Title: Optima
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00090046/00029
 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: March 1990
 Record Information
Bibliographic ID: UF00090046
Volume ID: VID00029
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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March 1990

Amsterdam 1991

A MSTERDAM, the capital of the Netherlands, will
host the 14th International Symposium on
Mathematical Programming from August 5 to
9,1991.This is the triennialmeetingoftheMathe-
matica l Programming Society, andwe cordially
invite you to participate in the meeting and to contribute to
making it a success.
Amsterdam is known all over the world for a variety of reasons.
Its historic center covers a wide area of, mainly 17th Century,
buildings along "grachten" (canals). The cultural attractions in-
clude theRijksmuseum, with several Rembrandts (Nachtwacht),
Vermeers, Frans Ha Is, etc.; the Vincent van Gogh Museum, with
a huge collection of van Goghs; the StedelijkMuseum,formodern
art; the Royal Concertgebouw Orchestra, and the National Bal-
let. Moreover, we mention the liberal atmosphere, yielding a rich
supply of pleasures of various kinds.
The Symposium will takeplace in the buildings of the University
of Amsterdam in the city center, with several hotels and restau-
rants of diverse categories nearby. The meeting offers invited and
contributed talks in parallel sessions, and we call for papers on
all theoretical, computational, andpractical aspects four field.
We have chosen a particularly late deadline for the submission
of papers (June 1, 1991) so as to encourage the presentation of
very recent results.
Last October we sent out the First Announcement to a large
number of people, including all members of the Society. It con-
tains some more information and is reprinted in this issue of
OPTIMA. The Second Announcement will appear this Fall and
will be sent to all those who have returned the Preregistration
Form in the First Announcement.
We look forward to seeing you in Amsterdam and to offering
you a pleasant and fruitful symposium.

Council Meets in

the Black Forest

Bernhard Korte and Klaus Ritter
were the organizers of the VIth
Biennial Oberwolfach Confer-
ence on Mathematical Program-
ming. Between 60 and 70 mathe-
matical programmers met from
January 7 to January 13 at the
"Mathematisches Forschungsin-
stitut" in Oberwolfach. They
attended more than 50 presenta-
tions on recent research; they
enjoyed the informal atmos-
phere and the scenic surround-
ings; and many participated in
the traditional hike on Wednes-
day afternoon.



1 I I ~- -~-- ---- ~- '- -

e w n ne M

14th International Symposium on Mathematical Programming

Amsterdam, The Netherlands, August 5-9, 1991

First Announcement

The International Symposium on Mathematical Programming is the triennial scientific meeting of the Mathematical Programming Society.
The 14th Symposium will be held at the University of Amsterdam, August 5-9, 1991. It is jointly organized by the University of Amsterdam,
the Centre for Mathematics and Computer Science (CWI) in Amsterdam, Eindhoven University of Technology, and the Erasmus University
in Rotterdam.

Chairmen: J. K. Lenstra, A. H. G. Rinnooy Kan, A. Schrijver. International Program Committee: A. Auslender, M. Avriel, E. Balas, M. L. Balinski,
C. Berge, R.E. Bixby, V. ChvAtal, A. R. Conn, R.W. Cottle, G.B. Dantzig, J. E. Dennis,Jr., L.C.W. Dixon, A. M. Geoffrion, F. Giannessi, J.-L. Goffin,
D. Goldfarb, E. G. Golshtein, R. L. Graham, M. Gr6tschel, P. L. Hammer, M. Held, A.J. Hoffman, K. L. Hoffman, T. Ibaraki, M. Iri, E. L.Johnson, P. Kall,
R. Kannan, R. M. Karp, A. V. Karzanov, M. L. Kelmanson, V. Klee, K. 0. Kortanek, B. Korte, J. Krarup, H. W. Kuhn, E. L. Lawler, C. Lemar6chal,
F. A. Lootsma, L. LovAsz, O. L. Mangasarian, G. P. McCormick, N. Megiddo, G. Mitra, B. Mond, G. L. Nemhauser, W. Oettli, M. W. Padberg, B. T. Polyak,
M.J.D. Powell, A. Pr6kopa, W. R. Pulleyblank, M.R. Rao, K. Ritter, S.M. Robinson, R. T. Rockafellar, J.B. Rosen, H.E. Scarf, R. B. Schnabel,
P. D. Seymour, J. Stoer, E. Tardos, M.J. Todd, A. W. Tucker, H. Tuy, A. F. Veinott,Jr., R.J.-B. Wets, A. P. Wierzbicki, P. Wolfe, L. A. Wolsey, M.-Y. Yue.
Organizing Committee: O.J. Boxma, A. M. H. Gerards, J. L. dejong, G. A. P. Kindervater, M. Labbe, B.J. Lageweg, G. de Leve, M. W. P. Savelsbergh,
A.J.J. Talman, H. C. Tijms, L. N. van Wassenhove. Advisory Committee: M. Grotschel (chairman), H. Konno, R. B. Schnabel, M.J. Todd.

Call for papers. Papers on all theoretical, computational and
practical aspects of mathematical programming are welcome.
The presentation of very recent results is encouraged. For this rea-
son, a particularly late deadline for the submission of titles and
abstracts has been set.

Dates and deadlines
September, 1990: Second Announcement
April 1, 1991: Deadline for early registration
June 1, 1991: Deadline for submission of titles and abstracts
August 5-9, 1991: The Symposium

Topics. Sessions on the following topics are organized. Sugges-
tions for further areas to be included are welcome.
- Linear, integer, mixed-integer programming
- Interior-point and path-following algorithms
- Nonlinear, nonconvex, nondifferential, global optimization
- Complementarity and fixed point theory
- Dynamic and stochastic programming, optimal control
- Game theory and multicriterion optimization
- Combinatorial optimization, graphs and networks, matroids
- Computational complexity
- Approximative methods, heuristics
- Computational geometry, VLSI-design
- Implementation and evaluation of algorithms and software
- Large-scale mathematical programming
- Parallel computing in mathematical computing
- Expert, interactive and decision support systems
- Mathematical programming on personal computers
- Teaching in mathematical programming
- Applications of mathematical programming in industry,
government, economics, management, finance, transportation,
engineering, energy, environment, agriculture, sciences and

Structure of the meeting. The meeting will offer invited and con-
tributed lectures in parallel sessions. In addition, computer
demonstrations and survey lectures highlighting developments of
current interest are planned. During the plenary opening session,
the George B. Dantzig Prize (for original research with a major
impact on mathematical programming), the Fulkerson Prizes (for
outstanding papers in discrete mathematics), the Orchard-Hays
Prize (for excellence in computational mathematical program-
ming), and the A.W. Tucker Prize (for an outstanding paper by a
student) will be awarded. The program also contains a reception
and a banquet.

Site. The Symposium will take place in the Oudemanhuispoort
building of the University of Amsterdam, located in the historic
centre of Amsterdam, close to many attractions of various kinds.
Amsterdam is easily reachable by all means of public transporta-
tion and has direct air connections with many cities all over the

Preregistration. The Second Announcement, which will appear
in September 1990, will be sent to all those who return the
Preregistration Form below. It will contain additional and more
detailed information about the program, registration fees, social
events, hotels, traveling, etc.

Mailing address
14th International Symposium on Mathematical Programming
Paulus Potterstraat 40
1071 DB Amsterdam
The Netherlands
Telephone: +31-20-752120
Telefax: +31-20-6628136
Telex: 10761 omega.nl
Electronic mail: ismp@swivax.uucp, ismp@swi.psy.uva.nl

~ __s I ~I~ ~

MARCH 1990


number twenty-nine

Pnm wtnA 1


Preregistration Form

Please keep me on the mailing list for further information about the 14th International Symposium on Mathematical Programming.

name: O I plan to attend the Symposium.
name: I intend to give a talk.

Mailing address:

Institution (if not in mailing address):

My talk may be on the following subject:

Please return this form to:
14th International Symposium on Mathematical Programming
Paulus Potterstraat 40

1071 DB Amsterdam
The Netherlands

Nato Advanced Study Institute
on Combinatorial Optimization
Bilkent University
Ankara, Turkey
July 16-28, 1990

NATO is sponsoring an ASI, "New Fron-
tiers in the Theory and Practice of Combina-
torial Optimization: Applications in VLSI
Design," to be held at Bilkent University in
Ankara, Turkey, July 16-28, 1990. The ASI is
also sponsored by the University of Florida
(S. Tufekci), Bilkent University (M. Akgul)
and the University of Kaiserslauten (H. W.
Hamacher). The objective of this institute is
to disseminate the state-of-the-art knowl-
edge on combinatorial optimization with a
focus on the applications in VLSI design.
This two-week institute will be primarily in
the form of a workshop with lectures from
prominent, internationally renowned
scientists. It will be followed by an after-
noon poster session where a limited number
of papers on the theory and practice of
combinatorial optimization will be
discussed. Papers might be submitted for
these poster sessions on network optimiza-

tion, recent advances in linear program-
ming, integer programming, traveling
salesman problem, parallel algorithms,
matroids, polyhedral combinatorics, and
application of combinatorial optimization
on manufacturing decision problems
including VLSI design. There is a limited
number of financial grants available for
participants from the NATO countries. To
be considered for a financial grant, appli-
cants must provide background information
and a letter of recommendation from their
department head or from their dissertation
advisor no later than March 15, 1990. The
award notification will be mailed by May 5,
1990. Send applications and abstracts to DR.
SULEYMAN TUFEKCI, Associate Director,
Center for Optimization and Combinatorics
(COCO), Department of Industrial and
Systems Engineering, University of Florida,
Gainesville, Florida, 32611, USA.

Nordic MPS Meeting and
Formation of Geographical

Some MPS members from the Nordic
countries will arrange a meeting on "Algo-
rithms and Solution Procedures in Mathe-
matical Programming" on August 25 and 26,
1990 in Copenhagen. The meeting is sup-
ported in part by The Nordic Council of
Ministers and has two goals:
1. To increase contact between math program-
mers in the Nordic countries;
2. To discuss the formation of a Nordic section
of MPS.
Applications for participation and abstracts
must be sent to Stein W. Wallace, Haugesund
Maritime College, SkAregaten 103, N-5500
Haugesund, Norway, by April 30,1990. For
more information, please contact him at the
above address, or by phone (+47 4 721200) or
FAX (+47 4 715906). (e-mail is not functioning
properly at this time.) It is possible to apply
for partial coverage of travel costs for those
who do not have other sources.


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

MARCH 1990


number twenty-nine

S4 nI

COUNCIL from page one:

A mong the attendants were all of the
members of the Council of the Mathematical
Programming Society: George Nemhauser
(Chairman), Michel Balinski (Past Chairman),
Les Trotter (Treasurer), Egon Balas, Bill Cun-
ningham, Claude Lemarechal, and Alexander
Schrijver (Council Members-at-Large). It was
therefore decided to organize a rare event- a
Council meeting in between the triennial in-
ternational symposia. This meeting took place
on January 10 and was also attended by Bob
Meyer (Chairman of COAL), Clyde Monma
(Chairman of the Advisory Committee for the
1994 Symposium), Bill Pulleyblank (Editor of
Series B of the Journal), Mike Todd (Past Edi-
tor of Series A of the Journal), Laurence
Wolsey (Chairman of the Publications Com-
mittee), and Jan Karel Lenstra (Chairman of
the Executive Committee). I will summarize
the issues that were discussed below.
Meetings The 14th International Symposium
on Mathematical Programming will be held in
Amsterdam in 1991. You will find more about
it elsewhere in this issue. In the meantime, a
site for the 1994 symposium has to be selected.
A call for proposals has already appeared in
the previous issue of OPTIMA. Since then, the
Symposium Advisory Committee has sent
invitations to submit such a proposal to about
12 of our colleagues at American universities.
The Council suggested that our triennial
symposia might be held under co-sponsor-
ship of SIAM; the Chairman will explore this

The Society is a co-sponsor of the Conference
on Integer Programming and Combinatorial
Optimization that is being organized by Ravi
Kannan and Bill Pulleyblank and will be held
in Waterloo at the end of May 1990. The Coun-
cil felt that the Society should be catalytic in
this respect and encourage others who might
want to organize similar meetings.
Publications Due to an overflow of papers
that have been accepted for Series A of the
Journal, it is difficult to avoid a large backlog
for Series A while maintaining a regular pub-
lication schedule for Series B. The Council
discussed several remedies. As a result, we
have entered negotiations with our publisher,
North-Holland. There will most likely be a
substantial increase in the total annual vol-
ume of Series A over the next few years.
Committee on Stochastic Programming The
Council approved of new membership of this
committee: John Birge, Michael Dempster,
Jitka Dupavcova (Secretary), Yuri Ermoliev,
Kurt Marti, Andras Prekopa, Yves Smeers,
Tomas Szantai, Roger Wets (Chair), and Wil-
liam Ziemba.
Membership The Council invited the Chair-
man to appoint a general Membership Com-
mittee. It will have the task of advising the
Council on initiatives that could increase our
membership, e.g., by the creation of geo-
graphical sections.
Egon Balas and Claude Lemarechal agreed to
serve on an ad hoc Committee for Special
Membership Arrangements. This committee

will advise the Council on special arrange-
ments for members from countries with non-
convertible currencies. At present, we have an
arrangement for non-paying Hungarian
members, and we also received suggestions
for a Soviet membership from Professors
Golshtein and Levner. The Council prefers a
uniform policy to arrangements on a country-
by-country basis and feels that any arrange-
ment of this kind should be financially reason-
able for the Society and subject to periodic
(e.g., triennial) review.
Prizes The Council decided to change the
name of the Orchard-Hays Prize to the Beale-
Orchard-Hays Prize. The membership of our
four prize committees has already been an-
nounced in OPTIMA.
Administrativelssues The 1990 membership
list will contain information (telephone and
fax numbers, electronic addresses) that has
recently been collected. The Council decided
to give the members the option of paying their
dues by credit card, but decided against the
possibility of offering a three-year member-
ship at a reduced fee.
Algorithms and the Law The Council ex-
pressed concern about the fact that the interior
point approach for solvingresourceallocation
problems has recently been patented in the
U.S. and that some of these patents might
misrepresent the history of our field. The
Chairman was urged to appoint a Committee
on Algorithms and the Law. This committee
will be asked to investigate the situation and
to advise the Council on possible courses of

- II "-~

MARCH 1990


number twenty/-nine

PAGE 5 number twenty-nine MARCH 1990


Reports &



Georgia Institute of Technology
School of Industrial and Systems
Atlanta, GA 30332
G.L. Nemhauser and R. Rushmeier, "Perform-
ance of Parallel Branch-and-Bound Algorithms
for the Set Covering Problem," J-89-02.
G.L. Nemhauser and G. Sigismondi, "A
Strong Cutting Plane/Branch-and-Bound
Algorithm for Node Packing," J-89-08.
G.L. Nemhauser, G. Sigismondi and P.
Vance, "A Characterization of the Coefficients in
Facet-Defining Lifted Cover Inequalities," J-89-
G. Parker and M. Richey, "A Cubic Algorithm
for the Directed Eulerian Subgraph Problem," to
appear in European Journal of Operations
R. Rardin and C.A. Tovey, "Test Travelling
Salesman Problems of Intermediate Complexity."
A.E. Roth and J.H. VandeVate, "Decentralized
Paths to Stability in Two-Sided Matching."
D. Solow, R. Stone and C.A. Tovey, "Solving
LCP on Known P-Matrices is Probably not NP
R. Stone and C.A. Tovey, "The Simplex and
Projective Scaling Algorithms as Iteratively
Reweighted Least Squares Methods."
C.A. Tovey, "Asymmetric Probabilistic
Prospects of Stackelberg Players."
C.A. Tovey, "The Value of Information and
Cooperation in Bimatrix Games: An Average
Case Analysis."
C.A. Tovey, "Simulated Simulated Annealing."
C.A. Tovey, "Simplified Anomalies and
Reduction for Multiprocessor Precedence

Constrained Scheduling."
J.H. VandeVate and J. Wang, "Question-
Asking Strategies for Horn Clause Systems."
J.H. VandeVate, "Fractional Matroid Match-

System Optimization Laboratory
Operations Research Department
Stanford, CA 94305-4022
H. Hu, "On the Feasibilty of a Generalized
Linear Program," SOL 89-1.
H. Hu, "Semi-Infinite Programming," SOL 89-
R.W. Cottle, "The Principal Pivoting Method
Revisited," SOL 89-3.
A.S. Krishna, "Note on Degeneracy," SOL 89-4.
K. Zikan, "An Efficient Exact Algorithm for the
"LEAST SQUARES" Image Registration
Problem," SOL 89-5.
A. Marxen, "Primal Barrier Methods for Linear
Programming," SOL 89-6.

Mathematisches Institut der
Universitat zu K6ln
Weyertal 86-90
D-5000 K l6n 41
B. Fassbender, "A Sufficient Condition on
Degree Sums of Independent Triples for Hamil-
tonian Cycles in 1-Tough Graphs," WP 89-78.
A. Bachem, A. Dress and W. Wenzel,
"Varieties on a Theme by J. Farkas," WP 89-73.
W. Kern, "Verfahren der Kombinatorischen
Optimierung und ihre Gilltigkeitsbereiche," WP
U. Faigle and W. Kern, "A Note on the
Communication Complexity of Totally Unimodu-
lar Matrices," WP 89-70.
A. Bachem and M. Niezborala, "Numerische
Erfahrungen bei der Vektorisierunglinearer
Programmierungsalgorithmen," WP 89-68.
U. Faigle and W. Kern, "Note on the Conver-
gence of Simulated Annealing Algorithms," WP

U. Faigle, W. Kern and T. Gy6rgy, "On the
Performance of On-Line Algorithms for Partition
Problems," WP 89-66.
A. Bachem and A. Reinhold, "On the Com-
plexity of the Farkas-Property of Oriented
Matroids," WP 89-65.
A. Bachem and W. Kern, "A Guided Tour
through Oriented Matroid Axioms," WP 89-64.
M. Hofmeister, "Concrete Graph Covering
Projections," WP 89-62.

Mathematical Sciences Technical
Report Series
Department of Mathematical
Clemson University
Clemson, SC 29634-1907
R. Ringeisen and V. Rice, "Cohesion Stability
under Edge Destruction," TR 557.
R. Ringeisen and V. Rice, "When is a Stable
Graph not Stable or Are There Any Stable
Graphs Out There?" TR 557A.
E. Cockayne, B. Hartnell, S.T. Hedetniemi
and R. Laskar, "Efficient Domination in
Graphs," TR 558.
R. Ringeisen and V. Rice, "Cohesion Stable
Edges," TR 559.
R. Ringeisen and C. Lovegrove, "Crossing
Numbers of Permutation Graphs," TR 560.
M. Kostreva, A. Aoun, N. Brown, S. Chatto-
padhyay, R. Guidry, T. Ordoyne and R.
Zurovchak, "Linear Complementarity Theory:
1st Generation," TR 561.
B. Piazza and R. Ringeisen, "Connectivity
Generalized Prisms over G," TR 562.
B. Piazza, R. Ringeisen and S. Stueckle,
"Properties of Non-Minimum Crossings for
Some Classes of Graphs," TR 564.
B. Piazza, R. Ringeisen and S. Stueckle, "On
the Vulnerability of Cycle Permutation Graphs,"
TR 565.
J. Key and K. Mackenzie, "An Upper Bound
for the p-Rank of a Translation Plane," TR 566.
D. Shier and N. Chandrasekharan, "Algo-
rithms for Computing the Chromatic Polyno-
mial," TR 567.


- --


number twenty-nine

MARCH 1990

PAGE 6 number twenty-nine MARCH 1990
S *

Technical Reports &
Working Papers

J. Key and K. Mackenzie, "Ovals in the Design
W(2m)," TR 568.
P. Dearing, P. Hammer and B. Simeone,
"Boolean and Graph Theoretic Formulations of
the Simple Plant Location Problem," TR 569.
M. Kostreva, M. Wiecek and T. Ordoyne,
"Multiple Objective Programming with Polyno-
mial Objectives and Constraints," TR 571.
C. Williams, "A Knowledge-Based Approach to
Designing Experiments: Design Expert," TR
V. Rice and R. Ringeisen, "On Cohesion Stable
Graphs," TR 573.
J. Boland, R. Laskar and C. Turner, "On Mod
Sum Graphs," TR 574.
R. Laskar, S. Stueckle and B. Piazza, "On the
Edge-Integrity of Some Graphs and Their
Complements," TR 575.
R. Laskar, A. Majumdar, G. Domke and G.
Fricke, "A Fractional View of Graph Theory,"
TR 576.
J. Lalani, R. Laskar and S.T. Hedetniemi,
"Graphs and Posets: Some Common Parameters,"
TR 577.
M. Kostreva and M. Wiecek, "Linear Comple-
mentarity Problems and Multiple Objective
Programming," TR 578.
G. Isac and M. Kostreva, "The Generalized
Order Complementarity Problem," TR 579.

Research Initiative Program in
Discrete Mathematics and Com-
putational Analysis
Clemson University
Clemson, SC 29634-1907
R. Laskar, R. Rowley, R. Jamison and C.
Turner, "The Edge Achromatic Number of Small
Complete Graphs," URI-029.
T. Wimer, "Linear Algorithms on k-Terminal
Graphs," URI-030.
D.R. Shier, E.J. Valvo and R.E. Jamison,
"Generating the States of a Probabilistic System,"

D.R. Shier, "The Monotonicity of Power Means
Using Entropy," URI-032.
C. Jeffries, "Fluid Dynamics with Pressure
Diffusion," URI-033.
D.R. Shier and G.A. Vignaux, "Adaptive
Methods for Graphing Functions," URI-034.
P.J. Slater, "A Summary of Results on Pair-
Connected Reliability," URI-035.
C.L. Cox, "Implementation of a Divide and
Conquer Cyclic Reduction Algorithm on the FPS-
T-20 Hypercube," URI-037.
R.E. Fennell, "An Application of Eigenspace
Methods to Symmetric Flutter Suppresion,"
J.A. Reneke and J.R. Brannan, "Application of
RKH Space Methods to the Filtering Problem for
Linear Hereditary Systems, URI-039.
J.A. Reneke and R.E. Fennell, "Canonical
Forms for Distributed Systems Control II," URI-
J.A. Reneke and R.E. Fennell, "Convergence of
RKH Space Simulations of Stochastic Linear
Hereditary Systems," URI-041.
R.E. Fennell, R.E. Haymond and J.A. Reneke,
"RKH Space Simulation of Stochastic Linear
Hereditary Systems," URI-042.
C.R. Johnson and T.A. Summers, "The
Potentially Stable Tree Sign Patterns for
Dimensions Less than Five," URI-043.
M.E. Lundquist, "An Implementation of the
Preconditioned Conjugate Gradient Algorithm on
the FPS-T-20 Hypercube," URI-044.
S.T. Hedetniemi, R. Laskar, E.J. Cockayne
and B.L. Hartnell, "Efficient Domination in
Graphs," URI-045.
S.T. Hedetniemi, M.O. Albertson, R.E.
Jamison and S.C. Locke, "The Subchromatic
Number of a Graph," URI-046.
K.R. Driessel, "On Isospectral Surfaces in the
Space of Symmetric Tridiagonal Matrices," URI-
P.J. Slater and D.L. Grinstead, "On Minimum
Dominating Sets with Minimum Intersection,"
W.H. Ruckle, "Abstract of the Linearizing
Projection, Local Theories," URI-049.

W.H. Ruckle, "On Win-Lose Draw Games,"
W.H. Ruckle, "Computer Studies of Coalition
Formation Under Varying Dynamics," URI-051.
R.J. Lakin, "State Space Approximation of a
Multimode-Component System," URI-052.
E.O. Hare, S.T. Hedetniemi, R.C. Laskar and
G.A. Cheston, "Simplicial Graphs," URI-053.
G.S. Domke, S.T. Hedetniemi and R.C.
Laskar, "Fractional Packings, Coverings, and
Irredundance in Graphs," URI-054.
M.M. Kostreva, "Recent Results on Com-
plimentarity Models for Engineering and
Economics," URI-055.
S.T. Hedetniemi, G.A. Cheston, A. Farley
and A. Proskurowski, "Spanning Trees with
Specified Centers in Biconnected Graphs," URI-
J.D. Trout, Jr., "Vectorization of Morphological
Image Processing Algorithms," URI-057.
J.P. Jarvis, D.E. Whited and D.R. Shier,
"Discrete Structures and Reliability Computa-
tions," URI-058.
C.L. Cox, "On Least Squares Approximations to
First Order Elliptic Systems in Three-Dimen-
sion," URI-059.
G.S. Domke, S.T. Hedeniemi, R. Laskar and
G. Fricke, "Relationships Between Integer and
Fractional Parameters of Graphs," URI-060.
W.P. Adams and P.M. Dearing, "On the
Equivalence Between Roof Duality and La-
grangian Duality for Unconstrained 0-1
Quadratic Programming Problems," URI-061.
J.A. Reneke and M. Artzrouni, "Stochastic
Differential Equations in Mathematical
Demography: A Review," URI-062.
S.T. Hedetniemi and N. Chandrasekharan,
"Fast Parallel Algorithms for Tree Decomposing
and Parsing Partial k-Trees," URI-063.
B.B. King, "The Dynamics of the Motion of a
Filament: A Survey of the Literature," URI-064.
W.H. Ruckle, "A Discrete Game of Infiltration,"
R. Geist and S. Hedetniemi, "Disk Scheduling
Analysis via Random Walks on Spiders," URI-


MARCH 1990


number twenty-nine


Theory of Suboptimal R E V
By A. A. Pervozvanskii
and V. G. Gaitsgori
Kluwer, Dordrecht 1988
ISBN 90-277-2401-6

This is a research monograph concerned with
large and complex optimization systems, too
large to deal with analytically or numerically. For such
systems the notion of optimality is often dubious, and it
is usually furnished by the systems analyst or the decision
maker rather than the mathematician. In these situations,
insisting by all means on "optimality" may not be justified. An
alternative is to use a more realistic and "relaxed" approach by
exploiting the inner structure of the system, such as the "strong" and
"weak" bonds between its various subsystems. It appears that in
many practical models, after neglecting the weak bonds, the strong
ones recover a simpler system that can be solved by, e.g., aggregation
or decomposition. These solutions are the suboptimall decisions."
Their theory, and the ways of calculating and improving them in
relation to the unknown "optimal" solution of the original complex
problem, is the main theme of this book. A method for improving
suboptimal solutions is the "perturbation method."
Let us illustrate the method in a simple and ideal situation. Consider
a linear program (L, e) : Max (c + cc : (Ao + EA')x = b + eb', x 2 0) for
some e> 0. Suppose that the program is large and complex, so we do
not know its optimal solution x(e) and its optimal value f(e). How-
ever, suppose that its "reduced" program (L,0) is easy to solve for x(0).
If this suboptimal x(0) is a unique and nondegenerate basic solution,
and if the solution X(0) of dual of (L,0) is also unique, then for all
"sufficiently small" E > 0 we have the expansion
x(E) = x(0) + EX') + ... + e" x"') + O("^1).
Here the basic components of x00 are given recursively by
(1) = -(AB)'(Alx(O) b')
x('1)= -(A)-1 A1xW, k=1,2,...,m-1
while all nonbasic components are zero. (Here A, is a submatrix of A
consisting of the basic vectors.) Also
f(E) = f(O) + E[xT(O)c + )T(0)b' XT(0)A' x(0)] + O(e).
For example: Max{1.3x, x:1.1x, + 0.2x2= 1, x, 0,x2 0} is realization
of Max((1 + 3e)x, x : (1 + e)x, + 2ex2 = 1, x, > 0, x, > 0) at e = 0.1. The
basic part of the exact solution, for small E > 0, is (for m = 2) : XB(e) =
1 e + t2 + 0(E) = 0.90909.... Here the basic part of the suboptimal
solution x,(0.1) = 0.91 is obtained from the above recursive formulae
after solving the simple reduced program: Max(x, x2: x, = 1, x2 0).

I W X S If the primal or the dual are not
unique, then the expansions are
made around particular optimal
solutions obtained after solving
"auxiliary" programs such as Max
xT(O)(c (A1)TX(0)) over all optimal
solutions x(0) of (L,0). Of course,
the above ideas work only if the re-
duced program is relatively simple to solve and
if the original program (L,e) is locally stable at
-- 0 relative to > 0. The perturbation method is formu-
lated for linear and then extended to convex programs.
By "stability" the authors mean continuity of the optimal
value function f(e) -f(0) and (in the case of uniqueness) x(E)-+
x(0) as e-* +0. If this fails, then the programs are "singularly
perturbed." For such convex models
Min{f(x) + efl(x) : gO(x) + eg'(x) < 0 = f()
another "auxiliary" program is constructed by adding constraints of
the type vT g(x) < 0, where v is an extreme ray of the unbounded set of
Lagrange multipliers. The new feasible set is now smaller but, since
some "badly behaved" constraints are replaced by "nice" perturba-
tions, one may still obtain convergence f(e)-f*(0) and x(E) -+ x*(0) as
e + 0 and reformulate the perturbation method. (The asterisk refers
to the optimal value and the optimal solution of the reduced auxiliary
The book has six chapters. The first four deal with the s~iboptimal
decisions and the perturbation method for finite-dimensional pro-
grams. In the last two, the ideas are extended to models that include
differential equations in the constraints. Although the optimal solu-
tion is now often available (say in linear-quadratic problems of opti-
mal control), the perturbation method, in addition to providing infor-
mation about the robustness of optimal solutions, allows one to obtain
simpler control designs which are, as a rule, more reliable. The method
also shows how to avoid numerical difficulties if the algebraic Riccati
equation is large. Particularly interesting is a study of the relationship
between singularity and loss of controllability and/or observability.
This reviewer has partly used the book in a graduate course on
optimization attended by mathematicians and operations research-
ers. Although the evidence of efficiency of the perturbation method
for nonlinear programs was not convincing after three months of nu-
merical experimentation, the students have found the topics provoca-
tive and intriguing. (The difficult question of how far one can stretch
e> 0 from e= 0 to retain stability has cropped up repeatedly and,
typically, it could not be answered.) The selection of applications of
both stable and singularly perturbed programs is nonstandard, origi-
nal and, in fact, remarkable. It ranges from optimization problems in
input output analysis, interregional transportation problems and
Markov programming (here we find examples of "real life" singularly


MARCH 1990

Is(OK---------- -

PAE8nme wnt-ieMRH19

perturbed programs) to the engineering examples of suboptimal
regulator syntheses including linear models for continuous techno-
logical control problem and ecological system control.
The book is a revision of a Russian text that was published in 1979.
During the last 10 years there has been significant progress made in
parametric optimization that does not appear to have been closely
followed by the authors. No reference has been made in the book to the
school of parametric optimization from and around von Humboldt
University (Nozicka, Bank, Guddat, Klatte, Kummer, Tammer), and
no recent results on sensitivity by several other important contribu-
tors (e.g., Fiacco, Gal or Robinson) are mentioned. Had the authors
used point-to-set mappings and lower semicontinuity of the feasible-
set mapping in the definition of stability, their presentation would
have been more unified and smoother. Indeed, many of their results
can be readily extended to vector perturbations over "regions of
stability." The English translation is not always precise, and this
occasionally creates ambiguities (e.g., the claim: "For convex pro-
grams the existence of a Lagrange vector appears to be sufficient
condition of optimality" or "... there exists an interior point of the
feasible domain, i.e., the Slater conditions are fulfilled..." on p. 38; the
former is a sufficient condition for optimality and the latter claims are
not equivalent).
Prerequisites for reading most of the book are standard undergradu-
ate courses in real analysis and linear algebra, plus the essentials of
linear and nonlinear programming. The last two chapters require
some familiarity with control theory. The book is of interest to applied
mathematicians, operations researchers, and electrical engineers, to
both the students and the researchers. In summary, this is an original
and interesting book with many fresh ideas that excite the reader and
reassure him that one can still do useful and mathematically sound,
but not too technical, research in optimization.
The book appears in the new "Soviet Series" Mathematics and Its
Applications program and comes from the IIASA group. This pro-
gram is devoted to new emerging (sub) disciplines and their interre-
lationships. The idea is to publish books "which are stimulating rather
than definitive, intriguing rather than encyclopedic". The editor
Hazewinkel could not have made a better choice than including this
book in the series.

Theoretical and Computational Aspects of Simu-
lated Annealing
S:y P. J. M. van Laarhoven
I\VI Tract 51, Amsterdam, 1988

during the last several years, simulated annealing (a certain kind of
randomized local search procedure) has become a popular tool for ap-
proximately solving large scale discrete optimization problems. The

present book on simulated annealing is, to my knowledge, the second
one that has been written on that topic. The first one, Simulated
Annealing: Theory and Applications, was written by the author of the
present book, together with E. L. Aarts, and published by D. Reidel
Publishing Company in 1987, only one year before the second one.
Thus one may ask whether it was necessary to present a new book on
this subject after such a short period of time. To answer this question,
of course, one has to compare the two.
Firstly, the present tract is a slightly revised version of the author's
doctoral thesis (supervised by J. K. Lenstra and A. Rinnooy Kan),
whereas the first one is a monograph on simulated annealing, written
for a much more general audience (including physisists, electrical
engineers, but not biologists, according to what the authors state in the
preface). As a consequence, the present book by Laarhoven concen-
trates on his own results rather than presenting a survey of what has
been done in the field by other researchers. The basic theory of
simulated annealing (conditions for convergence to optimality) is not
treated in depth in either of the two books. Proofs are omitted except
for the simplest version of the convergence theorem in the homogene-
ous case. The main concern of the present tract is the (theoretical)
analysis of cooling schedules which do not satisfy the theoretical
conditions for convergence to optimality but are likely to yield good
results in practice. Rules for choosing the cooling schedule are ob-
tained by estimating certain parameters of the optimization problem
at hand, using Bayes' Theorem and rather involved mathematical
machinery. Applications and computational results are presented in
order to compare different cooling schedules and to support the
theoretical estimates.

Biological Delay Systems: Linear Stability Theory
Cambridge Studies in Biology: 8
by N. MacDonald
Cambridge University Press, Cambridge, 1989
ISBN 0-521-34084-5

This excellent book gives a survey on the most important methods and
results of the theory of delay equations arising from biological control
systems. The special structure of the considered delayed differential
equations is very well motivated by striking examples. A large part of
the book is dedicated to mathematical modelling and description of
the following biological systems: neurophysiology of the retina, insect
maturation times, maturation of blood cells, population models, incu-
bation times in the epidemiology, Neuron interaction, chemostat
models like the Monod model and others. These models are not an a-
posteriori justification for the development of an abstract "oversized"
theory but the a-priori motivation for the development of mathemati-
cal tools that work in the concrete situations arising from mathemati-

- -- ~----~-s~--~


number tiventy-nine

MARCH 1990



cal biology. The concept of the book is influenced bythe The answer is well known; instead of proving a pro-
work of K. L. Cooke. The intended application in bio- gram once it has been written, start its design from its
logical control does not require the embedding of delay proof. The construction of a loop begins with the proposal of
equations in the wider class of general functional differential a loop invariant. Several classical examples are proposed to il-
equations that one finds in the work of J. K. Hale. lustrate this method. The resulting programs are analyzed and, in
The book is essentially concerned with local, or linear, stability analy- some cases, improved along the line suggested by the analysis. The
sis. This requires the linearization about a fixed point and the study of authors give a good bibliography of previous works on this program-
the roots of a certain algebraic equation, the so-called characteristic ming method.
equation of the system, which is analogous to the characteristic equa- The effect of assignments are discussed, introducing the concepts of
tion in ordinary differential equations. The stability analysis requires weakest preconditions or strongest postconditions. The effects of
the localization of roots with negative real parts. This motivates the indexing and pointers are discussed. Procedure calls are taken into
intensive study of Hurwitz polynomials. In the field of discrete delay, account. This is a very deep review of essential programming features.
where the change of the state of the system at time t is affected by In the second part of the book recursion is considered. Induction is the
terms depending on t-T, the book treats first- and second-order keyword. The authors show how a recursive procedure can be proven
systems as well as higher-order systems and systems with two delays. to be correct by induction and how it can be analyzed, the recursive
Moreover, one finds an extended section on distributed delay where procedure giving an inductive or implicit definition of the number of
the present state of the system at time t is affected by an integral over operations which can be solved using ordinary mathematical ways.
all past states of the system. One also should mention the independent We have here the same situation as with iterative programming. It is
and commensurate delays as well as reducible delays and the role of better to start with the proof of the program (an inductive relation on
linear subsystems. the function to compute, a special case of explicit definition) to build
The motivation and the presentation of the mathematical topics are of the program rather than first writing it, then trying to prove it.
excellent clarity. Every chapter is followed by many informative exer- Pertinent nontrivial examples are given to illustrate this method.

cises, with solutions given in an appendix. Thus, this volume will be
an excellent textbook for any graduate course on delay equations, and
it easily can be used for private studies. In general, this outstanding
book can be recommended strongly for students at the graduate level
and for research workers in mathematical biology and control theory.

Algorithms-The Construction, Proof, and Analy-
sis of Programs
by P. Berlioux and P. Bizard
Wiley, Chichester, 1987

The concern of this book is to help the reader to write correct pro-
grams. In every science, it is well known that any number of examples
will never prove a theory; testing a program may show that it contains
bugs, never that it is correct. There is a unique way to guarantee the
value of a program, to prove that it is correct from its text (it will
remain to guarantee that no typing error has been made when
entering it in the computer).
The first chapter gives the theoretical foundations of formal program
proofs, using Floyd's inductive assertions and Hoare's formalization.
The authors emphasize the fact that the result is not really satisfactory,
a lot of derivations for a very short and trivial program! The proof
could be simplified using less formal tools, as it is usually done in
mathematics. But even with less convincing proofs, the problem
remains to discover a loop invariant to start the proof.

Finally, the authors consider one of the methods which have been
proposed to transform recursion into iteration and its use to derive
iterative programs from recursive definitions, with some efficiency
This book has been written for people having some experience in
programming. It emphasizes the fact that program construction starts
with the proposal of what can be called "a recurrence hypothesis"
(loop invariant for iterative programming, recurrence relation for
recursive programming). It does not consider where this hypothesis
comes from. Like most programming books, building a program
starts with something like, "Assume that we have been able to do
that...." The questions remain: Why such a choice? Are you sure it is
the best? How did you find it? This is especially clear with towers of
Hanoi, "If n> 1, we begin by transferring a tower of height n-1 from rod
A to rod C, using B as an intermediary." Why do you do that? Without
an answer to this question, it is not clear that the resulting program is
the best possible one.
Nevertheless, it is clear that the most difficult disk to move is the
biggest one. It can be moved only if there is no other disk on it, so the
n-1 other disks must be somewhere else, on the two other rods. If so,
we can take this disk off of its rod, but we can put it on another rod only
if this rod is empty. Thus the n-1 other disks must be on the third rod,
and there is no other possible solution. A slightly different presenta-
tion gives a quite different result. The same remark is true for some
other programs of the book. For instance, the binary search can be
written in a simpler way, without extra tests before entering the loop.



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

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number twenty-nine



This book is not a book on how to invent a new program. It is a good
textbook on some methods now available to construct correct and
efficient programs, assuming that you have some idea of the method
to be implemented. It is clear, well-written, well-documented and
deep enough. There are many examples which are not all toy ex-
amples. This book is certainly worthwhile for any programmer or
informatics student who wishes to know what is meant by program
correctness, program efficiency or transformation of recursion into
iteration without going into a lot of unnecessary details. It will not
provide all the ways presently available to build, analyze, transform,
or improve a program, but it will introduce the reader to this wide new
area, the science of programming.

Introduction to Optimization
by E. M. L. Beale
Edited by L. Mackley
Wiley, Chichester, 1988
ISBN 0-471-91760-5

"The book is based upon a series of lecture notes written by Professor
E. M. L. Beale for his undergraduate course Introduction to Optimi-
zation,' given at Imperial College where he was a Visiting Professor in
Mathematics from 1967 until his death in December 1985." /Lynne
In this book the emphasis is put more on methods, algorithms and the
practical problems of why and how methods succeed or fail, rather
than on deep theory and rigorous proofs. As it contains different
applications of optimization in industry and many suggestions for
choosing efficient numerical procedures for solving concrete optimi-
zation problems, this book could be highly recommended to engi-
neers having to solve practical optimization problems. Moreover, it
would be a very good introduction for beginners in this area.
The book is divided into three parts. The first part, "Unconstrained
Optimization" (chapters 2-4), is concerned with the main techniques
for solving problems both for functions of one-variable and multi-
variable. Chapter 2 starts with considering the unconstrained optimi-
zation of functions of continuous variables and reviews iterative and
valley-descending methods.

Chapter 3, One-dimensional Optimization, describes a popular ap-
proach to solving this problem, i.e. Newton's method, the bisection,
the method of false position and its modification. A Wijngaarden's
method which uses both linear interpolation and bisection is
recommended. Finally, some insight into the sort of ideas that go into
development of optimization algorithms is given. Chapter 4 is about
multi-dimensional optimization. It clearly explains why there is no
single method which is effective for all problems of this type, resulting
in a vast literature on numerical methods for unconstrained optimiza-
tion of functions of n variables. Most of this chapter applies to finding
local optima of functions that are twice differentiable.
The methods used to solve linear programming problems and appli-
cations of linear programming in industry are treated in the second
part "Constrained Optimization: Linear Programming" (chapters 5-
9). Chapters 5 and 6 describe the simplex method for linear program-
ming and give the basic steps of the revised simplex method (also
known as the inverse matrix method). The efficient modelling and
systematic documentation of linear programming problems are re-
viewed here. Duality and its applications, dual simplex method and
examples are studied in detail in Chapter 7. This chapter also deals
with parametric programming in two basic forms, variation of the
objective function and variation of the right-hand side. Chapters 8and
9 answer the question of how to apply linear programming problems
in industry.
Nonlinear, discrete and dynamic programming are the topics of the
third part (chapters 10-12). Chapter 10 is concerned with nonlinear
programming. It starts by reviewing the basic theory of optimization,
i.e. Lagrange multipliers and the Kuhn-Tucker conditions and then
presents two methods which are in practical use. The first is based on
the concept of separable programming and the other on the reduced
gradient method. Classical approaches to integer programming and
its potential difficulties are discussed in Chapter 11. The cutting plane
method and the branch and bound methods are discussed as general
strategies, and a simple example makes the presentations clear.
Chapter 12 discusses dynamic programming as an alternative to
integer programming for some problems in combinatorial
optimization. The art of dynamic programming formulation is illus-
trated with a shortest-route problem. In general, this part shows how
the techniques of linear programming can be applied to solve nonlin-
ear and discrete optimization problems.

_I_ I ~I I 1_1 ~ __ ~

MARCH 1990


number twenty-nine

number twenty-nine

MARCH 1990


Volume 44, No.3
E.J. Anderson and A.S. Lewis, "An Extension of
the Simplex Algorithm for Semi-Infinite Linear
J.M.Y. Leung and T.L. Magnanti, "Valid Ine-
qualities and Facets of the Capacitated Plant
Location Problem."
R. Chandrasekaran and A. Tamir, "Open
Questions Concerning Weiszfeld's Algorithm for
the Fermat-Weber Location."
I. Adler, N. Karmarkar, M.G.C. Resende and G.
Veiga, "An Implementation of Karmarkar's
Algorithm for Linear Programming."
E. Balas, J.M. Tama and J. Tind, "Sequential
Convexification in Reverse Convex and Disjunc-
tive Programming."
M.W. Jeter and W.C. Pye, "An Example of a
Nonregular Semimonotone Q-Matrix."
D-Z. Du and X-S. Zhang, "Global Convergence of
Rosen's Gradient Projection Method."

Volume 46, No.1
R.H. Byrd, C.L. Dert, A.H.G. Rinnooy Kan and
R.B. Schnabel, "Concurrent Stochastic Methods
for Global Optimization."

E.S. Gottlieb and M.R. Rao, "The Generalized
Assignment Problem: Valid Inequalities and
E.S. Gottlieb and M.R. Rao, "(l,k)-Configuration
Facets for the Generalized Assignment Problem."
Y. Ye, "A 'Build-Down' Scheme for Linear Pro-
B. Kalantari, "Karmarkar's Algorithm with
Improved Steps."
C. Roos, "An Exponential Example for Terlaky's
Pivoting Rule for the Criss-Cross Simplex
H. Hu, "A One-Phase Algorithm for Semi-Infinite
Linear Programming."
K.C. Kiwiel, "Proximity Control in Bundle
Methods for Convex Nondifferentiable Minimiza-

Volume 46, No.2
P. Tseng and D.P. Bertsekas, "Relaxation
Methods for Monotropic Programs."
C.L. Monma, B.S. Munson and W.R.
Pulleyblank, "Minimum-Weight Two-Connected
Spanning Networks."

M.D. Asic, V.V. Kovacevic-Vujcic and M.D.
Radosavljevic-Nikolic, "Asymptotic Behaviour of
Karmarkar's Method for Linear Programming."
R. Ge, "A Filled Function Method for Finding a
Global Minimizer of a Function of Several
M.I. Henig, "Value Functions, Domination Cones
and Proper Efficiency in Multicriteria Optimiza-
R. Chandrasekaran and A. Tamir, "Algebraic
Optimization: The Fermat-Weber Location
F. Granot and J. Skorinkapov, "Towards a
Strongly Polynomial Algorithm for Strictly
Convex Quadratic Programs:An Extension of
M. Meanti, A.H.G. Rinnoy Kan, L. Stougie and C.
Vercellis, "A Probabilistic Analysis of the Multi-
knapsack Value Function."
R. Hettich and G. Gramlich, "A Note on an
Implementation of a Method for Quadratic Semi-
Infinite Programming."
J. Rohn, "A Short Proof of Finiteness of Murty's
Principal Pivoting Algorithm."

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I ~-----

PG12numberwn- M

C ONTRIBUTIONS for a Mixed Integer Programming library
of test examples are invited by Peter Conrad and Prof. R.C.
Daniel, Univ. of Buckingham, Buckingham, MK18 1EG, Eng-
land, Telephone: (0280) 81408. !Prof. Dr. Reiner Horst, Univer-
sitit Trier, Postfach 3825, 5500 Trier, FRG, has issued a call for
papers for a new Journal of Global Optimization to be published
beginning in 1991. JAIRO'90, the annual Conference of the Op-
erational Research Society of Italy, will be held in Sorrento, Oct.
3-5, 1990. Contact Prof. Antonio Sforza or the Secretariat, Insti-
tuto di Fisica, Matematica e Informatica, Facolta di Ingegneria,
University di Salerno-84084 Fisciano (Salerno), Tel. +39-89-
822233/822424. !JDeadline for the next OPTIMA is June 1,1990.

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

Journal contents are subject
to change by the publisher.

Donald W. Hearn, EDITOR
Elsa Drake, DESIGNER

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



II. I 1. II~-~----~ ~~----~------~-~--~

MARCH 1990


number twenty-nine

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