Title: Optima
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00090046/00022
 Material Information
Title: Optima
Series Title: Optima
Physical Description: Serial
Language: English
Creator: Mathematical Programming Society, University of Florida
Publisher: Mathematical Programming Society, University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: October 1987
 Record Information
Bibliographic ID: UF00090046
Volume ID: VID00022
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.


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N 22


13th International
Symposium on
Mathematical Programming
Chuo University, Tokyo, Japan
August 29-September 2, 1988

The organizers of the 13th Symposium have
recently mailed a Second Announcement
packet to all MPS members. Included are:
0L A description of the meeting sessions
O Meeting Registration Form
O Abstract Form
0 Hotel and Tour Registration Forms
The deadline for abstracts and meeting regis-
tration is May 1, 1988. The member advanced
registration fee is 26,000 yen (U.S. $175).
Hotel rates start at 6,800 yen and tours are
available from 4,500 to 17,500 yen. Travel,
hotel accommodations and tours are to be
handled by:
Japan Travel Bureau, Inc.
Foreign Tourist Division
Convention Center (Ref. CD 8-7201-88)
1-13-1 Nihombashi, Chuo-ku
Tokyo 103, JAPAN
Telephone: 03-276-7885
Telex: 24418 TOURIST J
Fax: 03-271-4134

Nominations for 1988
Society Elections

The Constitution of the Society sets
the term of office for all officers of the
Society at three years. Elections for all
offices (Chairman, Treasurer, and four at-
large members of Council) are to be held
four months prior to each triennial
International Symposium. The thirteenth
symposium will be held in Tokyo, August
29 September 2,1988, so the next election
will be held in April 1988. The new
members-at-large of the Council will take
office at the time of the Symposium, while
the Chairman-elect and Treasurer-elect
will take office one year later.
It further states that the Chairman is
to invite nominations. Candidates must be
continues, page two

number twenty-two

List of contents


-- ~- -

PAGE 2 0 T I M A nmber tweny-twonOCTBE19
9 I P 3.9Z,

Third SIAM Conference on Applied Linear Algebra

May 23-26, 1988
The Concourse Hotel
Madison, Wisconsin, USA

Conference Themes

l Large Scale Computing and Numerical Methods

l Inverse Eigenvalue Problems

O Qualitative and Combinatorial Analysis of Matrices

L Linear Systems and Control

Deadline for abstracts of contributed presentations and poster
presentations: December 10, 1987.

For additional information contact:
SIAM Conference Coordinator
117 South 17th St., 14th Floor
Philadelphia, PA 19103-5052.
Telephone: (215)564-2929 or E-Mail to: SIAM @ Wharton, Upen.edu.

1988 Society Elections from page one

members of the Society. They may be
proposed either by Council or by any six
members of the Society. No proper nomi-
nation may be refused, provided the can-
didate agrees to stand. The Chairman
decides the form of the ballot. It also states
that the Council shall pass by-laws gov-
erning elections designed to promote
international representation on the
Council, which has not to date been done.
Accordingly, the Council has agreed
to the following procedure:
(1) Nomination to any office is to be
submitted to me by February 1, 1988. Such
nomination is to be supported in writing
by the nominator and at least five other
members of the Society.
(2) In keeping with what seems to

have become a tradition the next Chair-
man should be a North-American resident,
so the membership is requested not to
nominate for Chairman a resident of
another continent.
(3) When the ballots are counted, the
four at-large candidates for Council
receiving the highest number of votes will
be elected, except that not more than two
members having permanent residence in
the same country may be elected.

M. L. Balinski
Chairman 1986-1989
Laboratoire d'Econom6trie
Ecole Polytechnique
75230 Paris Cedex 05

1989: Competition for
Young Statisticians from
Developing Countries

The International Statistical Institute (ISI)
announces the Fourth Competition among
young statisticians from developing
countries who are invited to submit a paper
on any topic within the broad field of
statistics, for possible presentation at the
47th Session of ISI to be held in Paris,
France, in 1989.

Participation in the competition is open to
nationals of developing countries who are
living in a developing country, who will not
be older than 32 years of age in the year
during which the Session is to be held.

Papers submitted must be unpublished,
original works which may include univer-
sity theses.

The papers submitted will be examined by
an international Jury of distinguished
statisticians who are to select the three best
papers presented in the competition. Their
decision will be final.

The authors of the winning papers will be
invited to present personally their papers at
the Session of ISI concerned, with all
expenses paid (i.e. round trip airline ticket
from his/her place of residence to Paris
plus a lump sum to cover living expenses).

Manuscripts for the Competition should be
submitted in time to reach the ISI not later
than November 1, 1988.

The rules governing the preparation of
papers, application forms and full details
are available on request from the ISI Perma-
nent Office to which interested individuals
should write for further information. The
address is as follows:

The Director
Permanent Office
International Statistical Institute
428 Prinses Beatrixlaan
2270 AZ Voorburg
The Netherlands

- --- -- -- ------ -- ---~


0 P I MA number twenty-two


PAG 3 0____ P ubrtenytoOTBR18

Nominations for the A.W. Tucker Prize Invited

The A.W. Tucker Prize for an out-
standing paper authored by a student
was established recently by the Mathe-
matical Programming Society. The first
award will be made at the 13th Interna-
tional Symposium of the Mathematical
Programming Society to be held in
Tokyo, August 29 September 2, 1988.
In advance of the Symposium the
awards committee will screen the
nominations and select at most three
finalists. The finalists will be invited,
but not required, to give oral presenta-
tions at a special session of the sympo-
sium. The awards committee will select
the winner and announce the award
prior to the conclusion of the sympo-
"igibility The paper may concern
.v aspect of mathematical program-
ming; it may be original research, an
exposition or survey, a report on
computer routines and computing
experiments, or a presentation of a new
and ingenious application. The paper
must be solely authored and completed
since January 1, 1985. The paper and
the work on which it is based should
have been undertaken and completed
in conjunction with a degree program.
All students, graduate or undergradu-
ate, are eligible. Nominations of
students who have not yet received the
first university degree are especially

Nominations Nominations must be
made in writing to the chairman of the
awards committee by a faculty member
at the institution where the nominee
was studying for a degree when the
paper was completed. Letters of nomi-

nation must be accompanied by four
copies each of: the student's paper; a
separate summary of the paper's con-
tributions, written by the nominee, and
no more than two pages in length; and
a brief biographical sketch of the
nominee. The awards committee may
request additional information. Nomi-
nations and the accompanying docu-
mentation are due January 15, 1988.

Selection The awards committee will
select the finalists by May 15, 1988. The
winner will be selected by the awards
committee at the symposium, subse-
quent to the oral presentations by the
finalists. Selection will be based on the
significance of the contribution, the
skillfulness of the development, and
the quality of the exposition. The
winner will receive an award of $750
(U.S.) and a certificate. The other
finalists will also receive certificates.
The society will pay partial travel
expenses for each finalist to attend the
symposium. A limit of $500 on travel
reimbursements is likely. The institu-
tions from which the nominations
originate will be encouraged to assist
any nominee selected as a finalist with
additional travel expense reimburse-

The members of the awards committee
are: Robert G. Bland, Cornell Univer-
sity; Harold W. Kuhn, Princeton
University; Alan C. Tucker, State
University of New York at Stony
Brook; and Laurence A. Wolsey,
University Catholique de Louvain.
Nominations should be sent to: R.G.
Bland, School of OR/IE, Upson Hall,
Cornell University, Ithaca, NY 14853,
USA. w

Call for Nominations
for the D.R. Fulkerson
This is a call for nomination for the D.
Ray Fulkerson Prize in discrete mathe-
matics which will be awarded at the
XIIIth International Symposium on
Mathematical Programming to be held
in Tokyo, Japan, August 29-September
2, 1988.

The specifications for the Fulkerson
Prize read:

"Papers to be eligible for the Fulkerson
Prize should have been published in a
recognized journal during the six
calendar years preceding the year of
the Congress. This extended period is
in recognition of the fact that the value
of fundamental work cannot always be
immediately assessed. The prizes will
be given for single papers, not series of
papers or books, and in the event of
joint authorship the prize will be

The term "discrete mathematics" is
intended to include graph theory,
networks, mathematical programming,
applied combinatorics, and related
subjects. While research work in these
areas is usually not far removed from
practical applications, the judging of
papers will be based on their mathe-
matical "quality and significance."

The nominations for the award will be
presented by the Fulkerson Prize
Committee (Manfred Padberg, Chair-
man, Martin Gr6tschel and Gian-Carlo
Rota) to the Mathematical Program-
ming Society and the American Mathe-
matical Society.

Please send your nominations by
January 15, 1988, to: Prof. Manfred
Padberg, Tisch Hall, Room 517, New
York University, 40 West 4th Street,
New York, N.Y. 10003, U.S.A. wa

b~ -----C~- -- ------~ ---------~


OPTIMA number twenty-two


PAGE~~~~~_ 411 OPT I ubrtetytoOTBR18

- Technical Reports & Working Papers

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

G.G.L. Meyer, "Convergence of Relaxation Algorithms by
Averaging," 86/06.
G.G.L. Meyer and L.J. Podrazik, "A Parallel First-Order Linear
Recurrence Solver," 86/07.
S. Suri, "Computing the Geodesic Diameter of a Simple Polygon,"
J. Wang and W.J. Rugh, "On Parameterized Linear Systems and
Linearization Families for Nonlinear Systems," 86/11.
S.K. Ghosh, "On Recognizing and Characterizing Visibility Graphs
of Simple Polygons," 86/15.

Systems Research Center
The University of Maryland
and Harvard University
College Park Campus
Engineering Research Building (093)
The University of Maryland
College Park, Maryland 20742

A.L. Tits and E.R. Panier, "A Superlinearly Convergent Feasible
Method for the Solution of Inequality Constrained Optimization Prob-
lems," SRC TR 85-13.
A.L. Tits and E.R. Panier, "A Superlinearly Convergent Method of
Feasible Directions for Optimization Problems Arising in the Design of
Engineering Systems," SRC TR 85-37.
A.L. Tits, J.N. Herskovits and E.R. Panier, "A QP-Free, Globally
Convergent Locally Superlinearly Convergent Algorithm for Inequality
Constrained Optimization," SRC TR 86-65.
A.L. Tits and E.R. Panier, "Globally Convergent Algorithms for
Semi-Infinite Optimization Problems Arising in Engineering Design,"
SRC TR 87-28.
K. Nakajima, S. Masuda, T. Kashiwabara and T. Fujisawa,
"Efficient Algorithms for Finding Maximum Cliques of an Overlap
Graph," SRC TR 86-58.
K. Nakajima and S. Masuda, "An Optimal Algorithm for Finding
a Maximum Independent Set of a Circular Arc Graph," SRC TR 86-68.
K. Nakajima, S. Masuda, T. Kashiwabara and T. Fujisawa, "An
NP-Hard Crossing Minimization Problem for Computer Network
Layout," SRC TR 86-80.
K. Nakajima, N.J. Naclerio and S. Masuda, "The Via Minimiza-
tion Problem is NP-Complete," SRC TR 87-42.
K. Nakajima, S. Masuda, T. Kashiwabara and T. Fujisawa,
"Crossing Minimization in the Straight-Line Embedding of Graphs,"
SRC TR 87-43.
K. Nakajima, N.J. Naclerio and S. Masuda, "Via Minimization
for Gridless Routing," SRC TR 87-46.

Institute fur Okonometrie und Operations
Fheinische Friedrich-Wilhelms-Universitat
Nassestrasse 2
D-5300 Bonn, West Germany

H.J. Pr6mel, "Counting Unlabeled Structures," WP 86409-OR.
H.J. Pr6mel, "Partition Properties of q-Hypergraphs," WP 86410-
Y.Yamamoto, "Orientability of a Pseudomanifold and Generaliza-
tions of Sperner's Lemma," WP 86411-OR.
H.J. Pr6mel and B. Voigt, "A Partition Theorem for [0,11," WP
B. Korte and L. Lovasz, "The Intersection of Matroids and
Antimatroids," WP 86413-OR.
W. Cook, "Cutting-Plane Proofs in Polynomial Space," WP 86414-
Y. Yamamoto, "A Path Following Algorithm for Stationary Point
Problems," WP 86415-OR.
L. Babai, "A Las Vegas-NC Algorithm for Isomorphism of Graphs
with Bounded Multiplicity of Eigenvalues," WP 86416-OR.
R. Schrader, "Structural Theory of Discrete Greedy Procedures,"
WP 86417-OR.
R.v. Randow, "On an Optimal Location Problem in a Triangle,"
WP 86418-OR.
A. Frank, "On Connectivity Properties of Eulerian Digraphs," WP
R.E. Bixby and D.K. Wagner, "A Note on Detecting Simple
Redundancies in Linear Systems," WP 86420-OR.
N. Korte and R.H. M6hring, "A Simple Linear-Time Algorithm to
Recognize Interval Graphs," WP 86421-OR.
A.J.J. Talman and Y. Yamamoto, "A Globally Convergent
Simplicial Algorithm for Stationary Point Problems of Polytopes," WP
O. Goecke, "A Greedy Algorithm for Hereditary Set Systems and a
Generalization of the Rado-Edmonds Characterization of Matroids," WP
U. Faigle and G. Gierz, "The Bandwidth of Planar Distributive
Lattices," WP 86424-OR.
H.J. Pr6mel, "Almost Bipartite-Making Graphs," WP 86425-OR.
U. Faigle, O. Goecke and R. Schrader, "Church-Rosser Decompo-
sition in Combinatorial Structures," WP 86426-OR.
R. Kannan and L. Lovisz, "Covering Minima and Lattice Point
Free Convex Bodies," WP 86427-OR.
U. Faigle and R. Schrader, "On the Convergence of Stationary
Distributions in Simulated Annealing," WP 86428-OR.
K. Cameron and H. Sachs, "Monotone Path Systems in Simple
Regions," WP 86429-OR.
U. Faigle and R. Schrader, "Simulated Annealing eine Fall-
studie," WP 86430-OR.
C.R. Coullard, J.G. del Greco and D.K. Wagner, "Representa-
tions of Bicircular Matroids," WP 86431-OR.

_ ~ I~ I


0 P TI M A number twenty-two


PAGE- 5 OP- T I-- M~ -s--- A- nubrtet-woOTBR18

Technical Reports & Working Papers continued

P. Erd6s, L. Lovasz and K. Vesztergombi, "On the Graph of
Large Distances," WP 86432-OR.
U. Faigle, R. Schrader and R. Suletzki, "A Cutting-Plane
Algorithm for Optimal Graph Partitioning," WP 86433-OR.
D. Lejuan and Y. Minyi, "On a Generalization of the Rado-Hall
Theorem to Greedoids," WP 86434-OR.
O. Goecke and R. Schrader, "Minor Characterization of Branching
Greedoids a Short Proof," WP 86435-OR.
G.J. Chang, "MPP-Greedoids," WP 86436-OR.
R.E. Bixby and R. Fourer, "Finding Embedded Network Rows in
Linear Programs 1: Extraction Heuristics," WP 86437-OR.
G.J. Chang, "Total Domination in Block Graphs," WP 86438-OR.
G.J. Chang and C.-S. Wu, "Graphs Whose Cycles Are of Length t
Modulus k," WP 86439-OR.
O. Holland and M. Gr8tschel, "A Cutting Plane Algorithm for
Minimum Perfect 2-Matchings," WP 86440-OR.
B. Korte and R. M6hring, "Zur Bedeutung der Diskreten Mathe-
matikfiar die Konstruktion Hochintegrierter Schaltkreise," WP 86441-
G.J. Chang, "Problems in Sun-Free Chordal Graphs," WP 86442-
H.J. Pr6mel, "Aspects of Asymptotic Graph Theory," WP 86443-
W. Cook, R. Kannan and A. Schrijver, "An Analogue of Chvdtal
utling Plane Proofs for Mixed Integer Programming Problems," WP

A.B. Gamble, A.R. Conn and W.R. Pulleyblank, "The Network
Penalty Method," WP 86445-OR.
A.M.H. Gerards and A. Seba, "Total Dual Integrality Implies
Local Strong Unimodularity," WP 86446-OR.
H.J. Pr6mel and B. Voigt, "Ramsey Theorems for Finite Graphs,"
WP 86447-OR.
M. Bartusch and R.H. M6hring, "Scheduling Project Networks
with Resource Constraints and Time Windows," WP 86448-OR.
H.J. Primel and B.Voigt, "A Short Proof of the Restricted Ramsey
Theorem for Finite Set-Systems," WP 86449-OR.

Department of Geography and Environmental
The Johns Hopkins University
Baltimore, Maryland 21218

J. Current, C. ReVelle and J. Cohon, "The Minimum Covering/
Shortest Path Problem," #86-03.
J. Current, C. ReVelle and J. Cohon, "An Interactive Approach to
Identify the Best Compromise Solution for two Objective Shortest Path
Problems," #86-04.
J. Current, C. ReVelle and J. Cohon, "The Median Shortest Path
Problem: A Multiobjective Approach to Analyze Cost vs. Accessibility in
the Design of Transportation Networks," #86-05.

Journals & Studies

Vol. 39, No. 2

J.E. Dennis, Jr., A.M. Morshedi and K. Turner, "A Variable-
Metric Variant of the Karmarkar Algorithm for Linear Programming."
R. Chandrasekaran, J-S. Pang and R. E. Stone, "Two Counterex-
amples on the Polynomial Solvability of the Linear Complementarity
A.H.G. Rinnooy Kan and G.T. Timmer, "Stochastic Global
Optimization Methods. Part I: Clustering Methods."
A.H.G. Rinnooy Kan and G.T. Timmer, "Stochastic Global
Optimization Methods. Part II: Multi Level Methods."
G. deGhellinck and J.-Ph Vial, "An Extension of Karmarkar's
Algorithm for Solving a System of Linear Homogeneous Equations on the
P.H. Calamai and J.J. More, "Projected Gradient Methods for
Linearly Constrained Problems."

K.G. Murty, "Some NP-Complete Problems in Quadratic and
Nonlinear Programming."
L.S. Lasdon, J. Plummer, B. Buehler and A.D. Waren, "Optimal
Design of Efficient Acoustic Antenna Arrays."
P.L. Jackson and D.F. Lynch, "Revised Dantzig-Wolfe Decomposi-
tion for Staircase-Structured Linear Programs."
I. Diener, "On the Global Convergence of Path-Following Methods
to Determine all Solutions to a System of Nonlinear Equations."
A.B. Poore and C.A. Tiahrt, "Bifurcation Problems in Nonlinear
Parametric Programming."
M.E. Posner and H. Suzuki, "A Dual Approach for the Continu-
ous Collapsing Knapsack Problem."
M. Guignard and S. Kim, "Lagrangean Decomposition: A Model
Yielding Stronger Lagrangean Bounds."


Vol. 39, No. 1


-----~ -~-~


0 PT IM A number twen ~-two



c'?^'3^-'';^'^=- = E- ;- iE- 3 S--- --l- a- ------------- ---~^ G A-l^--k. r -a 2 H T ~ f;I -UT^ . -B

Data Structures and Network Algorithms
By R. E. Tarjan
SIAM, Philadelphia, 1983
ISBN 0-89871-187-8

This is a beautiful book which I recommend to anyone who is
interested in data structures or graph algorithms. The author gives a
grand tour of tree based data structures and their applications to
efficient graph algorithms.
In each chapter R. E. Tarjan describes and analyses the most
efficient and recent solutions to the problem at hand. The presentation
is very elegant and readable. The reader is not only introduced to
important algorithmic paradigms but also to the techniques of analy-
sis of algorithms. The author also gives a survey of advanced results
which are not treated in the book. The book is most valuable to the
active researcher, but it can also be used as a graduate text. It deserves
a prominent place on our bookshelves.
-K. Mehlhorn

By R. Sedgewick
Addison Wesley, New York, 1983
ISBN 0-201-06672-6

This is a good sophomore text for computer algorithms and data
structures. It is clearly written and involves good intuition on the
structure of algorithms. There are numerous practical algorithms
described in the book, many in recently developed areas. These
include pseudo random number generation, curve fitting, string
matching, convex hull, polynomial interpolation, graph algorithms
and more. Some of the content appears for the first time in textbook
form the RSA cryptosystem and the Rabin Karp string matching
algorithm which is beautifully explained here but generally not well
Most of the algorithms are compactly described using Pascal-like
programs. This enables implementation of the algorithms without
much further work. The emphasis throughout is on practical algo-
rithms, that is, fast and relatively non-complex algorithms. This
philosophy of exposition is well justified in the introductory remarks

00 Journals & Studies

Vol. 39, No. 3

Vol. 40, No. 1

R.E. Bixby, O.M.-C. Marcotte and L.E. Trotter, Jr., "Packing and
Covering with Integral Feasible Flows in Integral Supply-Demand
T.M. Doup, G. van der Laan and A.J.J. Talman, "The (2`' -2)-
Ray Algorithm: A New Simplicial Algorithm to Compute Economic
A. Ramanathan and C.J. Colbourn, "Counting Almost Minimum
Cutsets with Reliability Applications."
A. Balakrishnan, "LP Extreme Points and Cuts for the Fixed-
Charge Network Design Problem."
J. Kyparisis and A.V. Fiacco, "Generalized Convexity and
Concavity of the Optimal Value Function in Nonlinear Programming."
Y. Ye and M. Kojima, "Recovering Optimal Dual Solutions in
Karmarkar's Polynomial Algorithm for Linear Programming."
C. Michelot and 0. Lefebvre, "A Primal-Dual Algorithm for the
Fermat-Weber Problem Involving Mixed Gauges."
A.R. Mahjoub, "On the Stable Set Polytope of a Series-Parallel

S.-P. Han, "A Successive Projection Method."
J.F. Bard, "Convex Two-Level Optimization."
H. Imai, "On the Convexity of the Multiplicative Version of
Karmarkar's Potential Function."
R.L. Tobin, "A Variable Dimension Solution Approach for the
General Spatial Price Equilibrium Problem."
G.G.L. Meyer, "Convergence of Relaxation Algorithms by
J. Renegar, "A Polynomial-Time Algorithmn, Based on Newton's
Method, for Linear Programming."
R.W. Chaney, "Second-Order Necessary Conditions in Semismooth

0 PTI M nube twnt-toOTBR98


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OPT I M A number twenty-two




by the author. It also sets the tone for the book as a text primarily for
practitioners. There are some references for state-of-the-art develop-
ments in the field, numerous good exercises and overall more material
than one could hope to cover in a term.
This book includes very little analysis and is not suited for a
theory or analysis of algorithms course. It is almost a cookbook type,
but a very good one at that. For people who are looking for an update
of Aho, Hopcroft and Ullman, this is not the one. However, for all the
objectives set up by the author, it is an excellent, up-to-date reference.
It is highly recommended for the purpose of developing intuition for
the way good computer algorithms work.
-D. Hochbaum

Polyhedral Combinatorics and the Acyclic
Subdigraph Problem
By Michael Jiinger
Heldermann, Berlin, 1985
ISBN 3-88538-207-5
The Linear Ordering Problem: Algorithms and
By Gerhard Reinelt
Heldermann, Berlin, 1985
ISBN 3-88538-208-3

One of the most promising approaches available to cope with NP-
complete combinatorial linear optimization problems is based on
insights into the structure of the associated polytope. As it is unlikely
to obtain a complete, computationally manageable linear description
of the polytope whose vertices correspond in a 1-1 manner to the
feasible solutions of the combinatorial optimization problem, we have
to restrict ourselves to partial descriptions. Their embodiment in
algorithms based on linear programming techniques, however, lead
to impressive computational results. But it is neither a trivial task to
find "good" relaxations nor to provide an efficient separation algo-
rithm, if it is possible at all for the relaxed polytope, since results do not
simply carry over from other problems.
These two books contain the result of a joint study of the Acyclic
Subdigraph Problem (ASP), which is NP-complete and equivalent to
many important problems in combinatorial optimization and eco-
nomics (e.g. Linear Ordering Problem, Matrix Triangulation, Paired
Comparison Ranking).
The book of Michael Jiinger presents an elaborate investigation of
the polyhedral structure of the ASP. After reviewing fundamental
results of related topics and providing an almost self-containing
introduction into the field of Polyhedral Combinatorics, the Acyclic
Subdigraph Problem and a series of related problems are proven to be
NP-complete. The partial non-redundant linear description of the
polytope associated with the ASP consisting of new classes of facet-
inducing inequalities namely Dicycles, M6bius Ladders and Fences
- developed in this book leads to a polynomial separation algorithm

for weakly acyclic digraphs. From this and the ellipsoid method, it
follows that the corresponding optimization problem for weakly
acyclic digraphs can be solved in polynomial time.
Employing these results, an LP-based cutting plane algorithm for
the Linear Ordering Problem has been developed by Gerhard Reinelt
which allowed the solution of problems which had been intractable
before. The algorithm mainly consists of two parts. The first part
iteratively determines a partial linear description of the Linear Order-
ing Polytope using those subclasses of facet-inducing inequalities of
the type mentioned above for which efficient cutting-plane recogni-
tion procedures had been developed. If this process ends with an
integral solution which happened with almost all tested problems -
the optimum for the complete problem has been found. Otherwise, an
upper bound and an LP-relaxation has been found which together
with a heuristically determined lower bound are taken as input for a
branch and bound procedure which guarantees that an optimum will
be found. The code, despite being theoretically non-polynomial and
neither trivial to implement nor to test, turned out to be efficient on all
of a large set of real-world problems (triangulation of I/O-Tables),
which are considered to be important in economic analysis as well as
on randomly generated problems.
These two books present in a clear, comprehensive and compact
style the theoretical and computational results of a complex joint
project of the two authors together with Martin Gr6tschel. It should be
of great value for those working on related topics and for those
interested in the economic results as well as for everyone who is
interested in an introduction to the advanced techniques of Polyhe-
dral Combinatorics.
-0. Holland

Numerical Optimization 1984
Edited by P. T. Boggs, R. H. Byrd and R. B. Schnabel
SIAM, Philadelphia, 1985
ISBN 0-89871-054-5

This volume contains some selected papers presented at the
SIAM Conference on Numerical Optimization.
Section 1 includes seven papers about "Nonlinearly Constrained
Optimization." A. R. Conn and R. Fletcher, respectively, discuss how
to overcome some disadvantages of the sequential quadratic pro-
gramming method. Instead of using a solution to the quadratic
subproblem to determine a search direction, followed by a line search
on the L, penalty function, Fletcher uses an L1 penalty formulation for
the quadratic programming problem in conjunction with a trust
region strategy. A. R. Conn gives the details of a method that derives
the search direction directly from the L, merit function.
In his paper L. S. Lasdon presents the generalized reduced
gradient algorithm and the successive linear programming algorithm
and discusses several applications of these methods. Most of the
results are well known.
The following four papers describe new approaches for some
well-known methods like a trust region strategy for nonlinear equal-
continues on page eight


0 P TI M A number twoenty/-two


U P I A nmbe twettitwoOCTOBER 1987


ity constrained optimization, sequential truncated quadratic pro-
gramming methods, and inexact quasi-Newton methods.
Section 2 consists of four papers dealing with "Optimization
Software." The contents of the article of Gill, Murray, Saunders and
Wright can essentially be found in the monograph, "Practical Optimi-
zation," of the authors. Rather new are some details of the program
NPSOL, which is one of the best implementations of the SQP method.
Powell reports about numerical results of two SQP methods for
constrained optimization that are applied to some "difficult" test
problems. He draws attention to some inefficiencies of the SQP
methods having been reported in the articles of Conn and Fletcher too.
The following two articles discuss the development of high level
modeling systems which do not expect the user to be familiar with the
details of NLP algorithms. In his essay Nazareth is concerned with
some fundamental aspects. Brooke, Drud and Meeraus describe a
general algebraic modeling system and explain the key features of
their modeling language.
Section 3 deals with "Global Optimization." "The computation of
the global minimum of an objective function is a rather hard problem.
Only a few solution methods have been developed so far. This section
contains four quite different approaches to this problem.
Levy and Gomez present the tunneling method. This algorithm
is composed of a sequence of cycles. Each cycle consists of two phases,
a minimization phase to find a local minimum and a tunneling phase
to obtain a good starting point for the next minimization phase.
Unfortunately, there is no guarantee for getting the global solution,
and no error bounds are given. So the method is at best of some
heuristic value.
Rinnooy Kan and Timmer review global optimization methods,
with special emphasis on stochastic methods. Most stochastic meth-
ods consist of two phases. In the global phase, the objective function
is evaluated at a number of randomly sampled points. In the local
phase, the sample points are manipulated, to yield a candidate global
minimum. There is no absolute guarantee of success. However, the
global phase can yield an asymptotic guarantee in a stochastic sense.
Comparing the computational behaviour of various methods, the so-
called multilevel method turns out to be the most promising.
Rosen considers the problem of finding the global minimum of a
concave quadratic function with many linear variables. Using the
special structure of the problem he presents an efficient branch and
bound method, which gives lower and upper bounds on the mini-
mum objective function value. Some computational results on a
variety of test problems are reported.
Walster, Hansen and Sengupta report results of numerical test-
ing of a global unconstrained minimization algorithm. This algorithm
has been presented by Hansen [Numer. Math. 34 (1980), 247-270]. It
uses interval arithmetic to obtain bounds on the global minimum and
the solution points.
-Wilhelm Forst

A Source Book on Matroid Theory
Edited by Joseph P.S. Kung
BirkhAuser, Stuttgart, 1986
ISBN 0-8176-3173-9

This volume contains 18 important papers in matroid theory
from the period 1932-1982, all but one reprinted in full. The editor
acknowledges that this anthology is not enclyclopedic in its coverage
of matroid theory. Nevertheless, he believes "that the papers included
give a balanced picture of the structural theory of matroids and ...
indicate some of the most exciting connections of matroid theory with
other areas of mathematics."
In the introduction, the editor has compiled a list of books, lecture
notes, and expository papers in matroid theory. This list contains 31
items. The five chapters of the book are entitled: Origins and Basic
Concepts, Linear Representation of Matroids, Enumeration in Geo-
metric Lattices, The Tutte Decomposition, and Recent Advances. Each
chapter begins with an editorial commentary on the papers it con-
tains. These commentaries summarize the main definitions and theo-
rems of the papers and comment on the relation between the terminol-
ogy used there and current usage. In addition, the editor lists related
work and, in the case of the older papers, comments on those concepts
and results that have spawned the most follow-up work. The com-
mentary on the first chapter also contains a complete survey of all the
matroid literature that appeared before 1945. For those works from
this period that are not reprinted in full, a short review is included
emphasizing those aspects of the work that have so far proved of most
The earliest papers reprinted in this volume are by Whitney,
Birkhoff, and MacLane. Five papers of these three men are repro-
duced. Three of these are from Volumes 57 (1935) and 58 (1936) of the
American Journal of Mathematics: Whitney's seminal paper "On the
Abstract Properties of Linear Dependence," Birkhoff's paper that
establishes the fundamental link between simple matroids and geo-
metric lattices, and MacLane's paper that shows the existence of non-
representable matroids.
The most recent papers represented in this volume are Seymour's
"Decomposition of Regular Matroids" [J. Combin. Theory Ser. B 28
(1980), 305-354] and Kahn's and Kung's "Varieties of Combinatorial
Geometries" [Trans. Amer. Math. Soc. 271 (1982), 485-499].
Some care has evidently been taken over the physical details of
the production of this book, and a fine product has resulted. The one
minor criticism one can make here is that the print in Rota's paper on
M6bius functions is a little faint in parts. This book is a very valuable
addition to the matroid literature that all who work in or near the
subject will want to own.
-James Oxley


U PT I M A number twentu-two


PAGE~-- -- 9~ OPI Anubrtwnytw COBR18


An Introduction to Linear Programming
By G. R. Walsh
Wiley, Chichester, 1985
ISBN 0-471-90719-7

This book is a second edition of an extended version of a course
of lectures that Walsh gave to second-year mathematics students at
the University of York. The major change from the first edition is the
addition of chapter 5 devoted to the Ellipsoid Algorithm. The first four
chapters cover an Introduction to Linear Programming, the Simplex
Method, Duality and the Revised Simplex Method, and Applications.
The level of presentation of this material is difficult to character-
ize; it is too dense with equations and proofs to be appreciated by an
American Operations Research undergraduate student but not truly
advanced enough for a graduate scholar. My opinion is that this is an
ideal reference book for the instructor of an introductory Linear
Programming course. The proofs are presented clearly and with such
detail that they would be a valuable aid for any teacher trying to
organize his/her lectures. There are very few typographical errors
and the examples and exercises are excellent in probing to the heart of
the subject matter at hand.
A few critical remarks though are in order. The way the equations
are presented and referred to makes reading some of the material a
laborious chore. In various places terms are used without definition
-iirid results are presented without reference, which also adds confu-
sion. Certain material is covered too quickly, for example, the two-
phase variant of the Simplex Method. I did not always agree with the
choice of starred material (optional for the first reading), for example,
the Dual Simplex Method and Sensitivity Analysis are starred while
the Revised Simplex Method using artificial variables is not. While
certain results, e.g. the Fundamental Theorem of Duality, are pre-
sented with organized and clear proofs, others, e.g. Konig's Theorem
and the Integrality of the Assignment Polytope, are proven using
nonstandard and nonrigorous methods. It is too bad that Walsh
decided to write this new edition so soon before the breakthrough of
Karmarkar's method. In light of all the new research produced in the
last 18 months, the large number of pages devoted to the Ellipsoid
Algorithm seems a bit overdone. However, it is perhaps the clearest
presentation of this work now available for the new student.
In summary, as I stated earlier, I would recommend this book for
any instructor of Linear Programming and for introductory students
who desire a reference book that provides more rigor than most
textbooks of today.
-Donna Crystal Llewellyn

Mathematical Programming Techniques
By N. S. Kambo
EWP, New Delhi, 1984

This is a comprehensive volume dealing with the available
methods in mathematical programming (or optimization tech-
niques), which are commonly adopted nowadays. It consists of 16
chapters with headings: (1) Introduction, (2) Convex Sets and Func-
tions, (3) Linear Programming, (4) Duality in Linear Programming, (5)
Transportation and Assignment Algorithms, (6) Methods for Special
Linear Programs and Integer Programming, (7) Kuhn-Tucker Opti-
mality Conditions, (8) Convex Programs and Duality, (9) Uncon-
strained and Transformation Optimization Techniques, (10) Quad-
ratic Programming and Complementarity Problems, (11) Nonlinear
Programming Methods, (12) Geometric Programming, (13) Goal
Programming, (14) Stochastic Linear Programming, (15) Dynamic
Programming, and (16) Game Theory, respectively.
As a whole, the materials contained are well chosen and also well
arranged so that they can be used as a one-year course or two one-
semester courses of basic study for those in operations research and
engineering, as well as for those graduate students specializing in
optimization techniques.
More precisely, Chapter 1 gives a general description of the
mathematical programming problem and displays 11 interesting
special examples that can be formulated as mathematical program-
ming problems. Chapter 2 may be regarded as a brief introduction to
convexity analysis that is certainly an indispensable tool for the study
of optimization techniques. Chapters 3, 4, 5 and 6 treat the most
frequently used linear programming methods and some useful spe-
cial algorithms.
Although the treatment of linear programming techniques forms
an important portion of the book, the most attractive and readable
part seems to be those chapters from 7 to 13 dealing with various
nonlinear problems and techniques. Especially, the treatment of
Kuhn-Tucker optimality conditions (Chapter 7) with particular
emphasis on convex programs (Chapter 8) appears both concise and
Chapter 14 introduces the chance-constrained linear program-
ming techniques initiated by A. Charnes and W. Cooper in the 1960s.
This chapter may easily be read and understood by any student who
knows the elements of probability theory or mathematical statistics.
Chapters 15 and 16 may be viewed as very concise introductions
to Richard Bellman's dynamic programming and John von
Neumann's elements of game theory, respectively. Consistent with
the main objective and the presentation style of the whole book, these
two chapters are concerned with techniques and processes for solving
some problems of practical interest. Actually, Chapter 16 deals only
with two-person games and finite matrix games.
As may be observed, this book has several notable features,
namely the clear exposition of all those basic concepts that are needed
in the formulation of problems and techniques, the proper propor-
tionality of the materials displayed in each chapter in accordance with
their own importance and usefulness for applications, and the consid-
continues on page ten

I ~ ~-~----~


O PT I M A number twenty-two


PAGE~~~~~~I 10 0 ubrtenItoOTBR18


erable variety of worked examples illustrating various important
techniques, algorithms and applications. By and large, theorems and
proofs are stated precisely and rigorously and are also easily acces-
sible to beginners. Moreover, each chapter ends with a good number
of exercises that are undoubtedly very useful for students as well as
for the self-taught.
This book contains an appendix which may be omitted in reading
by those who have already learned calculus and linear algebra.
However, the references and further reading containing about 190
items at the end of the book seem to be of high reference value for
teachers and researchers.
It is known that some important ideas used in mathematical
programming techniques are actually suggested or implied by each
other, e.g. conjugate gradient methods and Powell's method, etc.
Also, some useful methods are frequently generated or derived from
some old ones or their suitable combinations by avoiding certain
weakpoints. These facts, as the reviewer sees it, have not been well
explained in this book. Moreover, comparisons between the advan-
tages and shortcomings of various methods are also seen to be lacking
or not adequately discussed.
Some expressions displayed in the book may be obviously sim-
plified or shortened. For example, the derivation on pages 41 and 42
is simplified by using the symmetry in y, and yi. There are also
numerous typographical errors observed in various parts of the book.
Generally, the reviewer has the opinion that this volume is not
only a textbook for students and teachers but also a useful reference
book for applied mathematicians and technicians who are using
optimization techniques in their research. The reviewer sincerely
hopes that the future edition of this book will eliminate all the
typographical errors, and if possible, add some brief historical re-
marks or references to each chapter.
-L. C. Hsu

Computational Geometry. An Introduction
By F. P. Preparata and M. I. Shamos
Springer, Berlin, 1985

After reading the first pages of this book, I was impressed by the
authors' well-done work. On one hand they use a very lively style for
their explanations while on the other hand there is the endeavor to be
precise, clear and lucid.
So it is not surprising that in Chapter 1 of this book the basic
definitions which are used later are carefully introduced. One learns
here the history and definition of computational geometry as well as
fundamentals of algorithms and geometry. Furthermore, a model of
computation (primitives, transformability, algebraic decision tree),
which remains undefined in many other books, is formulated. This
model forms the basis for all subsequent investigations of the com-
plexity of an algorithm. Generalizing this author's procedure one can
observe that the book is self-contained. This fact is of particular
importance since the authors intended to give an introduction (as
stated in the subtitle) to computational geometry. Moreover, it was

originally conceived as an early undergraduate textbook.
What are the contents of computational geometry and how have
they been explained by this book? The first systematic investigations
in this field emerged at the same time as the ensuing fields of
applications became more relevant: computer-aided design or engi-
neering, computer graphics and robotics.In these investigations some
problem classes of a particularly fundamental character have crystal-
ized. These problem classes, all covered by the book, are: geometric
searching and retrieval, convex hull constructions, proximity, inter-
section, and the geometry of rectangles. In the treatment of these
subjects the main interest of the authors lies not only in the presenta-
tion of readily usable techniques and programs but in the declaration
of the interactions between design and analysis leading to the result:
"good" algorithms. For that purpose the book contains the descrip-
tions of the most important methods for solving every problem
ending with the optimal algorithms. In some places this procedure
may be long-winded. However, in most cases these lectures on the
importance of different data structures or on one of the fundamental
elements of computational geometry, are very interesting. The funda-
mental elements of computational geometry are binary search, divide
and conquer, Voronoi-diagrams and sweep algorithms. In the fore-
ground of the analysis of algorithms are, as usual, the respective
worst-case behavior and only in a few cases the average behavior. Let
it be noted, in addition, that there are three performance measures
(preprocessing time, processing time, storage) used simultaneously
Regarding the valid assertion for this area, "At this time it is
typical of computational geometry, the planar problems are well
understood, while very little is known in R3 and even less for higher
number of dimensions", this book illustrates impressively that so far
many questions could be solved by an optimal algorithm. In the
explanation of those 2- or 3-dimensional optimal solutions, a lot of
figures make it possible for the reader to easily understand very
complicated and complex details. Because of this, it is very pleasant to
read the book.
Every chapter is extended by Notes and Comments. Here not
only are additional alternatives of algorithms given but also historical
background, recent developments and points for further investiga-
tions noted. Finally, concluding each chapter are some exercises
closely related to the chapter.
This book is not easy to criticize, but I should make two com-
ments. Linear programming is also a central problem in computa-
tional geometry. Thus I was disappointed and surprised that the
results of Megiddo, 1984 (in which for arbitrary but fixed dimension
a linear algorithm for linear programs is given) are not worked out.
Furthermore, in some places the authors are not successful in finding
serious helpful applications. There are a few misprints which can be
easily corrected.
In summary, this book is well written and thoroughly and
didactically reasoned. I would recommend it to every instructor as an
educational handbook as well as to those who want a reference book
on computational geometry, since it is singular in this field and up 1t
date. It includes titles of references up through 1985.
-A. Wanka

_I ~ _


OPTIMA number twenty-two


PAGE 11 0P T I M Anumber twnty two OTOBER 198


Handbook of Mathematical Economics,
Volume III
Edited by K. J. Arrow and M. D. Intriligator
North-Holland, Amsterdam, 1986
ISBN 0-444-86128-9

The third and last volume of the Handbook covers mathematical
approaches to welfare economics and to economic organization and
planning. These topics are organized into the following five chapters:
Social Choice Theory by Amartya Sen, Agency and the Market by
Kenneth J. Arrow, the Theory of Optimal Taxation by J. A. Mirrlees,
Positive Second Best Theory: A Brief Survey of the Theory of Ramsey
Pricing by Eytan Sheshinski, and Optimal Economic Growth, Turn-
pike Theorems and Comparative Dynamics by Lionel W. McKenzie.
SThe material on mathematical approaches to economic organization
and planning is divided into three chapters, namely Organization
Design by Thomas A. Marschak, Incentive Aspects of Decentraliza-
tion by Leonid Hurwicz, and Planning by Geoffrey Heal.

Elaboration of various chapters differ widely. One finds 100
pages of a very comprehensive and detailed account of social choice
theory at one extreme and 10 pages of brief sketch of some ideas from
the literature on the economic theory of the principal-agent relation at
the other extreme.
Despite the diversity of elaboration on various parts of mathe-
matical economics, which is almost inevitable in a book by more than
30 authors, the Handbook is a treasure for researchers and graduate
students because of its unique coverage of the state of the art as of the
late 1970s. I believe it will serve for many years as a definitive source,
reference, and teaching supplement for the field of mathematical
-Milan Vlach

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1 _ I


OPTIMA number twenty-two


~AGE 12 OPTIMA number twenty-two OCTOBER 1987
7 I



Siegfried Schaible, formerly of the University of Alberta, has
moved to the Graduate School of Management, University of
California, Riverside...The EURO IX TIMS XXVIII joint conference
will be in Paris, July 6-8, 1988...1985 ORSA Lanchester Prize Honor-
able Mentions were awarded to Vasek Chvatal for his book on
Linear Programming and to Mordecai Haimovich and Alexander
Rinnooy Kan for their paper "Bounds and Heuristics for Capaci-
tated Routing Problems"...Rinnooy Kan and Peter Hammer re-
ceived 1986 EURO Gold Medals for their contributions to combina-
torial analysis...Richard Karp has been named the John von Neu-
mann Lecturer at the 35th SIAM Anniversary Meeting in Denver.

Deadline for the next O P T I M A is January 1, 1988.

_______________________________________________ ~1~ ---

Books for review should be sent to the
Book Review Editor, Prof. Dr. Achim
Bachem, Mathematiches Institute der
Universitit zu K81n, Weyertal 86-90,
D-5000 K6ln, West Germany.

Journal contents are subject to
change by the publisher.

Donald W. Hearn, Editor
Achim Bachem, Associate Editor
Published by the Mathematical
Programming Society and
Publication Services of the
College of Engineering,
University of Florida.


303 Weil Hall
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University of Florida
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OPTI M A number twenty-two

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