dr. Michael Ilendy of
Massey University, New Zealand, and I
have, over the last eight years, been investi-
gating claims that Darwin's theory is not
respectable science but mere belief. A
graph theoretic model of evolution has been
constructed and solution techniques for the
model have been I1.. 1ti., i. using combina-
torial optimization techniques. When the
techniques are applied to data gained from
modern biochemical methods, they produce
solutions which do not support these
It would require millions of years to
verify by observation whether or not the
process of evolution actually takes place.
Thus all that can be done is to look for
evidence which suggests that evolution has
or has not taken place in the past. This is in
some ways unsatisfactory as it means that
the theory cannot be tested by the scientific
method in the same way as other scientific
theories, such as Einstein's photoelectric
But there is evidence to suggest that
each living species possesses a very detailed
description of itself in the form of a DNA
code, which is apparently used to build
genes. There is the I. i1 il' that, if the
theory of evolution is .- I,' when species
evolve their DNA codes II evolve too. So
an analysis of the protein codes from diffe-
rent species may be quite revealing.
What was done was to search for
ancestral relationships among five different
proteins from 11 vertebrate species. The

proteins can each be characterized by a
string of fixed length from an alphabet of
four symbols called nucleotides. For each
protein, the 11 strings (one for each species)
can be aligned and analyzed comparatively.
It turns out that any 11 species could
be related in over 34 million ways. But it
was found in this investigation that for each
independent protein, the simplest possible
pattern of relationship was remarkably
The five different proteins are inde-
pendent of each other so it seems that the
ancestral relationships of the species which
can be deduced by these patterns support
the idea of some kind of evolutionary
process. I1, is because without such a
process it is not clear why the patterns
would be so .,iiiI .11 Also it is interesting to
note that the pattern tends to conform .- II
with evolutionary trees produced by numer-
ical taxonomists when studying bone struc-
ture and fossil records.
Having read thus far, you are probably
thinking this is all very well, but what has it
to do with mathematical programming? To
justify the publication of this article in
OPTIMA we shall now briefly outline a
graph theoretic model of evolution and some
combinatorial optimization techniques
which can be used to analyze it.
The theory of evolution predicts that
existing biological species have been linked
in the past by common ancestors. A dia-
gram showing these links is i;: .1 a phylo-
genetic tree or '. i '. i'. A typical phylo-
geny is given in Figure 1. Since the time of
Charles Darwin, many scientists have con-
structed phylogenies which link both
existing and extinct species in the fossil
record. When the fossil record is inadequate
for a set of species, it may be possible to
determine its evolutionary history from a
knowledge of existing species in the set.
Suppose we wish to construct a
phylogeny for a given set of species with
little fossil evidence. We must use only

Alligator Turtle Man Monkey Sheep Cow Pig Horse

Figure 1: A Phylogenetic Tree

existing species. It is useful to use informa-
tion about the versions of a protein called
cytochrome c. It seems that every iP ii.
species possesses a version of this protein as
it appears to be essential for respiration.
Each version can be represented by a string
of 312 letters chosen from the following
four: A, C, G, and U (nucleotides). It is
interesting to compare strings: Man and
Rhesus Monkey differ at only one site of the
312. However, the reader will be relieved to
know that man and bread mold differ at 129
Our model is concerned with con-
structing a phylogeny which can be thought
of as a weighted tree in the graph theoretic
(Continued next page)

Next MP Symposium at MIT

I I, .11'- Council is pleased to an-
nounce that I'. .. . Jereim y -I 1 ...
Professor of Operations Research and Co-
director of the ).R. Center at M.l.T., .I11
be Chairman for organizing the 12th Inter-
national Symposium on Mathematical Pro-
grammingi The Symposium will take place
on the M.I.T. Campus in August, 1985.
-AlIex Orden

August 1983

Number 10

TESTING, continued

sense. Each of the given species is repre-
sented by a node in the phylogeny. The
other nodes represent other existing or
extinct species. The weight of each arc in
the phylogeny is defined to be the number
of sites at which the strings it connects
differ. The objective is to find a phylogeny
which spans the given set of species and
which is of minimum total weight as a sum
of the weights of its arcs. The objective is

S1 S4


Figure 2: The S1 S4 arc



private substitutions. A possible ip.i i ,I, i.; tree
is given in Figure 3. The total number of
substitutions in this tree is 12. The objective
is to find a spanning tree which minimizes
the total number of substitutions.

We now iI!ii,.i ii. the ideas just
presented by returning to the example
problem. A natural first attempt at solution
is to use either the Prim or Kruskal method
for the minimal i iin; ,:. tree problem

Figure 3: A Spanning tree for the five species

(MSTP). Let's see how this approach turns
out for our example. The number of substi-
tutions necessary for each pair of strings is
given in Table 2.
S2 S3 S4 S5

3 4 2 3
5 3 4

known to biologists by the somewhat Finding the phylogeny of maximum
contradictory title of maximum parsimony, parsimony for the species in a realistic study
To make this clearer, we now furnish a is no easy task. The number of possible
small artificial example which has been phylogenies has been enumerated assuming
constructed for expository purposes. Sup- various restrictions.2'3 As the number of
pose we have five species: S1, S2,.... S5, possibilities grows astronomically, complete
with strings that are only eight characters enumeration is out of the question. The
long rather than the usual 312 characters, model appears on the surface to be a mini-
The strings are given in Table 1, where each mal spanning tree problem which is, of
row is the string for a species: course, straightforward to solve. However,
the introduction of additional sequences
1 2 3 4 5 6 7 8 representing extra species (either existing or
extinct) often leads to a phylogeny with
S1 A G U G U U A A greater parsimony (a tree of less weight).
S C A A G U U A A Therefore, the model can be seen to be a
S3 C G U C C G A A variation of the Steiner tree problem on the
3 n-cube. This problem is notorious for its
S4 A A U G U U C A intractability and indeed the phylogeny
S5 C G U G U U C U model has been shown to be NP-complete.4
Given this gloomy state of affairs, it seems
Table 1 unlikely that a polynomial time algorithm
exists for the general problem. Yet all is not
As the sequences have been aligned, lost. It has been possible to modify existing
each column corresponds to a site. minimal spanning tree algorithms by using a
What we want to do is to connect the clustering algorithm to produce a phylogeny
five species by a ..inTiii:. tree where each of relatively low weight. What are clustered
species is represented by a node of the tree. are collections of columns of the matrix of
Suppose we join S1 and S4 directly by an data. This phylogeny of low weight is then
arc in the tree as shown in Figure 2. If we analyzed with view to either proving that it
compare S1 and S4 we see that the two is of maximum parsimony or modifying it so
strings differ at sites 2 and 7 only. At site 2 that it becomes one of maximum parsimony.
S1 has a G and S4 has an A. We label the S1 The approach is to use the clustering algo-
- S4 arc with the symbols 2GA to denote rithm to partition the matrix of data verti-
one difference between the strings. These cally. This breaks up each original string
three symbols are together called asubstitu- into a number of smaller substrings. Each
tion. We also add the substitution 7AC to set of substrings represents a separate,
the arc to denote the difference at site 7. As smaller problem. These smaller problems are
there are no other differences there are no then analyzed and if necessary a further
other substitutions associated with the S1 decomposition is made. Eventually the sub.
S4 arc. Given one of the two strings and the problem can be solved directly. The weights
substitutions, we can deduce the other of their solutions provide valid lower bounds
string. \\ i.1 we wish to do is to construct a which are used to prove the minimality of
spanning tree for (S1, S2, S3, S4, S,) and either the original phylogeny or a modifica-
label the arcs of the tree with the annro- tion thereof.

Applying a MSTP algorithm we can
obtain (among other minimal trees) the
tree given in Figure 3. There is the possi-
bility of the introduction of new strings
in order to reduce the total number of
substitutions. This is brought about by
using a process called coalescement. This
process can be explained as follows. Suppose
we have a substitution at site n between
nucleotides X and Y which appears on two
adjacent arcs in a spanning tree, as shown in
Figure 4(a). The tree can be modified to
produce a spanning tree with one less
substitution by the introduction of a new
string Sm, (called a Steiner point) which
differs from the Si string only at site n. It
has a Y rather than an X there. This process
can be used repeatedly to reduce the number
of substitutions. In applying it to our tree
we can remove one instance of duplication
in both 2GA (on arcs S1 S4 and S4 S5 )
and 1CA (on arcs S3 S1 and S S2 )
substitution. This produces the tree shown
in Figure 5, which has 10 substitutions. We
have introduced two new strings: S6 and
To discover whether this tree is a
minimal .- i,,. r, tree we analyze Table 1,
Consider the three sites: 1,2, and 7. If
substitutions corresponding to the other

Table 2

TESTING, continued

sites are removed, the tree collapses to the
one in Figure 6. It has one Steiner point.
The introduction of more than one Steiner
point would lead to a tree with more substi-
tutions. Can we create a tree with fewer
substitutions by having no Steiner points?
This is a normal MSTP. The substrings based
on sites 1, 2, and 7 are given in Table 3. Any
minimal solution to the MSTP for this data
has five substitutions. Therefore, we know
that sites 1, 2, and 7 jointly require at least
five substitutions in any phylogeny. The
other sites: 3, 4, 5, 6 and 8 require at least
one substitution each as their columns in
Table 1 each have two nucleotides. Thus,
any phylogeny must have at least 5 + 1 + 1 +
1 + 1 + 1 = 10 substitutions. As the phylo-
geny constructed in Figure 6 has exactly 10
substitutions, it must be minimal. It is not
uniquely minimal.
We now return to the general, large
problems. Sometimes the site decomposi-
tion process produces subproblems which
are small enough to be solved by a branch
and bound algorithm. This branch and
bound algorithm guarantees to produce all
phylogenies of maximum parsimony on any
data set with no more than 12 species in
reasonable computing time. So it was used
to calculate directly the phylogenies for the
11 species problems mentioned earlier.

2 7


Table 3

There is no guarantee that the decom-
position technique just described will
converge to a phylogeny of maximum
parsimony when applied to a large data set.
However, it has been used interactively with
a computer and has uncovered minimal
solutions to all data sets to which it has been
applied (up to 23 species).
The theory of evolution predicts that
similar phylogenies should be obtained from
different protein sequences. We have tested
this specific prediction from the theory,
rather than the general theory itself. Our
results are consistent with the theory of


Firgure 4: The Coalescement Process

S3 ,4
S7 S^, Is AC
S 2AG s,

Figure 5: The Minimal Phylogeny

S23 S, S

This idea of testing specific predictions
from an hypothesis, rather than the hypo-
thesis itself, is inherent in the writing of
one of the leading scientific philosophers of
the day, Karl Popper.s It is more clearly
expressed by Lakatos.6
There may be exceptions when dif-
ferent protein sequences will lead to dif-
ferent trees as, for example, in the serial
symbiosis theory. Also in the pre-cellular
evolution a network with circuits may be a
far better model than a tree. An interesting
philosophical question would arise if the
results of this work had falsified the predic-
tion that the phylogenies would be similar.
This would not necessarily disprove the
theory of evolution as it may be that the
strings simply changed so rapidly that they
lost all information about their early history.
It could be argued that because protein
strings from different species can be aligned
so readily that this, in itself, is independent
evidence that the proteins retain evolu-
tionary information.
This article has indicated a new
application for various techniques of com-
binatorial optimization. Minimal spanning
tree methods, matching, and branch and
bound enumeration are useful in the con-
struction of phylogenies. The next challenge
is to sharpen the decomposition technique
so as to be able to guarantee success with
larger data sets.

Figure 6: A Phylogeny for Sites: 1, 2 and 7


1) Penny, David, L. R. Foulds, and M. D.
Hendy, "Testing the Theory of Evolution
by Comparing Phylogenetic Trees Con-
structed from Five Different Protein Se-
quences," Nature 297 (1982) 197-207.
2) Foulds, L. R. and R. W. Robinson,
"Determining the Asymptotic Numbers of
Phylogenetic Trees," Lecture Notes in
Mathematics, No. 829, Combinatorial Math-
ematics VII, Springer-Verlag, Berlin (1980)
3) Foulds, L. R. and R. W. Robinson,
"Enuneration of Binary Phylogenetic
Trees," Lecture Notes in Mathematics, No.
884, Combinatorial Mathematics VIII,
Springer-Verlag, Berlin (1981) 187-202.
4) Foulds, L. R. and R. L. Graham, "The
Steiner Problem in Phylogeny is NP-
Complete," Adv. in Appl. Math., 3 (1982)
5) Popper, K., Unended Quest: An Intel-
lectual Autobiography, Fontana, London
6) Lakatos, I., in Method and Appraisal in
Physical Science (ed. C. Howsen). pp. 1-40,
Cambridge, University Press, (1976).

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edited by Pierre Hansen
Annals of Discrete Mathematics, Vol. 11
North-Holland, Amsterdam, 1981

This volume contains 26 papers, which were presented partly at th<
Workshop on Applications of Graph Theory to Management, Brussels
March 1979; partly at the Xth Mathematical Programming Symposium,
Montreal, August 1979.
These X-rays of discrete optimization reveal a particularly healthy
field. There is still room for innovation and for fresh approaches to
traditional applications.
The book shows a good balance between theory and applications:
14 papers are theoretical (even though many of them are algorithmically
oriented); 8 deal with specific applications, including network design,
cutting-stock, location, school timetabling, fault detection, maintenance,
traffic assignment and even sports scheduling, while the four remaining
ones are computational.
Another distinctive feature of the book is its breadth: 8 papers deal
with graphs, while the other ones cover many important areas of discrete
optimization, ranging from submodular functions to totally dual integral
systems, from the geometry of numbers to ordered semigroups (matroids
are the only noticeable absence). As for current research trends, 8 papers
deal with complexity aspects, 5 with polyhedral combinatorics, 2 with
heuristics, 2 with threshold functions.
The basic ingredient of a proceedings volume is the quality of its
individual papers. Here the quality is indeed excellent This, perhaps,
ultimately explains the large success the volume is having on the market
Bruno Simeone, University of Rome

The Theory of Games and Markets, VIII, 554 p
Joachim Rosenmiiller
North-Holland, Amsterdam, 1981

Rosenmilller's book contains a careful and rigorous treatment of
many parts of modern game theory. Omitted are multiple-stage games, the
analysis of the role of information in games, and a treatment of games
modelled as atomless measure spaces of players. All other parts of game
theory are represented. As the title promises some room is given to the
presentation of relations between games and markets.
Although cooperative game theory and characteristic function forms
of games dominate the book, non-cooperative games and the normal and
extensive forms are not neglected. On the contrary, a detailed anaylsis of
dynamic game models is given, leading from game trees via dynamic games
to differential games. Though differential games are not represented in the
most general possible framework the use of differential manifolds,
Hamilton-Jacobi-Systems, partial differential equations and measurable
mappings requires a good mathematical background of the reader. The
chapter on two-person-zero-sum and -non-zero-sum games reveals the
connection between game theory and optimization theory. In this context
I consider it useful that a presentation of the Lemke-Howson algorithm,
which cannot be found in most treatments of game theory, is included.
Also it is nice that a thorough treatment of those structures needed in the
riii,.l, 11-. of individual decision making precedes the proper game theoret-
ical part of the book.
For some economists a more extensive economic motivation and
interpretation would have perhaps been helpful. Yet, I recommend this
book as a very good and useful one for students of mathematics as well as
of economics. It provides enough material for several courses in game
theory. I found it useful to partially base my lectures on games and
decision theory at Bonn University on this book.
W. Trockel, Bonn University

Books for review should be sent to the Book Review Editor, Prof Dr.
Achim Bachem, Institut fiir Operations Research, Nassestrasse 2, D-5300
Bonn 1, W. Germany.

Algebraic Methods in Graph Theory
Vol. I and Vol. II
edited by L. Lovasz and Vera T. Sos
Amsterdam-Oxford-New York, 1981

The two volumes "Algebraic Methods in Graph Theory" are the
proceedings of a conference of the same title organized by the Attila Jozsef
University and the JSnos Bolyai Mathematical Society in Szeged, Hungary,
August 24-31, 1978. The conference intended to give an account of the
state-of-the-art in the field. This is reflected in the 850 pages of these
The title chosen for the conference only loosely ties together the
many combinatorial disciplines that are the topics of the various papers.
Since it is impossible here to treat the papers individually (there are 47 of
them!), I will just attempt a general outline of the main themes.
There are two classical approaches to study graphs algebraically.
One may try to study graphs through their automorphism groups and thus
draw from the powerful methods of group theory. On the other hand, the
representation of a graph by its adjacency matrix yields a spectral theory
for graphs. Furthermore, the vertex-edge incidence matrix leads to the
investigation of the matroidal properties of a graph. Stopping short before
matroids, chain-groups provide a means to attack, for example factoriza-
tion problems of graphs.
Thus the topics include more general combinatorial structures
ranging from relational structures, hypergraphs and matroids over partial
geometries and association schemes (of interest for the Shannon capacity
of a graph) to two-graphs. In particular, the interplay between graphs and
matroids receives much attention (arboresences, matching, matroid union,
decomposition, etc.) and a study of matroid constructions from the
point of view of exterior algebra is presented.
Other investigations go in the opposite direction and ask for the
realizability of given structures by certain graphs (this problem is com-
pletely solved for graphical regular representations of finite groups).
Moreover, the methods of the theory of graphs and related combinatorial
structures are applied to other fields, e.g., number theory and geometry.
In recent years, the algorithmic aspect of combinatorics has become
increasingly important. Several papers deal with the problem to efficiently
construct a combinatorial object and/or to efficiently verify a certain
property (graphicness of matroids, listing the circuits of planar graphs, the
general matroid matching problem).
Of course, in the more than four years since the conference, much
progress has been achieved and many of the results in the papers of the
proceedings have been complemented and extended (to give just one
example: Seymour's decomposition of regular matroids). Some of the
papers mention pertinent recent developments "added in proof." Never-
theless, the two volumes will be of interest to every researcher in the field
of graph theory and related areas since they provide survey articles as well
as special research results covering a wide range of theory and applications
and still open problems. If this review whets the appetite of the reader to
take a close look at these proceedings, it has fulfilled its purpose.
Last but not least, the reader should not be too disappointed if he
cannot learn about "the minimization of truth" as promised in the table of
contents. The volumes offer other rewards.
Ulrich Faigle, University of Bonn

by R. Michael Hord
Springer Verlag
Berlin-Heidelberg-New York, 1982

Dr. Slotnik's conception of the first "supercomputer" was origi-
nated in the mid-sixties. The ILLIAC IV was put into operation 1975.
In the shortlived world of computers this belongs to history today. How-
ever, the present trend to more parallelism in hardware and software
structures creates new interest in this unique computer. The book is a

P~ 3~


comprehensive report of the in'.. ,a_.il,' and implementation activities
presenting a lot of detailed information, analysing hardware and software
problems and explaining success and failures. Computer experts of many
special fields may derive great benefit from it for design and development
of hardware, operation systems, programming environment, user's soft-
ware, etc., for unconventional multiprocessor structures. More than
half of the book is dedicated to application problems which have a demand
for high processing power, as for example, in the field of hydrodynamics,
picture processing, seismology, and astronomy. This selection of applica-
tion fields, however, is hardly representative for potential users of large
future parallel computers.
G. Fritsch, Erlangen-Niirnberg

Modern Applied Mathematics Optimization and Operations Research
edited by Bernhard Korte
North-Holland, Amsterdam New York, 1982

"Optimization and Operations Research" was the title of a summer
school organized by the Institute of Operations Research of the University
of Bonn, and the 17 State-of-the-Art articles of this volume are basically
the written versions of the lectures. The volume is divided into seven parts
1. !o.. with the following topics: Foundations, Convex Analysis, Poly-
hedral Theory, Complexity, Nonlinear Programming, Control and Approx-
imation Theory and Numerical Analysis, Combinatorial Optimization,
Game Theory, Statistics, and Economics.
All articles are of high quality some are excellent from the didac-
tical point of view. However most of the monographic articles address
readers who have at least a basic knowledge of the area. This book is
1. i ..Ii. I a welcome contribution to the literature on "applicable" mathe-
matics and should be of utmost interest and use to everybody who is
working in fields like mathematical economics or operations research, and
who is willing to discuss and apply modern mathematical methods. More-
over the book is ideally suited to serve as background text for teaching or
the basic reference for a seminar on modern applied mathematics.
l.Derigs, University of Bonn


Volume 27, No.1

D. Goldfarb and A. Idnani, "A Numerically Stable Dual Method for
Solving Strictly Convex Quadratic Programs."
M. L. Overton, "A Quadratically Convergent Method for Minimizing
a Sum of Euclidean Norms."
R.D. Armstrong and P.O. Beck, "The Best Parameter Subset Using
the Chebychev Curve Fitting Criterion."
D. F. Karney, "A Duality Theorem for Semi-Infinite Convex
Programs and Their Subprograms."
J. G. Ecker and M. Kupferschmid, "An Ellipsoid Algorithm for
Nonlinear Programming."
D. P. Bertsekas, "Distributed Asynchronous Computation of Fixed
Volume 27, No. 2

Ge Ren-pu and M. J. D. Powell, "The Convergence of Variable
Metric Matrices in Unconstrained Optimization. "
R. G. Jeroslow, 't nti. r,, Duality in Semi-Infinite Convex Optimi-
A. I....I i and A. LeNir, "QN-Like Variable ti...... Conjugate
T. -i.,Ihi... "Local and Superlinear Convergence for Truncated
Iterated Projection Methods."
R. W. Cottle and R. E. Stone, "On the Uniqueness of Solutions to
Linear Complernentarity Problems."
J. B. Orlin, "Maximum-Throughput Dynamic Network Flows."

(Journal contents are subject to change by publisher)


NATO Advanced Study Institute on
Computational Mathematical Programming
July 23 to August 2, 1984
Bad Windsheim, Germany F.R.

The Committee on 'i....il.... (COAl,) of the Mathematical Pro-
gramming Society announces a summer school on Computational Mathe-
matical .... .......... to be held in Bad Windsheim, West Germany, from
July 23 to August 2, 1984, under the sponsorship of NATO (Advanced
Study Institute). The ASI consists of tutorials with the emphasis on new
mathematical programming algorithms, software products, computational
experiments, numerical test results, and practical optimization models.
The following topics will be treated: large linear systems; integer pro-
gramming; model building in linear and integer programming; networks;
nonlinear programming; model building and computational aspects in
nonlinear programming: large scale nonlinear programming; geometric
programming; nondifferentiable optimization; global optimization;genera-
tion of test problems. experimental design and comparative performance
evaluation; optimal control; stochastic optimization: parallel ..... ** I;,
Some time will be reserved for participants of the ASI to lecture about
their own research activities. A limited fund is available for participants
from NATO-counlries to cover a part of tie travelling and accommodation
costs. Participation is possible only by invitation. I'or more information
and an application fornn. write to Klaus Schittkowski, Institut fiir Iifor-
matik, Univcrsitat Stuttgart. Azenbergstr. 12, I)-7000 Stuttgart 1, Germany

The Fourth Mathematical
Programming Symposium, Japan

IThis annual symposium will be held on November 14-15, 1983 at
the International Conference Center Kobe, Kobe, Japan. The symposium
will consist of the ii.. ,,.. three sessions:
1. Mathematical programming, general. Chairman: M. Kojima. 2.
Markov Decision Process. Chairman: K. Sawaki. 3. Applications. Chair-
mal: T. Morildyo.
The first two sessions will consist of three or four talks of expos-
itory nature and those presenting original development. No contributed
paper will be called for, and only invited papers will be presented.
Participation from abroad will be welcomed. The conference
language is Japanese but non-Japanese participants may use English.
For further information contact Organizing Chairmnu, Professor
Masao Iri, Faculty of Engineering, University of Tokyo, Bunkyo-ku, Tokyo
113, Japan, or Program Chairman, Professor R. Manabe, Kobe University
of Commerce, Tarumi, Kobe 655, Japan.
-R. Manabe

Herbert E. Scarf (Yale) has been awarded the John von Neumann Theory Prize by
ORSA/TIMS. The award cited Professor Scarf's contributions in the computation of fixed
points, in (s,S) policies in inventory theory, in balanced games, and in general equilibrium
theory in economics. . .Haverly Systems, Inc. of Denville, N.J. has received an award for
"excellence in exporting" from U.S. President Reagan. The company's major software
products include linear :.i. ... iiiiiinI. systems and other packages designed to solve optimiza-
tion problems in a variety of applications. . Ubaldo Garcia Palomares (Univ. Simor'
Bolivar) is visiting Argonne National Laboratory from June 15 to December 15, 1983. ..A
workshop on "Algorithms and Software for Nonlinear Optimization" will be held Sept.
21-23, 1983 in Cetraro, Italy. Contact Mrs. Chiara Zanini, Via Bernini, n.5, 87036
Qi ali..n.;.Ii., di Rende (Cosenza) Italy, Tel. i11':: 1,, 839711-839738 ... New MPS dues for
I'!: 1 have been announced: 32 US dollars, 20 UK pounds, 68 Swiss francs, 250 French
francs, 84 German marks, or 94 Dutch guilders.
The Discrete Applied Mathematics journal is preparing a special issue on network
algorithms and applications. I'1. I- submit papers (deadline was August 15, I'1 : .), to Profes-
sor Darwin Klingman, David Burton Jr. Centennial Chair in Business Decision Analysis,
Department of General Business, (SB 4.138, University of Texas, Austin, Texas 78712. All
contributions will be tl.. ...i. .1 refereed.
Deadline for the next (: I' I i is December 1, 1983.

This public document was promulgated at a cost of $426.1.5 or
$0.61 per copy to inform researchers in mathematical programming of
recent research results.

303 Weil Hall
College of Engineering
University of Florida
Gainesville, Florida 2''611 FIRST CLASS MAIL

Princeton University
School of Engineering & Applied
Princeton, NJ 08544


Maintained by the Mathematical Programming Society (MPS)

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 33-221, POB 218, Yorktown Heights, NY 10598,
U.S.A; Telephone 914-945-1642, Telex 137456.
Some of these meetings are sponsored by the Society as part of its world-wide support of activity
in mathematical programming. Under certain guidelines the Society can offer publicity, mailing lists and
labels, and the loan of money to the organizers of a qualified meeting.
Substantial portions of meetings of other societies such as SIAM, TIMS, and the many national OR
societies are devoted to mathematical pr. :!i.nmmiii and their schedules should be consulted.


September 21-23: International Workshop on Algorithms and software for nonlinear optimization,
Cetraro (Cosenza), Italy. Contact: Mrs. Chiara Zanini, CRAI, Via Bernini No. 5, 87036
Quattromiglia di Rende (Cosenza), Italy. Telephone (0984) 938711.


June 12-14: SIAM Conference on Numerical Optimization, Boulder, Colorado, U.S.A. Contact: Hugh
B. Hair, SIAM Services Manager, 1405 Architects Iltiildi., 117 South 17 Street, Philadelphia,
Pennsylvania 19103, U.S.A. Telephone 215-564-2929.

July 23 August 2: NATO Advanced Study Institute on Computational Mathematical P i i.IIniin.:
Bad Windsheim, Federal Republic of Germany. Contact: Dr. Klaus Schittkowski, Institut fir
Informatik, Azenbergerst. 12, 7000 Stuttgart 1, Federal Republic of Germany. Telephone
0711 2078 335. Sponsored by the Society through the Committee on Algorithms.


August 5-9: 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 617-253-7165. Official
triennial meeting of the MPS.

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