MATHEMATICAL PROGRAMMING SOCIETY NEWSLETTER November 1990
QRC ANIZERS of the 14th
International Symposium on
Ma thematical Programming have
nmiled the second announcement of
the conference which will be held August 5 9,
1991, at the University of Amsterdam and is being
chaired by Jan Karel Lenstra, Alexander Rinnooy
Kan and Alexander Schrijver.
The meeting will open on Monday, August 5, in the Lutherse
Kerk, the main auditorium of the university, with a plenary
address by W. R. Pulleyblank. The session will include awarding
of the society prizes: Fulkerson Prize (for discrete mathematics,
joint with AMS), George B. Dantzig Prize (for major contribution
in mathematical programming, joint with SIAM), Beale-Orchard-
Hays Prize (for computational mathematical programming) and
the A. W. Tucker Prize (for outstanding student paper).
There will be a reception on Monday evening and a banquet on
Wednesday evening, both at 18.30. The MPS business meeting
will be Wednesday afternoon at 1630.
One-hour invited lectures by leading experts in all aspects of
mathematical programming will highlight the technical program,
and there will be many parallel sessions with invited and contrib-
uted papers. The invited lecturers will include E. H. L. Aarts, R.
E. Bixby, A. R. Conn, T. M. Cook, J. E. Dennis, Jr., C. C. Garcia,
M. Grdtschel, R. M. Karp, K. Kennedy, L. G. Khachiyan, C.
Lemarichal, K. Mehlhorn, C. H. Papadimitriou, D. F. Shanno,
and R. E. Tarjan. Two special memorial sessions will honor
Robert Jeroslow and Darwin Klingman. CONTIUES, PAGE TWO
P T I M A
CONFERENCE NOTES 4
TR & WP 5-6
BOOK REVIEWS 7-9
---- --- --- ---i -
PAGE 2nmbert- eNOVEMBER199
E arly registration deadline
is April 1; the abstracts for
contributed papers are due
June 1; and hotel reservations
should be made by July 1.
Registration fees before April 1
are NLG 240 and NLG 340 for
members and nonmembers,
respectively. After April 1 the
fees are NLG 300 and NLG 400.
(On Oct 15,1990, 1 NLG was
US $ 0.57.) Student fees are
one-half these rates with
certification of student status.
The banquet fee is NLG 75.
Addresses and forms are
contained in the second
announcement which also
includes information on travel
and the city. The symposium
secretariat address is:
Paulus Potterstraat 40
1071 DB Amsterdam
(+31-20-6752120 after April 1)
Thirty mathematical pro-
grammers from the Nordic
countries gathered in
Copenhagen August 25 and
26 for a two-day conference.
During the conference it was
decided to form a Nordic
section of MPS. A board was
elected, consisting of Stein
W. Wallace, Haugesund
Maritime College, Norway
(leader); Jens Clausen,
University of Copenhagen,
Denmark; and Kaj Holmberg,
Linkoping Institute of
Technology, Sweden. It was
decided to run a short
meeting in two years and to
set up a system for automatic
distribution of electronic mail
to all members.
The membership has in-
creased from 25 to about 34
during this year. It is felt
that the increase is a result of
the activities surrounding the
formation of the geographi-
cal section and the meeting
in Copenhagen. The Nordic
section covers Norway,
Sweden, Denmark, Finland
Call for Papers
ORSA Journal on
Special Issue on
The ORSA Journal on Comput-
ing is dedicating a special issue to
the subject of computational
geometry. The rapidly growing
field of computational geometry
has addressed many problems of
interest in operations research and
has provided new algorithmic
techniques for tackling a variety of
optimization problems. Con-
versely, many well-established
methods of operations research
have contributed to the progress in
geometric algorithms. This special
issue is designed to stimulate the
interplay between computational
geometry and operations research
and to enhance the application of
techniques form computational
geometry to problems arising in
operations research. The special
issue will provide the advantage of
grouping together high-quality
papers in the area, as well as the
benefit of speedy review and
minimal publication delays.
Manuscripts are solicited over a
wide range of topics within
computational geometry and its
applications including but not
Manufacturing, Robotics and
Shortest Paths, Networks
All manuscripts will be promptly
and carefully refereed. High-
quality manuscripts not accepted
in the special issue due to space
limitations will be considered, with
the authors' permission, for
inclusion in a regular issue of the
Authors should submit four copies
of their manuscript to either of the
Joseph S.B. Mitchell
School of Operations Research
and Industrial Engineering
Engineering Theory Center
Ithaca, NY 14853 USA
Tel: (607) 255-9148
Jan Karel Lenstra
Department of Mathematics
and Computing Science
Eindhoven University of
PO Box 513
5600 MB Eindhoven
by no later than June 1, 1991. To
expedite handling, authors should
prepare their manuscripts
consistent with the Instructions
for Authors that appeared in
Volume 2, Number I of the ORSA
Journal on Computing; a copy is
available from the Editors.
- "I ~
Editor-in-Chief: Peter L. Hammer, Rutcor, Hill Center for the Mathematical Sciences.
Rutgers University, Busch Campus, New Brunswick, NJ 08903.
THE 1990 PROGRAMME
27: Computational Methods in Global Optimization
Editors: Ed. P.M. Pardalos & J.B. Rosen
Contains a .ariet.i of dreerminisic computational ai urrithmn
and ne'A approaches for sol' ing global opuimi.atiion
problems. Papers include. nes approja-he foir sol ing
reterst cone'., programs, interior point approaches ; for
ncnconr.ew quadratic programming, di.alit: technique'.
inter-al analysis, and branch and bound methods.
26: Automated Manufacturing Systems
Editor: Ed. J.B. Mazzola
Ree.irhi feature' stdl e-ol-lhe-art operajiiorj-reitnarch-based
articles on the design, planning, and control of automated
produ:iiori ..sit mi. *\m.on, irh topics addressed in thi..
,s;ue are production planning. Isa :ut, rojiin ,. and
,cheduinLu in tle\ible manuia.cturing si',tem. ,utomratid
i m.ritbl: >i cm.. fle' lhie-rirm nuilaituriinC TreL hnolug.
imci.tmcnt0 dec.iion-. and tlii appphliao. n ot ilrreniariled
craph, to model behavior in pr.dJu..ilo n ..'.trmn'.
Production Planning and scheduling
Editor: M. Que ranne
Application in produ'nai-n planning and ..hcdulin~ Topics
include hVirarihical planning and dt.od-mpor]iinrm approlachli-.
rhi inerfacet: het.i een planning nJid s duljing fun iihor.r ,
eur'.e. of niodel, for productii n. c,:hedulinri surne oni
sequencing theorN. implitnmcnrialon -it Oipcralloiri re,:jrcht
nicihods in practice.
25: Optimization with Dala Perturbation,. A Collection of
Editor: V. Fiacco
-entral themes are the theory and application of senit'.iilt.
stability and parametric analysis of solutions to optimization
problems whose data is subject to perturbation Classes of
problems addressed include aariational inequaJities.
stochastic, semi-inrinite, integer, nonlinear, geometric. linear
and mult-objecti\e programs. Results also coter a side
scope, ranging from optimal .alLie and solution point
continuity and differeniuabilit to parametric methods for
general nonlinear programs, including recent results based
on singularity theory) and continuation methods. There is
esen included one paper in the area of simulation
optimization and sensitivity analysis. to eemplifl. recent
extensions to discrete e\ent s\csems. Many important earlier
results have been simplified and unified in uhat promises to
be a brilliant collection of tutorial surses.s.
24: Operations Research in China
Editor: lue Min)i
Development of operations research in China gue; back for
about 35 years. Most of the papers written b- Chinese
operations researchers were published in Chinee and are
rarely accessible to reader- outside China The purpose of
this volume is to gne a presentation of the development in
variouss branches of operations research in China. The
volume contains surveys as well as numerous contributed
papers, both on methodological and applied issues
23: Intransilise Preferences
Editor: ~1 .\. Gehrlein
An important contributionn to &cision anal,'i-. iia'ir;ne
papers on ari no l) pecls Uil [hi' thLeaor. .-Conrihuti.-rin dlja
mith moJel. ranging fromin intransic-it.' and iTh lcs .- nairTe'
efficien-'. mn'ea rcm:nt on init set,. linr ar ,'itOr.' .r ,
partial orders. .cling theer, prclerent re- .rsail', c-pec-i
utilities iith nonlinear threlhold-. indridual judt nicR i
tatst.:s fr,,r stock marker ini.-lctinents, etc.
22: Supercomputers and large-Scale )Opimizalion
Editor: J. Ben Rosen
Research oii alcorilhni; and rclaied solt'-.are tor the: 'i.iliior
of larire-scale optirrnzaiion prorblern- on -uperconiputt r'- an
parallel machine. Parer- cc,;er nariui dir;..ion ,.
research including ne', approach hes ii.o ol i. n- .rr', Luii
li car prograniming aridd related pnrcbl.ms on :-c. and
parallel maIrnahii.is, parallel soluaoii of large g -.cale jnc rah:rji:.
ner- ork.., nail\ prahlemi, relaiLd I.) OptimiZatlCn i. i-
inctLer pro: r.am- 3ind appli.ators
A\ 411..BL 1 \ OLL %IS:
21. EL H.I. Cre.:nbet & F CGlo..r. L.inkages with
Arlilitial Intelligence, I v
n20 J. B. Sh-.t.r Networks Optimitalion and AppliLalion,.
19 Ed P C F thburn & I H. la a-lic, Choict- under
IS Ed F \ Loutcau. a o., [acilii. ILocation Analysis:
Theory and Applications, 1989
17: Ed. A Ku.iak & \ .E. \\ ilhelm, Analisis, Modelling
and Design of Modern Production Systems. 1989
16: Ed. R L. Keene% a.o.. Multi-Attribute Decisinn Making
via O.R.-Based Expert systems. 1989
15: Ed. K.E. Stecke & R. Sun. Flexible Manufacturing
Syslems: Operations Research Models and Applicalions II.
14: Ed. R.R. Meyer & S A. Zemnos. Parallel
Optimization on Noel Computer Architectures. 19.'
13. Ed. B. Someone a.o., Fortran Codes for Network
12: Ed R.G. Jeroslo'a. Approaches to Intelligent Decision
10-11: Ed. T. Ibaraki. Enumeratise Approaches on
Combinatorial Optimization, 2 '.ol. 198'
8-9: Ed. S.L Albin & C.M. Harris, Statistical and
Computational Problems in Probability Modelling
2 vols. 198I
7: Ed. I. Blazcin.i: a.o Scheduling under Resource
Constraint: Deterministic Models. 1986
6- Ed. J.P. Osleeh & S J. Radick. Locational Decisions:
iMehodology and Applications. 19.6
3-4-5: Out ot print
2: Ed. R.G Thompson & R.M. Thrall. Normalie -Analsi,
for Policy Decisions. Public and Prisate, 1985
I- Ed. F. Archeii & F. laffioli, Stochaslics and
Price per volume incl. postage: S 153.60, or S 80.00 for members ORSA,'TIMS. Please request extensive prospectus for 'hole
series: sol. 1-27, 1984-1990. Proposals for new volumes should be addressed to Peter L. Hammer, Editor-in-Chief.
Ho* to order: Please send your order either to your usual agent or directly to our Basel Head Office as mentioned below.
In the United States please address your order to: J.C. Baltzer AG, Scientific Publishing Company,
P.O. Box 8577. Red Bank. NJ 07701-8577.
S .CK irAL E v G, SC~IENII mPmiUmBi~LSHEUINGS~ COMPANY
WelsIIpat 0 CH408BslSwtean
O 1) T I imllP
Optimization Days 1991
May 8-9, 1991
All those interested in optimization
methods and their present or potential
applications are invited to participate.
Those who can give talks on new
methods of optimization and their
applications are especially welcome.
Sessions will consist of invited and
contributed talks. Papers presenting
original developments as well as those
of expository nature will be considered.
The languages of the conference will be
French and English. Plenary speakers
E. Balas USA
R. Horst Germany
D. Shanno USA
P. Toth Italy
Contributors are encouraged to submit
a paper for publication in a special issue
of the journal INFOR devoted to the
Optimization Days 1991.
Two copies of a 100-200 word summary
defining clearly the content of the
paper, together with the registration
form, should be forwarded before
January 31, 1991, to:
Dr. Martin Desrochers or
Dr. Brigitte Jaumard
Ecole de Hautes Etudes Commerciales
5255 avenue Decelles
CANADA H3T 1V6
Tel: (514) 340-6048
Fax: (514) 340-5665
Authors will be notified of the accep-
tance of their talks by March 1, 1991.
Summaries of the talks will be distrib-
uted at the conference. For more
information, please contact the above.
15th IFIP Conference on
System Modelling and
September 2-6, 1991
At this conference, recent results will
be discussed in sessions on Optimiza-
tion and Systems Theory, Linear and
Nonlinear Programming Algorithms,
Optimal Control, Stochastic Optimiza-
tion, and Applied Modelling and
Optimization. Further sessions may be
organized based on contributed
Plenary talks will be given by I.V.
Evstigneev, U.E. Kalman, R. Kl6tzler, B.
Kummer, J.E. Lagnese, D.Q. Mayne, V.S.
Michailevich, S.E. Shreve, P.L.M.J. Toint,
J.P. Vial and J. Zowe.
Three copies of extended abstracts of papers
to be presented should be received by the
conference secretariat by January 10, 1991.
They should be two to four pages in length
(typewritten, single-spaced) and should
present original unpublished results by the
Acceptance of contributed papers is decided
by the International Program Committee;
abstracts arriving after the deadline cannot
be considered. Notification of acceptance
will be March 15, 1991.
The conference is to be held at the Univer-
sity of Zurich, downtown Zurich, Switzer-
land. Accommodation will be provided in
nearby hotels at the rate of about Swiss
Francs 80-150. The registration fee will be
Swiss Francs 270 for early registration. A
social program is arranged.
The conference language is English. Selected
papers will be published in the Conference
The conference Secretariat is:
Dr. K. Frauendorfer
Institute for Operations Research
University of Zurich
CH-8044 Zurich, Switzerland
Tel: +41-1-257 37 71
Fax: 01/252 1162 UNI ZH IOR
Telex: 817 260 uniz ch
E-mail: ifip91 at czhrzula (earn or bitnet).
-- II ~
S.. : A
PAGE 5 number thirhj-one NOVEMBER 1990_
Department of Industrial and
303 Weil Hall
University of Florida
Gainesville, Florida 32611-2083
C-S. Lin and C-Y. Lee, "Single Machine
Stochastic Scheduling with Dual Criteria," RR#
R. Uzsoy, C-Y. Lee and L.A. Martin-Vega,
"Scheduling Semiconductor Test Operations:
Minimizing Maximum Lateness and Number of
Tardy Jobs on a Single Machine," RR# 90-4.
W.W. Hager and D.W. Hearn, "The Dual
Active Set Algorithm and Quadratic Networks,"
C-Y. Lee, R. Uzsoy and L.A. Martin-Vega,
"Efficient Algorithms for Scheduling Batch
Processing Machines," RR# 90-8.
Rutgers Center for Operations
P. O. Box 5062
New Brunswick, New Jersey 08903
F.S. Roberts, "No-Hole Non-Adjacent Color-
ings," RRR 11-90.
P. Hansen and M. Zheng, "Shortest Shortest
Path Trees of a Network," RRR 12-90.
Y. Crama and F.C.R. Spieksma, "Approxima-
tion Algorithms for Three-Dimensional Assign-
ment Problems with Triangle Inequalities," RRR
P. Hansen and M. Zheng, "An Algorithm for
the Minimum Variance Point of a Network,"
C. Wang, "On Critical Graphs for Opsut's
Conjecture," RRR 15-90.
A. Gu6noche, P. Hansen and B. Jaumard,
"Efficient Algorithms for Divisive Hierarchical
Clustering with the Diameter Criterion," RRR
P. Hansen, M.V. Poggi de Aragdo and C.C.
Ribeiro, "Boolean Queries Optimization and the
0-1 Hyperbolic Sum Problem," RRR 17-90.
D.S. Hochbaum and R. Shamir, "Strongly
Polynomial Algorithms for the High Multiplic-
ity Scheduling Problem," RRR 18-90.
Y. Pinto and R. Shamir, "Efficient Algorithms
for Minimum Cost Flow Problems with Convex
Costs," RRR 19-90.
D.S. Hochbaum, R. Shamir and J.G.
Shanthikumar, "A Polynomial Algorithm for
an Integer Quadratic Non-Separable Transpor-
tation Problem," RRR 20-90.
I. Adler and R. Shamir, "A Randomization
Scheme for Speeding Up Algorithms for Linear
and Convex Programming Problems with High
Constraints-to-Variables Ratio," RRR 21-90.
Y. Crama, P. Hansen and B. Jaumard,
"Finding Spurious States of Neural Networks,"
A.E. Roth, U.G. Rothblum and J.H. Vande
Vate, "Stable Matchings Optimal Assignments
and Linear Programming," RRR 23-90.
E. Boros and P.L. Hammer, "Cut-Polytopes,
Boolean Quadric Polytopes and Nonnegative
Quadratic Pseudo-Boolean Functions," RRR 24-
CONTINUES ON FOLLOWING PAGE
9Cl ~~--~---~---s~-- ---------~
Technical Reports &
T.J. Carpenter, I.J. Lustig, J.M. Mulvey and
D.F. Shanno, "A Primal-Dual Interior Point
Method for Convex Separable Nonlinear
Programs," RRR 25-90.
I.J. Lustig, R.E. Marsten and D.F. Shanno,
"On Implementing Mehrotra's Predictor-
Corrector Interior Point Method for Linear
Programming," RRR 26-90.
M.J. Rosenblatt and U.G. Rothblum,
"Optimality of 'Cut Across the Board' Rule for
Constrained Optimization Problems with an
Application to an Inventory Model," RRR 27-
E. Boros, P.L. Hammer and R. Shamir,
"Balancing Rooted Data Flow Graphs," RRR
S.R. Arikati and U.N. Peled, "A Linear
Algorithm for the Group Path Problem on
Chordal Graphs," RRR 29-90.
F. Tardella, "On the Equivalence Between Some
Discrete and Continuous Optimization
Problems," RRR 30-90.
P. Favati and F. Tardella, "Convexity in
Nonlinear Programming," RRR 31-90.
C. Mao-cheng, "An Algorithm for Optimum
Common Root Functions of Two Digraphs,"
C. Mao-cheng, "An Algorithm for an Eulerian
Trail Traversing Specified Edges in Given
Order," RRR 33-90.
S.D. Flam, "Solving Convex Programs by
Means of Ordinary Differential Equations,"
M.B. Cozzens and F.S. Roberts, "Meaningful-
ness of Conclusions About Greedy Algorithms
for T-Colorings," RRR 35-90.
J. Kahn, "Coloring Nearly-Disjoint
Hypergraphs with n+o(n) Colors," RRR 36-90.
J. Kahn, "On a Problem of Erdds and Lovdsz,"
D. Sakai and C. Wang, "No-Hole (r+l)-
Distant Colorings," RRR 38-90.
P.C. Fishburn and F.S. Roberts, "Elementary
Sequences, Sub-Fibonacci Sequences," RRR 39-
A. Bagchi and B. Kalantari, "New Optimality
Conditions and Algorithms for Homogeneous
and Polynomial Optimization Over Spheres,"
B. Avi-Itzhak and S. Halfin, "Non-Preemptive
Priorities in Simple Fork-Join Queues," RRR
Z. Fiiredi, J. Kahn and P.D. Seymour, "On
the Fractional Matching Polytope of a
Hypergraph," RRR 42-90.
Operation Research Group
The Johns Hopkins University
Baltimore, MD 21218
U.G. Rothblum, H. Schneider and M.H.
Schneider, "Characterizations of Max-Balanced
M. Hartmann and M. Schneider, "An
Analogue of Hoffman's Circulation Conditions
for Max-Balanced Flows," #90-02.
C. ReVelle and V. Marianov, "The Probabilis-
tic FLEET Model with Individual Vehicle
Reliability Requirements," #90-03.
C. ReVelle and D. Serra, "The Maximum
Capture Problem Including Relocation," #90-04.
V. Marianov and C. ReVelle, "The Standard
Response Fire Protection Siting Problem," #90-
R. Klimberg, C. ReVelle and J. Cohon, "A
Multiobjective Approach to Evaluating and
Planning the Allocation of Inspection Re-
M.H. Schneider, "Max-Balanced Flows," #90-
C. Neti, M.H. Schneider and E.D. Young,
"Maximally Fault-Tolerant Neural Networks:
Computational Methods and Generalization,"
U.G. Rothblum, H. Schneider and M.H.
Schneider, "Scaling Matrices to Prescribed
Row and Column Maxima," #90-09.
CORE (Center for Operations
Research and Econometrics)
University Catholique de
34 Voie du Roman Pays
L. Qi, "Bisubmodular Functions," D.P. 8901.
J.P. Sousa and L. Wolsey, "Time Indexed
Formulations of Non-Preemptive Single-
Machine Scheduling Problems," D.P. 8904.
S.P. Anderson, A. de Palma and J.-F. Thisse,
"Social Surplus and Profitability under
Different Spatial Pricing Policies," D.P. 8910.
C. Bousba and L. Wolsey, "Finding Minimum
Cost Directed Trees with Demands and
Capacities," D.P. 8913.
R.G. Jeroslow, R.K. Martin, R.L. Rardin and
J. Wang, "Gainfree Leontief Problems," D.P.
A. Wagelmans, S. van Hoesel and A. Kolen,
"Economic Lot-Sizing: An 0 (n log n)-
Algorithm that Runs in Linear Time in the
Wagner-Whitin Case," D.P. 8922.
L. Wolsey, "Formulating Single Machine
Scheduling Problems with Precedence Con-
straints," D.P. 8924.
J.J. Gabszewicz and J.F. Thisse, "Location,"
K.M. Anstreicher, "On the Performance of
Karmarkar's Algorithm Over a Sequence of
Iterations," D.P. 8934.
R.K. Ahuja and T.L. Magnanti, "Some Recent
Advances in Network Flows," D.P. 8936.
K.M. Anstreicher, "A Combined Phase I -
Phase II Scaled Potential Algorithm for Linear
Programming," D.P. 8939.
R.L. Rardin and L. Wolsey, "Valid Inequali-
ties and Projecting the Multicommodity
Extended Formulation for Uncapacitated Fixed
Charge Network Flow Problems," D.P. 9024.
K.M. Anstreicher and P. Watteyne, "A
Family of Search Directions for Karmarkar's
Algorithm," D.P. 9030.
I II^---- -~~-~~------------
This book gives an excellent overview of
the numerical techniques that are neces-
sary for efficient computer implementation of the
simplex method. Therefore, the book is at the
forefront of mathematical programming, numerical
mathematics and computer science.
Based on proper matrix algebra knowledge, the book is self-
contained. First, basic knowledge of linear programming is
presented; detailed studies of numerical algorithms follow;
finally, some advanced techniques are discussed.
Although the new methods (Ellipsoid method Khachian 1979,
Interior point methods Karmarkar 1984) of linear program-
ming are mentioned in the introduction, their numerical algo-
rithms are not discussed in the book. The efficient implemen-
tation of interior point methods needs some different numeri-
cal techniques. These are important to understand by one who
implements linear programming software, but when this book
was prepared, the technology of implementation of the interior
point methods was not yet clear. Therefore, the book is re-
stricted to the computational and implementation methods of
the simplex method.
The first of the three main parts deals with the linear program-
ming problem, with some classical methods (Chapter 1), and
contains a description of the simplex method (Chapter 2).
The second part is the body of the book. Numerical techniques
and implementational strategies are discussed here. Chapter 3
deals with external and internal representations of linear pro-
gramming problems. Chapter 4 contains the necessary funda-
mentals of numerical analysis. Chapter 5 is devoted to the
factorization strategies of the basis matrix with LU factoriza-
tion as the primary tool. Accuracy, stability and strategies to
control the density (fill in) are considered as well. Refined
updating and solving strategies (Bartels-Golub, Forrest-Tomlin,
Fletcher-Matthews) are discussed in Chapter 6. Entering and
leaving variable selection strategies are demonstrated in Chap-
Computer Solutions of
by J. L. Nazareth
OUP USA, 1988
The book is well written. It can be a useful handbook for
researchers, teachers and students who are interested in linear
programming or anyone who is a linear programming user and
wants to understand more deeply how a linear programming
package works. The second part of the book can also be the
material for a second semester of an advanced linear program-
Simulated Annealing and Boltzmann
by Emile Aarts and Jan Korst
John Wiley, Chichester, 1989
Simulated annealing is a method for solving combinatorial
optimization problems. Itavoidsbeing trapped in local optima,
as usually happens with local search. To escape from a neigh-
boring local optimum, a generated feasible solution is accepted
with a certain probability, even if it is worse than the preceding
one. The Boltzmann machine is a neural network model. One
E W S ters 7 and 8. The latter discusses
selection rules for finding an
initial feasible solution (first
phase methods), while the
former is devoted to second
phase pivot rules. The last two
chapters of the second part
summarize the algorithmic elements and
suggest a complete implementation of the
simplex method. Further implementational as-
pects and the usage of mathematical programming
systems in practice are also discussed.
The third part of the book contains further issues of linear
programming. Chapter 11 discusses duality theory, the dual
simplex method and sensitivity analysis. Decomposition algo-
rithms, like Dantzig-Wolfe and Benders decomposition, and
their implementational strategies are presented in Chapter 12.
The last chapter is a short description of homotopy methods. It
presents Dantzig's self-dual parametric simplex algorithm as a
specific implementation of the homotopy method.
PAE NVEBE 19
of its remarkable features is massive parallelism. ,
As such, it is suitable for parallel execution of the f
simulated annealing algorithm. IJk
In Chapters 1 and 2 of the book the local search a a v
and simulated annealing algorithms are intro-
duced, and the analogy of the latter method with
the physical annealing process is shown. In Chap-
ter 3 the asymptotic convergence of the simulated
annealing algorithm is discussed using the theory of Markov
chains. Chapter 4 deals with a polynomial-time implementa-
tion of simulated annealing, which provides an approximation
of an optimal solution. Chapters 4 and 5 are also devoted to an
analysis of the empirical performance of the algorithm and its
application in the solving of combinatorial optimization prob-
lems, such as: travelling salesman, max cut, independent set,
and graph coloring. Chapter 6 discusses how to speed up the
algorithm by execution on parallel computers since the effi-
ciency of the simulated annealing method is poor for some
problems. Chapter 7 focuses on the subject of neural comput-
ing. Chapter 8 introduces different types of Boltzmann ma-
chines whose state transitions are studied again using Markov
chains to show the analogy with parallel simulated annealing.
Chapter 9 shows that 0-1 optimization problems can be associ-
ated with Boltzmann machines so that maximizing the consen-
sus function is equivalent to solving the optimization problem.
Chapters 10 and 11 deal with how to solve classification
problems using Boltzman machines, which are important to
pattern recognition, and how a Boltzmann machine is able to
The book gives a clear introduction to simulated annealing and
Boltzmann machines, where most propositions are carefully
proved and accompanied by worked examples. It also presents
many recent research results and provides a detailed survey of
the relevant literature. One possible disadvantage of the mono-
graph is that the performance of the simulated annealing
algorithm is not compared with that of other modern ap-
proaches for solving approximately large combinatorial opti-
mization problems, for instance, tabu search.
However, the book can be warmly recommended
to graduate students and other researchers in
combinatorial optimization, parallel processing,
neural networks, and artificial intelligence.
New Computer Methods for Global
by H. Ratschek and J. Rokne
Ellis Horwood, Chichester, 1988
The enormous practical need for solving global optimization
problems, coupled with a rapidly advancing computer tech-
nology, has allowed one to consider problems which a few
years ago would have been considered computationally in-
tractable. As a consequence, we are seeing the creation of a
large and increasing number of diverse algorithms for solving
a wide variety of multiextremal global optimization problems.
By definition, a global optimization problem seeks at least one
global minimizer of a real-valued objective function that pos-
sesses (often very many) different local minimizers in the
feasible set D Rn. It is well-known that in practically all disci-
plines where mathematical models are used, there are many
real-world problems which canbe formulated as multiextremal
global optimization problems.
Standard nonlinear programming techniques have not been
successful for solving these problems. Their deficiency is due
to the intrinsic multiextremality of the formulation and not to
the lack of smoothness. One can observe that local tools such as
gradients, subgradients, and second order constructions such
as Hessians, cannot be expected to yield more than local
solutions. One finds, for example, that a stationary point is
often detected for which there is even no guarantee of local
minimality. Moreover, determining the local minimality of
_sl ~ I I ~ I~
PAEume to NO
such a point is known to be NP-hard in the sense
of computational complexity even in relatively
simple cases. Apart from this deficiency in the
local situation, classical methods do not recognize g v
conditions for global optimality.
For these reasons global solution methods must
be significantly different from standard tech-
niques, and they can be expected to be and are much
more expensive computationally. Fortunately, in many
practical global optimization applications, the multiextremal
feature involves only a small number of variables. Moreover,
many global optimization procedures take advantage of helpful
specific features of the problem structure which are often
present. On the other hand, several methods have been proposed
recently to solve very general and difficult'global problems. In
these cases, sufficiently accurate approximations of global
solutions can only be detected for small problem sizes. How-
ever, general global optimization method s often provide useful
tools for transcending local optimality restrictions, in the sense
of providing valuable information about the global quality of
a given point. Typically, such information will give upper and
lower bounds for the optimal objective function value and
indicate parts of the feasible set where further investigations of
global optimality will not be worthwhile.
One of several directions of recent research in general global
optimization methods uses interval analytical tools which
have been most successful when incorporated in branch and
bound techniques and combined with local methods. This
book, which is authored by two well-known experts in the
field, gives a thorough introduction to interval analysis and
recently proposed interval methods for global optimization.
Chapter 1 gives a very short and rudimentary presentation of
some classical nonlinear programming techniques. This chap-
ter reflects very much the intention of the author to demon-
strate, in a simple way, how interval methods and local proce-
dures can be combined in principle rather than to provide the
state of the art in nonlinear programming. The second chapter
Contains a nice overview of the basic principles of
interval analysis, including interval Newton
methods and the Hansen-Greenberg realization.
9, w s Chapter 3, on unconstrained global optimization,
discusses three branch and bound interval meth-
ods for globally minimizing a real-valued func-
tion over a box in R": the algorithm of Moore-
Skelboe, the Ichida-Fuy algorithm and the Hansen
algorithm. Convergence properties are derived, the ad-
vantage of isotone inclusion functions is demonstrated and
several acceleration devices are proposed. Chapter 4, which
has the somewhat awkward heading, "Unconstrained Optimi-
zation over Unbounded Domains," generalizes these methods
to the unconstrained minimization problem where, in contrast
to Chapter 3, it is not assumed that an initial box containing an
optimal solution is known. Such a generalization is achieved
by an appropriate compactification of the Euclidean space Rn
and its realization on a computer. The final chapter is devoted
to constrained global optimization problems which are diffi-
cult to handle directly by interval methods. The algorithms
discussed are interesting combinations of interval and local
methods, but the proposed way to overcome the difficulties
arising from constraints by means of relaxation with flexible
tolerances needs further investigation and comparison with
The technical prerequisites for this book are rather modest and
are within the reach of most undergraduate university pro-
grams. Each method is demonstrated by illustrative examples.
An extensive bibliography is given.
Summarizing, this book provides a welcome introduction to
the field. It may well serve as a textbook for students, but it
contains interesting material for the experts as well.
*A MM0 I *1
P.T. Harker and J.-S. Pang, "Finite-Dimensional Variational
Inequality and Nonlinear Complementarity Problems: A Survey of
Theory, Algorithms and Applications."
S.M. Robinson, "Mathematical Foundations of Nonsmooth
S. Lawphongpanich and D.W. Hearn, "Benders Decomposition for
P. Tseng, "Further Applications of a Splitting Algorithm to
Decomposition in Variational Inequalities."
T.L. Friesz, R.L. Tobin, H.-J. Cho and N.J. Mehta, "Sensitivity
Analysis Based Heuristic Algorithms for Mathematical Programs
with Variational Inequality Constraints."
J. Kyparisis, "Solution Differentiability for Variational Inequali-
L. McLinden, "Stable Monotone Variational Inequalities."
C. Blair, "Representation for Multiple Right-Hand Sides."
C.C. Gonzaga, "Polynomial Affine Algorithms for Linear Pro-
K.A. Ariyawansa, "Deriving Collinear Scaling Algorithms as
Extensions of Quasi-Newton Methods and the Local Convergence
of DFP- and BFGS-Related Collinear Scaling Algorithms."
M. Conforti, M.R. Rao and A. Sassano, "The Equipartition
Polytope I: Formulations, Dimension and Basic Facets."
M. Conforti, M.R. Rao and A. Sassano, "The Equipartition
Polytope II: Valid Inequalities and Facets."
S.T. McCormick, "Making Sparse Matrices Sparser: Computa-
D.T. Luc, "Recession Cones and the Domination Property in
H. TH. Jongen, D. Klatte and K. Tammer, "Implicit Functions and
Sensitivity of Stationary Points."
M.S. Gowda, "On Q-Matrices."
; 4611 1 1 '
I.J. Lustig, "Feasibility Issues in a Primal-Dual Interior-Point
Method for Linear Programming."
S.C. Boyd and W.R. Pulleyblank, "Optimizing Over the Subtour
Polytope of the Travelling Salesman Problem."
M.J.D. Powell and Y. Yuan, "A Trust-Region Algorithm for
Equality Constrained Optimization."
H. Kawasaki, "Second Order Necessary Optimality Conditions for
Minimizing a Sup-type function."
M. Fukushima, "A Successive Quadratic Programming Method for
a Class of Constrained Nonsmooth Optimization Problems."
K. Kamiya, "Computation of Equilibria in an Economy with
Increasing Returns to Scale Technologies."
L. Qi, "Quasidifferentials and Maximal Normal Operators."
R. Mifflin, "On Superlinear Convergence in Univariate Nons-
M. Hartmann and LE. Trotter, Jr., "A Topological Characteriza-
tion for Closed Sets Under Polar Duality in Q"."
A quarterly journal for:
U Aeronautical, chemical, civil, electrical, environmental, and mechanical engineers engaged in optimal design U Modelers
concerned with optimal parameter selection such as chemists, geophysicists, physicists, and statisticians U Software and algorithm
developers in computer science, mathematics, and operations research U Mathematical scientists concerned with existence of
solutions and with the design and analysis of continuous and discrete algorithms.
I CONTENTS / February 1991, Volume 1, Number 1
Variable Metric Method for Minimization; William C. Davidon; A New Variational Resultfor
Quasi-Newton Formulae, Roger Fletcher; On the Performance of Karmarkar's Algorithm
over a Sequence of Iterations, Kurt M. Anstreicher; Composite Nonsmooth Programming
with ..... ', i .. .'.i. V. Jeyakumar; Local and Superlinear Convergence for Par-
tially Known Quasi-Newton Methods, John R. Engels and Hector J. Martinez; Minimization
of Locally Lipschitzian Functions, Jong-Shi Pa.'.. 1-. i .. I i. .i N .. .... i: 1 I
Simplical Algorithm for the Nonlinear Stationary Point Problem on an Unbounded
Polyhedron, Y. Dai, G. van der Laan, A.J.J. Talman, and Y. Yamamoto; A Polynomial-Time
Predictor-Corrector Algorithm for a Class of Linear Complementarity Problems, Jiu Ding
and Tien-Yien Li; A New Proof of Superlinear Convergence for Broyden's Method in Hilbert
Space, C.T. Kelley and Ekkehard W. Sachs; On the Solution of Large Quadratic Program-
ming Problems with Bound Constraints, Jorge J. Mord and GerardoToraldo; Convergence of
Iterates of an Inexact Matrix Splitting Algorithm for the Symmetric Monotone Linear Comple-
mentarity Problem, O. L. Mangasarian, On the Convergence of the Multidirectional Search
Algorithm, Virginia Torczon.
To contribute a paper to the SIAM Journal on Optimization,
send submissions to:
Attention: John E, Dennis, Jr.
Box 7541, Philadelphia, PA 19101
Special Prepublication Offer
I year ( 1991 r ,I '- ,r- ,j.,i- Mexico) / $109 (elsewhere)
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5150.00) (L S C ru.n li -i. i 175.00 (elsewhere).
Offer erpires lanann
* MANAGING EDITOR
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Center for Research on Parallel Computing
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PAGE 2 numbe tirton NER9
ARNEGIE-MELLON has bestowed its highest faculty
honor on Egon Balas who was named a University Profes-
sor in June, 1990. -A workshop in large-scale optimiza-
tion is being organized for July 29-31, 1991 in Coimbra,
Portugal. Contact Prof. Joaquim J. Judice, Dept. de Matematica,
Universidade de Coimbra. $Summer schools in Nonsmooth
Optimization and NP-Completeness are being organized for
June, 1991 at ERICE (Trapani), Sicily. Contact Prof. F.
Giannessi, Universita di Pisa, Dipartimento di Matimatica, via
F. Buonarroti, 2-56127, Pisa, Italy, email: diparmat at
icnucevm.bitnet. fDeadline for the next OPTIMA is February
Books for review should be
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Prof. Dr. Achim Bachem,
Mathematiches Institute der
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to change by the publisher.
Donald W. Hearn, EDITOR
Achim Bachem, ASSOCIATE EDITOR
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