Title: Optima
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00090046/00038
 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: November 1992
 Record Information
Bibliographic ID: UF00090046
Volume ID: VID00038
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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The Cornell Computational Optimization Project (CCOP) -
now in its sixth year supports computational and theoretical
activities in both discrete and continuous optimization through a
computationalfacility, ..,i i. i l. ,,1..., -r ,,!.t-. t -1,,.rl -term visitors
and seminars, and post-doctoral research associates. Funding is pro-
vided by the National Science Foundation, the Air Force Office of
Scientific Research and the Office of Naval Research.
Faculty associated with the program are all members of Cornell's
Center for Applied Mathematics, with primary affiliations in the
Department of Computer Science and the School of Operations
Research and Industrial Engineering, and include R.G. Bland, T.F.
Coleman, D.B. Shmoys, E. Tardos, M.J. Todd, L.E. Trotter r., C.F. Van
Loan and S.A. Vavasis. Among the visitors have been M. Gr6etschel,
L. kh, !,, il, and L. Lovisz.
Projects include a computational study of minimum cost network
flow algorithms; heuristics for traveling salesman problems; inves-
tigations into crew .-i,. ,, ii-. covering and packing problems;
studies in interior-point methods; large-scale bound-constrained
nonlinear optimization; complexity in nonlinear optimization; and
parallel optimization and linear algebra.
The recently established Center for Applied Optimization at the
University of i i..r., -i i an informal center which encourages joint
research and applied projects among faculty n.'n'i iit it !i, .t I._ t-
ments, especially in engineering, mathematics and business.
The initial list of affiliated faculty include R. L. Francis, S. T. Tufekci,
C-Y Lee, Sherman Bai, Tom Kisko, and Don Hearn from Industrial
& Systems Engineering (ISE); Bill Hager and Bernhard Mair from
Mathematics; Kirk Hatfield from Civil Engineering and Harold
Benson, Gary Koehler and Selcuk Erenguc from Decision and Infor-
mation Sciences. Hager and Hearn are co-directors of the Center, and
Panos Pardalos is currently visiting the ISE Department and the
Individual and joint research includes acceleration of decomposition
methods, new dynamic programming techniques for lotsizing
models, network optimization methods, optimal control problems,
optimization of elastic materials, inverse problems, multicriteria
optimization, and global and discrete optimization. Current and
pending applied projects include modeling and PAGE TEN -


Centers at

Florida and

Georgia Tech

; .. -i l.. 1. : -: .







Dimitri Bertsekas
Jann Cook
Joseph Dunn
David Gay
Masao Iri
Leon Lasdon
Jorge More
James Orlin
Roman Polyak
J. B. Rosen
David Shanno
Yinyu Ye

John Birge
Thomas Coleman
Chris Floudas
Philip Gill
Narendra Karmarkar
S. Lawphongpanich
Walter Murray
Michael Overton
Aubrey Poore
Ekkehard Sachs
Richard Tapia
Stavros Zenios

Christian Bischof
George Dantzig
Anders Forsgren
Jean-Louis Goffin
C.T. Kelley
P. O. Lindberg
Anna Nagurney
P. Panagiotopoulos
Mauricio Rescende
Michael Saunders
Andre Tits

Andrew Conn
Renato DeLeone
Masao Fukushima
Donald Goldfarb
Hiroshi Konno
Robert Meyer
George Nemhauser
Jong-Shi Pang
K. Ramakrishnan
Robert Schnabel
Philippe Toint

ALTHOUGH only invited talks will be presented, everyone is welcome to attend the con-
ference. Moreover, it is anticipated that some funds will be available for the support of
graduate students and to support the participation of women, minorities and persons with
disabilities; please contact the organizers. To obtain the latest information concerning the conference,
send an e-mail message to "coap@math.ufl.edu" and in the body of the message, put the phrase "send
meeting". The contact people for the conference are Bill Hager (fax: 904-392-6254), Don Hearn (e-mail:
hearn@ise.ufl.edu), and Panos Pardalos (phone: 904-392-9011).





University of Twente
Enschede, The Netherlands
June 2-4, 1993

Graphs and Combinatorial Optimiza-
tion will beheld at the Faculty ofApplied
Mathematics, University of Twente,
Enschede, The Netherlands.
The workshop will focus on recent re-
sults and developments in graph theory
and combinatorial optimization as well
as applications of operations research,
computer science and economics. A
proceedings volume devoted to the 3RD
Prospective participants are asked to
register before Dec. 18,1992. There is no
registration fee.
For more information contact:
Prof. U. Faigle (0031-53-893462) or
Prof. C. Hoede (0031-53-893429:
Faculty of Applied Mathematics
University of Twente
P.O. Box 217
7500 AE Enschede
The Netherlands.

Number Thirty-Eight NOVEMBER 19C


University of Florida
Gainesville, Florida /Feb. 15-17, 1993

The conference will bring together researchers who are working on many different
aspects of large scale optimization: algorithms, applications and software. It has
been endorsed by the MPS, ORSA and SIAM. Currently, the list of invited speakers
includes the following people:

PAE 3ubr ThryEgtNOEBR19





3rd International Conference

July 7-9, 1993
Zaragoza, Spain

Structural optimization is well-established as an
important research field. The practical applica-
tions of optimization techniques are important in
the design of aircraft, automotive design, civil
and mechanical engineering and computing.
Computer aided structural design and optimiza-
tion software provide a sophisticated means of
finding solutions for certain engineering prob-
lems. The objective of this conference is to bring
together researchers and engineers in this field.
The previous international conferences, OPTI 89
and OPTI91, were very successful with many
international delegates representing universities,
private and public research centers and industry.

Design Optimization;
Shape Optimization;
Knowledge Based and Heuristic
Materials Selection and Topographical Changes in
Optimum Design;
Design of FEA/BEM Adaptive Grids;
Design Sensitivity Analysis in Linear and
Nonlinear Structures;
Expert Systems in Optimum Design;
Optimization in Reliability-based Design;
Optimization and Technical Codes;
Integrated Packages for Optimum Design;
Testing of Optimization Software;
Analytical Advances in Optimum Design;
Multicriterion Optimization;
Methods for Large and Continuum Structures,
Optimization and Supercomputing;
Optimal Control Structures;
Approximation Methods in Structural Optimization;
Others falling within the scope of this conference.
Three copies of an abstract of no more than
300 words clearly stating the purpose, results
and conclusions of the work to be described
in the final paper should be submitted to the

Conference Secretariat by Oct. 30, 1992, for
review. A camera-ready manuscript of the
final full-length paper must be received by
March 5, 1993.
The published proceedings of the Conference
will be available to delegates at the time of
registration. The language of the conference
will be English.
There is an airport in the city with 30-minute
flights to Madrid and Barcelona and 90-
minute flights to London and Paris. There are
also several trains a day connecting Zaragoza
with Madrid and Barcelona.
Conference Chairmen:
Dr. C.A. Brebbia, Wessex Institute of Technol-
ogy, Ashurst Lodge, Ashurst, Southampton,
S04 2AA, UK.
Tel: 44 (0) 703 293223; Fax: 44 (0) 703 292853;
E-Mail: CMI@uk.ac.rl.ib;
International E-Mail: CMI@ib.rl.ac.uk.
Dr. S. Hernandez, Department of Mechanical
Engineering, University of Zaragoza, Maria de
Luna, 50015 Zaragoza, Spain.
Tel: 34 (9) 76 516200; Fax: 34 (9) 76512932.
For more information contact:
Sue Owen, Conference Secretariat OPTI 93
Wessex Institute of Technology
Ashurst Lodge, Ashurst
Southampton, Hants S04 2AA UK
Tel: 44 (0) 703 293223; Fax: 44 (0) 703 292853;
E-Mail: CMI@uk.ac.rl.ib;
International E-Mail: CMI@ib.rl.ac.uk.



The World Congress on Optimal
Design of Structural Systems

Rio de Janeiro, Brazil
Aug. 2-6, 1993

The purpose of this meeting is to bring together
designers and researchers to present the latest
advancements in Structural Optimization and
Computer-Aided Structural Design. Topics
ranging from the mathematical foundations of
this field to software development and practi-
cal applications in mechanical, structural, aero-
space, civil, chemical and naval engineering
will be discussed. Closely related fields also are
covered, provided that the treated subject is
related to design optimization or automation.

Papers which consider Optimal Design of
Multidisciplinary Systems, incorporating struc-
tural engineering interacting with other disci-
plines, are particularly relevant to the conference.
State-of-the-art tutorials and surveys which cover
thebroadspectrumofStructuralCOpi l.n,1! II. 1 ll
be given. Commercial and academic software of
interest to the Structural Optimization community
will be presented.
The conference will be held on the campus of the
; 11i; ,r, TI,- r I I.. .. if .i.i I located in one of
the most charming parts of Rio de Janeiro, in front
of Guanabara Bay and at the foot of the Sugar Loaf.
Nearby is the famous Copacabana beach, where
most of the major hotels, shops and restaurants are
located. Bus transportation will be provided for
Rio is a cosmopolitan city containing many lodg-
ing facilities, restaurants, shops and cultural activi-
ties. Rio has beaches, mountains, forests, parks,
and islands. All of this beauty is flavored by the
easy grace and natural hospitality of the inhabit-
ants, the Cariocas, a people in love with life, music
and dance.
A social program will be arranged for participants
and their guests. A selection of pre- and post-
meeting tours is planned. In particular, a very nice
one-day cruise to beautiful tropical islands is
scheduled for the Sunday before the conference.
Deadlines for authors:

Receipt of abstracts of about 500 words, Oct.
30, 1992; notification of acceptance, Jan. 1,
1993; receipt of final papers, April 15, 1993.
Mailing address:
Prof. J. Herskovits, Mechanical Engineering
COPPE, Federal University of Rio de Janeiro
Caixa Postal 68503, 21945-970
Rio de Janeiro, Brazil
Phone: (55) 21 280 7043;
Fax: (55) 21 290 6626.


Number Thirty-Eight




RUTCOR Rutgers
Center for Operations
Busch Campus
Rutgers University
P.O. Box 5062
New Brunswick, NJ 08903

P. Hansen and F.S. Roberts, "An
Impossibility Result in Axiomatic
Location i .' .. .." RRR 1-92.
L. Eeckhoudt and P. Hansen,
SI,.,. i .. ',.. ,, Changes in Risk
with Tail-Dominance," RRR 2-92.
P. Hansen and B. Jaumard,
"Reduction of Indefinite Quadratic
"'i. '' i- to Bilinear Programs,"
RRR 3-92.
I. Maros, "A Practical Anti-
D. .. ; .. i. i Row Selection
Technique in Network Linear
... ,,,"i.;.'.." RRR 4-92.
J.-M. Bourjolly, P.L. Hammer,
W.R. Pulleyblank and B.
Simeone, I'. ..I.,,.-Combinatorial
Bounding of Maximum 2-
Satisfiability," RRR 5-92.
P.L. Hammer and A. Kogan,
"Horn Functions and their DNFs,"
RRR 6-92.
E. Boros, P.L. Hammer, M.E.
Hartmann and R. Shamir,
i'.), '. l, j Problems in Acyclic
Networks," RRR 7-92.
P.L. Hammer and A. Kogan,
"Horn Function Minimization and
Knowledge Compression in
Production Rule Bases (Extended
Abstract)," RRR 8-92.

E. Boros, Y. Crama, P.L. Ham-
mer and M. Saks, "A Complexity
Index for P-...,,.;,',.i",h!' Problems,"
RRR 9-92.
P.-C. Chen, P. Hansen and B.
Jaumard, "Partial Yi ..-I;. in
Vertex Enumeration," RRR 10-92.
I. Maros, "Performance Evaluation
of MINET Minimum Cost Netflow
Solver," RRR 11-92.
P. Hansen, B. Jaumard and G.
Savard, "New Branch and Bound
Rules for Linear Bilevel Program-
ming," RRR 12-92.
P.-C. Chen, P. Hansen, B.
Jaumard and H. Tuy, "Weber's
Problem with Attraction and
Repulsion," RRR 13-92.
P.L. Hammer and A.K. Kelmans,
"On Universal Threshold Graphs,"
RRR 14-92.
Y. Crama and A.G. Oerlemans,
"A Column Generation Approach
to Job Grouping for Flexible
Manufacturing Systems," RRR 15-
E. Boros, P.L. Hammer and X.
Sun, "i:-'-. .,, '.", of Q-Horn
Formulae in Linear Time," RRR
E. Boros and P.L. Hammer, "A
Generalization of the Pure Literal
Rule for Satisfiability Problems,"
RRR 20-92.
N.V.R. Mahadev and F.S.
Roberts, "Amenable Colorings,"
RRR 21-92.

CWI Department of
Operations Research,
Statistics and System
Theory Reports
Postbus 4079
1009 AB Amsterdam, The

J.P.C. Blanc, P.R. de Waal, P.
Nain, "A new Device for the
'* I,, ,';. :I- Problem of Optimal
Control of Admission to an M/M/c
Queue, BS-R 9101.
O.J. Boxma, "Analysis and
Optimization of Polling Systems,"
BS-R 9102.
M. Kuijper, "Descriptor Represen-
tations without Direct i ... li ,, i,
Term," BS-R 9103.
H.J.A.M. Heijmans, J. Serra,
"Convergence, Continuity and
Iteration in Mathematical Morphol-
ogy," BS-R 9104.
H.J.A.M. Heijmans, .l.-, I.- ,... -
cal Discretization," BS-R 9105.
C. MacDiarmid, B. Reed, A.
Schrijver,' il,'... I Circuits in
Planar Graphs," BS-R 9106.

A.L.M. Dekkers, L. de Haan,
"Optimal Choice of Sample
Fraction in Extreme-Value
Estimation," BS-R 9107.
M. Kuijper, J.M. Schumacher,
"State Space Formulas for Transfer
Poles at i'.,:. i, "BS-R 9108.
A.J. Baddeley, M.N.M. van
Lieshout, i .... ,gt ...: of
0:-. 1,; ..',i Objects using Markov
Spatial Processes," BS-R 9109.
B. Gamble, W. Pulleyblank, and
B. Reed, "Right Angle Free
Subsets in the Plane," BS-R 9110.
O.J. Boxma, H. Levy, J.A.
Weststrate, "Efficient Visit
Frequencies for '. 'I, ,, Tables:
Minimization of I\,iatr, Cost,"
BS-R 9111.

~ 1~1~ ~

Number Thirty-Eight




Evolution ofRandom

Search Trees

Hosam M. Mahmoud
Wiley and Sons
ISBN 0-471-53288-2

This book is devoted to a small though important
., i, .i. p i.f .. i-.-i i. .I ., l.1, it i ... 1 .! ,nam ely
the behavior of random search trees constructed
by insertion. Many of the results are fairly recent
(from the second half of the 1980s to the present)
and due largely to the authors, Devroye and Pittel.
Search trees are of obvious practical use as data
structures, but the reader who enjoys the theoreti-
cal analysis of algorithms is well-served indeed.
Which problems are addressed '-. i r Itl,.r I I..
elements of a randomly permuted ordered set of
n objects are successively inserted into a labeled
tree by following a simple combinatorial rule. For
example, in the binary case, the familiar require-
ment is that an element in a node is larger than the
elements in its left subtree but smaller than the
elements in the right one. One may then ask for the
expectations and (limiting) distributions of the
number of leaves on a certain level (connected with
expected search and insertion time), the height, the
minimal path length, etc.

Recursive expressions for these parameters are not
hard to find by elementary combinatorial and
probabilistic arguments; some real fun starts when
the resulting generating functions are solved or
estimated. The means used are the combinatorial
theory of generating functions and related topics
in classical complex analysis. The book contains
many useful exercises.
Chapter 1 contains a summary introduction to the
tools used in the rest of the book. A few pages are
devoted to the very basics of graph theory and or-
der symbols. The next section is on ..,. I I ilI -
functions and complex analysis. The author states
in his preface that "... no special background, other
than prior exposure to a general introduction to
functions of complex variables, is assumed." This
seems a bit optimistic however; a good familiarity
with such subjects as asymptotic expansions, the
Mellin transform and the analytic continuation of
the Gamma function is certainly needed in order
to appreciate this book.
ext, a short and clear overview is given
of elementary probability theory up to
and including some central limit theo-
rems. The chapter ends with a few remarks on the
computer representation of trees. The author
adopts PASCAL as a universal programming lan-
guage which makes his book less self-contained
than it could be. The number of programs is small,
however, and it is possible to read the book with-
out the "background of one year in programming"
the author assumes.

"... the book can be highly
recommended to researchers in
complexity theory and discrete
mathematics because of its many
interesting applications of
generating functions."

In Chapter 2 the basic binary tree algorithms
(search, insert, traversal) are defined. The validity
of the random permutation model for the data
stream is demonstrated, and the probability dis-
tributions of(un)successful search time, height and
path lengths are studied, culminating in the strong
law of large numbers for the height by Pittel and
Chapter 3 generalizes these results to m-ary trees,
important in computer memory management
(paging). The recursions become much harder
now, and only partial results are known. Some
theorems are really curious and inspiring. For ex-
ample, the number of nodes has a variation which
is linear ii, .l nLnil.. r .l.-,. f, .- F.i. -ary trees with
m 26 but not for higher values. The remainder of
the chapter, again, is devoted to the analysis of
insertion depth and height.
Chapter 4 is relatively short and contains a similar
analysis of quad trees and k-d trees. The distribu-
tions of random variables considered appear to be
identical to their binary search tree equivalents.




Chapter 5 is devoted to faster search algorithms
guided by the structure of the keys (radix search).
The data structure used is the "trie". The actual
keys now are stored in the leaves, and adding a key
may increase the number of internal nodes consid-
erably. Hence, the main point of interest is space
re l| ,,. !. i.. , ,i i. ,. .. i. 1 -n tl i, -, '( i I
et al. are presented under the Poisson and Bernoulli
data models. The chapter ends with an analysis of
the key depth distribution and the expected height
of a trie.
In the final chapter of Mahmoud's book, one stud-
ies digital search trees. These combine some advan-
tages of binary search trees (storage in the internal
nodes) and tries (digital search). The methods and
results are analogous to those of the preceding
In summary, Mahmoud's book provides a clear,
:! 1 ; i; i .. ,J uniform presentation of a small yet
useful branch of complexity analysis. Most of the
book consists of fairly technical calculations, but
the author gives ample attention to issues of prac-
tical motivation. From this point of view, the book
is of interest to data engineers and 1-.!..I-. ,i- i. r ..
Even more so, the book can be highly recom-
mended to researchers in complexity theory and
discrete mathematics because of its many interest-
ing applications of generating functions.
k\. l t I- I I h u ... .. I , jl,,,rl
from some probability theory, a solid background
in classical analysis. This makes it suitable for stu-
dents in mathematics, rather than computer sci-
ence (at least in Holland).

Parametric Optimization:


Pathfollowing and Jumps

J. Guddat, F Guerra Vasquez and
H. Th. Jongen
Teubner and John Wiley & Sons
ISBN 0-471-92807-0

This is another significant research monograph
coming from the "German school" of parametric
optimization. Its style and quality will remind the
reader of the classic book, Nonlinear Parametric
Optimization, by Bank, Guddat, Klatte, Kummer
and Tammer (Akademie-Verlag, Berlin, 1982). In
the new monograph the authors study finite-
dimensional optimization problems with one
scalar param eter. I i i ...... L .--.. ~ h. p. ii i-,
following methods (also called continuation or
homotopy methods). These methods are impor-
tant in various situations ranging from solving
nonlinear (single- and multi-objective) optimiza-
tion problems to tracing dependency of the opti-
mal solutions and the optimal values on a specific
parameter in an economic or engineering system.
(A group of power systems engineers at this
reviewer's university has successfully imple-

"This monograph...will be
useful to the researchers in
numerical optimization and
mathematical modeling. For the
experts in parametric optimization,
especially in numerical parametric
optimization, [it] will become a
standard reference."

mented these methods in modeling real-life situ-
ations, a fact also reported in the monograph.)
The "paths" traced in the monograph are suffi-
ciently fine discretizations of local minimizers,
stationary points and generalized critical points
(i.e., points in the decision variable x and the sca-
lar parameter t, where the gradients of the objec-
tive function and active constraints are linearly
dependent). The path following is based on the
general predictor-corrector principle applied at
every iteration: From a given point on the path,
move t and construct a new initial point x (using,
e.g., Euler predictor) that falls within the radius of
local convergence of a corrector (e.g., a Newton,
Robinson, Wilson or Garcia-Palomares and
Mangasarian type method). In particular, an active
index set strategy is proposed to follow a function
of local minimizers. This strategy allows a change
of more than one index at a time. An important
feature of the proposed methods is that they in-
clude jumps from one connected component of
local solutions or critical points to another (not
necessarily of the o,, I !ni.J. The jumps are pos-
sible if certain types of turning points appear. For
an identification of points along a path and for
jumping criteria, the authors use a structure analy-
sis and singularity theory of Jongen and relevant
results of Kojima and several co-authors.
The theoretical background on the structure of
various interesting points is reviewed in a self-
contained introductory chapter (written by
Jongen). In i-,..] r ,1. to a classification of critical
points into five types (according to the so-called
I I I I.-,, tI i, I. I ..., L- r- I, thechapterremindsthe
reader about general important facts, such as the
role of the Mangasarian-Fromovitz constraint
qualification in the local descriptions of thefeasible
set and its intimate relationship with bifurcation.
All functions in the programs are assumed k times
continuously differentiable, where k is raised ac-
cording to the need. Several problems are actually
solved numerically and some particular strategies,
based on the experience of the authors, are sug-
gested in some instances.


Numbgpi;J 1, i I i -1, 1



Titles of the chapters are: 1. Introduction; 2. Theo- 5. Computational Methods in Probability Theory The prerequisites for reading and understanding

retical Background; 3. Pathfollowing of Curves of
Local Minimizers; 4. Pathfollowing Along a Con-
nected Component in the Karush-Kuhn-Tucker
Set and in the Critical Set; 5. Pathfollowing with
Jumps in the Set of Local Minimizers and in the Set
of Generalized Critical Points; 6. Applications.
The monograph contains almost 250 references.
The familiarity of the authors with a huge, and
often technical, literature on numerical algorithms
and various related topics in parametric and nu-
merical optimization is impressive.
This monograph should be of interest to graduate
students and researchers in every area of applied
mathematics that requires optimization. In par-
ticular, it will be useful to the researchers in nu-
merical optimization and mathematical modeling.
For the experts in parametric optimization, espe-
cially in numerical parametric optimization, this
monograph will become a standard reference.

Handbooks in Operations

Research and

Management Science

Volume 2, Stochastic Models
Edited by D.P. Heyman and M.J.
North Holland, Amsterdam
ISBN 0-444-87473-9

The book under review, Stochastic Models, is a
collection of 13 rather independent chapters on
stochastic topics which are useful in operations
research and management science.
The chapter titles and authors are: 1. Point Process
(R.F. Serfozo); 2. Markov Processes (A.F. Karr);
3. Martingales and Random Walks (H.M. T ,, 1. .;1
4. Diffusion Approximations (P.W. Glynn);

(W.K. Grassmann); 6. Statistical Methods (J.
Lehocky); 7. Simulation Experiments (B.
Schmeiser); 8. Markov Decision Processes (M.L.
Puterman); 9. Controlled Continuous Time
Markov Processes (R. Rishel); 10. Queuing Theory
(R.B.Cooper); 11.C u. ,,i, ,. ... I Walrand);
12. Stochastic Inventory Theory (E.L. Porteus);
13.Reliability ii a .t -. i ., Lir '. . ,l ,
J.G. Shanthikumar).
t is not possible to review adequately the con-
tents of each chapter here. Instead we concen-
trate on more general aspects. All in all, the
expository level is high. General definitions are of-
ten motivated by examples and preceded by spe-
cial definitions. The authors apparently have tried
to write on a non-technical level. Each chapter has
its own set of extensive references. An accumu-
lated subject index helps to find specific topics. We
conclude that Stochastic Models is valuable both as
a reference book and as an introduction to each of
13 different topics. It should be included in any
library of operations research, management sci-
ence, mathematics or statistics.
The above conclusions are unaffected by the fact
that Stochastic Models has several flaws. This is
perhaps to be expected in a work of such size and
scope, but it seems that many of these flaws could
have been corrected during the editing process. We
list some of them:

most chapters are not stated. Not all chapters can
be read assuming only "a calculus-based probabil-
ity course and the rudiments of matrix algebra."
For example, the concept of conditional expecta-
tion given a o-algebra is used in Chapters 3 and 4
without explanation. No reference is given for the
reader unfamiliar with this concept.
The subject index is incomplete. One example is the
reference to the Ito integral (used without defini-
tion on page 436) is missing.
No cumulative author index or cumulative set of
references has been provided.
C... 1,._ n -. I. 11 II, .... ...r which easily could have
been found with an English language spell checker,
e.g., invovled, on page 436.
In Chapter 1, E denotes expectations as well as
some state space (see the first two formulas on page
In Chapter 6, the book cited, Rao (1965), in the
context of minimum variance unbiased estimation,
should have been replaced by its second (1973)
edition. A more recent book reference concerning
this topic which I would have added is E.L.
Lehmann (1983), Theory of Point Estimation.
The reported flaws are minor compared to the
usefulness of Stochastic Models, but the book could
have profited from a more careful editing process.

". ..Stochastic Models is valuable
both as a reference book and as an
introduction to each of 13 different
topics. It should be included in any
library of operations research,
management science, mathematics
or statistics."





Structural Complexity


Vol. Iand Vol. II

EATCS Monographs on
Theoretical Computer Science, 11
and 22
J. L. Balcizar, J. Diaz and J.
Springer Verlag
1988 and 1990
ISBN 3-540-18622-0 (VOL. I)
ISBN 3-540-52079-1 (VOL. II)

This pair of monographs, written by three authors
from Barcelona, represents so far the standard text-
'.....k ..r t ',-,.t -nl, 1 ..t .( t I .II .5 it l,. it' t ,. ..t .
A. ..., ..h r .! f,,.m ..tit- ,,-itI..t,,..1 - it, .n ,.r,
our courses on structural complexity theory, and
from this fact the readership of the OPTIMA news-
letter may conclude that this reviewer will be bi-
ased in favor of these books. Still this will not
prevent me from reviewing it from the perspective
of the value of these books for those working in
mathematical programming or combinatorial op-
First, we must look at the basic concepts of com-
putational complexity. Researchers solving large-
scale optimization problems by nature should be
, r....I t',, in i p rt rt, .t' r, .t,. . .- b. .t -.... p r. b-
lems hl.i ir.. ,.fie,.ti .1- -- .i. i..l problems
which are solvable in principle, but are found to be
intractable for all practical purposes. It was, in fact,
a researcher in operations research, J. Edmonds,
who presented the idea that tractability of a com-
binatorial problem should equate to having a
polynomial time-bounded algorithm for its solu-
tion. The existence of a substantial class of prob-
lems, not known to be tractable, which can be
solved in polynomial time using a non-determin-

istic guess and verify method, but known to be-
have as the hardest problem of this type, was
verified by the fundamental work of S. Cook, D.
Karp and independently by L. Levin. The results
of these developments of the early 1970s are
known as the P=NP problem and the concept of
One reason these ideas are held to be fundamen-
tal is that they provide i I .- i 1 .1. -. 1 I .i i .
about complexity and intractability without going
into the details of a concrete machine model and
the algorithms running on it. The notions of poly-
nomial time and logarithmic, or polynomial
b .,. ti.-:1 1 I ..,!,-, i, r- ., -I_ .I r, n rIt 1 '
reasonable sequential models of computation.
Parallel models are a different story: the reasonable
Ii ,;e II -- I I p i, i ,1..! I. i- I i. w n to have the
power to do in polynomial time what sequential
machines can do in polynomial space.
D iLI,,llI ,, i-, ,, .i,,,,, ,i pi, it i...,.,. ,
there existed two directions in the re-
search: on the one hand, there was the
more abstract line where the concept of complex-
ity was investigated as a mathematical topic using
tools primarily originating from recursion theory.
On the other hand, a large amount of research was
aimed at improving algorithms for specific con-
crete problems, designing new and efficient data
structures or proving by difficult and complicated
combinatorial arguments a lower bound showing
that the known algorithms cannot be improved. In
case the bounds are not tight, such a lower bound
exhibits the gap between what has been achieved
and what is known to be in, ... -I I'. The two di-
rections in complexity theory converged on the
themes of NP-completeness, reductions and in-
tractability proofs for various logical systems and
decision problems. Still, in the 20 years that fol-
lowed the P=NP? problem turned out to be the
foremost unsolved problem in computational
complexity theory, and this situation remains
unchanged today.

Structural complexity theory finds its origins in
work performed by Juris Hartmanis and his stu-
dents in the late 1970s. Hartmanis and Berman
observed that the combinatorial problems shown
to be NP-complete turn out to be even more simi-
lar than what is expressed by the fact that they are
interreducible by polynomial time many-one re-
ductions; they are in :. I r'. r i l.. I. . by poly-
nomial time bijections, which means that the cor-
responding combinatorial decision problems are
isomorphic. Hartmanis and Berman went on to
propose the conjecture that this isomorphism
which holds for all known NP-complete problems
in fact extends to all possible NP-complete prob-
lems. Having observed that this is a hard-to-prove
conjecture (its truth would el, 1 i -- ',, they set
out to disprove it by constructing an NP-complete
problem which could not be isomorphic to a stan-
dard NP-complete problem like SATISFIABILITY,
on behalf of its structural properties. Thus the quest
for a sparse NP-complete set was initiated; this
ended in failure when S. Mahaney proved that
such sets could not exist, unless P=NP.

"The books provide a large
collection of fundamental
theory and tools which have been
found relevant for this research."

These two results have set the tone for subsequent
work in structural complexity theory performed
in the 1980s and which by now has attracted an
active community of researchers around the
world; this community has its own series of annual
conferences (IEEE Conference on structure in com-
plexity theory, with a seventh edition in 1992), and
a reasonable amount of coverage in general theory
conferences and scientific journals. The topics
involve the study of complexity hierarchies using
recursion theoretical tools, the study of complex-
ity classes defined using alternative modes of
computation (among which the probabilistic
models and the models based on interaction have
become extremely important), and the ongoing





study into machine models and the combinatorial
study of characterizing their finite computations
in terms of circuit models or descriptive

to contribute to operations research. It is evident
that a theory which proclaims that all interesting
operations research problems being worked on are
in fact equal (even though researchers trying to
solve those problems know quite different) risks
losing credibility even before having been used.
Still the structural framework has something to
contribute to those working on practical problems.
Over the past years I have been queried about the
i -.. i .,,i II ,t p I i ur, -i..-iii.,wouldbehardfor
NP or whether there could exist an NP-complete
problem having unique solutions. In both cases the
answer is negative, provided nothing bad hap-
pens. Here the bad thing that might happen
amounts to the collapse of the polynomial time
hierarchy which is generally believed to be infinite.
Structural complexity theory yields constraints on
1 .., rl,,_ ,,, ,-,I r I, -,, (., d ,,F ., ,l, it ,,,
look, even if we do not know the real state of af-
fairs. A more recent result which attracted much
interest in the spring of 1992 shows that a number
..I ., I!I.-,,... 11 ..'1-, 1, i i income binatorialoptim i-
zation cannot be solved approximately unless
P=NP. This result, which is an unexpected conse-
quence of the research on complexity classes based
on interactive computation, clearly has a direct im-
pact on operations research.
The two books present an extended introduction
into a number of relevant concepts and results in
structural complexity. The presentation is intuitive
without unneeded formalisms. The readers must
possess a reasonable amount of mathematical
maturity and a general knowledge of the funda-
:r,. m.,i-..f... p.ni iit, i -. .Previousexperience
up to the level of, for example, the textbook on
automata theory and formal languages by
Hopcroft and Ullman or the well-known mono-
graph by Garey and Johnson is a must. Also, the
exercises require a mathematical maturity.

The introductory sections are dense and concise:
models of computation in Chapter 1; time and
space bounded computations in Chapter 2; funda-
mental complexity classes in Chapter 3 and
reducibilities in Chapter 4. Do not skip these intro-

not be used until much later in the books. Part I
continues with more specialized structural no-
tions: non-uniform complexity in Chapter 5 and
uniform diagonalization in Chapter 7. Extension
of the modes of computation are presented in
Chapter 6 dedicated to probabilistic models and
Chapter 8 where the polynomial time hierarchy is
introduced. This completes the contents of volume
I which has provided the reader with a large col-
lection of concepts and tools, all compared nicely
with each other.
V olume II begins with more machine
model theory: the parallel models are
presented (Chapter 1) and the Fp !.illi I
computation thesis is discussed (Chapter 2). The
alternation model in Chapter 3 and the uniform
circuit complexity in Chapter 4 provide extensions
of the class of computational models. The subject
which originally motivated the whole research
program (the isomorphism conjecture and
Mahaney's proof of the non-existence of a sparse
complete set) can be found in Chapter 5. The struc-
tu .,ri I t p r, i. -..t. 'Li-in ,.,!. it-, i 'd, ... pl .i i ..1 .r. -
are to be found in Chapter 6. Chapters 7 and 9 deal
with ideas which have a clear origin in recursion
theory, such as relativizations and high- and low-
ness concepts, which have been found useful for
proving the sort of non-existence results on con-
crete problems mentioned in the introduction of
this review.

The final chapters on resource-bounded
Kolmogorov complexity and on interactive proof
systems deal with areas which have become sub-
stantially more important since the books have
appeared. Another indication of the time of
completion is the fact that the 1987 result by

of nondeterministic space bounded classes under
complementation (solving a problem from au-
tomata theory which had been open for 23 years!)
has been included as an appendix. This result and
the discovery of the collapse of various proposed
hierarchies in the same year, 1987, indicate the real
breakthrough of structural complexity theory.
Other important, more recent results not men-
tioned are the full closure of PP under all Boolean
operations (left as an open problem in Chapter 6)
and Kadin's result that a collapse of the Boolean
hierarchy implies that the Polynomial time Hier-
archy collapses as well.
The two volumes contain a well-written introduc-
tion into an active research area which look at first
sight only to be of indirect relevance for operations
research, but the most recent developments seem
to indicate otherwise. The books provide a large
collection of fundamental theory and tools which
have been found relevant for this research. How-
ever, publication came too soon in the sense that
the theory has been expanded substantially follow-
ing the completion of these books, therefore a large
number of important results are not included. One
should inspect the annual Structure in (c. -/I1, 't l,
Theory proceedings in order to remain up-to-date.
Thebooks are suitable for use in a graduate course,
but the course should include more recent mate-
rial from journals and conference proceedings as



PAGE 10 N u m beLr""~~lrThrty igt OVMBR 99

Vol. 56, No. 2

M. Deza and M. Laurent, "Facets
for the Cut Cone I."
M. Deza and M. Laurent, "Facets
for the Cut Cone II: Clique-web
T.F. Coleman and Y. Li, "A
Globally and '...i,,,r.'. ,il,
Convergent Alff,. Scaling Method
for Linear L, Problems."
J.-P. Crouzeix, J.A. Ferland and
S. Schaible, "Generalized
Convexity on Affine Subspaces
with an Application to Potential
K. Yokoyama, "e-C', "',"I,,t
Criteria for Convex Programming
1' ', N m Via Exact ,,, ii ;

Vol. 56, No. 3

J.E. '.1! I1 I1 and M.J. Todd,
.I..' ,j Combinatorial Optimiza-
tion Problems Using Karmarkar's

Y. Ye, "On Affine Scaling
iot ,i".,' for Nonconvex
Quadratic r i., M1... .. ."
P. Tseng and Z.-Q. Luo, "On the
Convergence of the Affine Scaling

C. Wallacher and U.
Zimmermann, "A Combinatorial
Interior Point Method for Network
Flow Problems."
J.W. Schmidt and S. Dietze,
"Unconstrained Duals to Partially
Separable Constrained Programs."
J. Pinter, "Convergence Qualifica-
tion of Adaptive Partition
Algorithms in Global Optimiza-
M.C. Ferris and A.B. Philpott,
"On Affine Scaling and Semi-
Infinite! ,i'.,', ,m .."


New Optimization Centers

at ornell, Florida and

Georgia Tech

solutions of water management
problems, evacuation modeling, and
warehouse location problems. Spon-
sors include the National Science
Foundation, the Army Research Of-
fice and the Florida Water Manage-
ment Districts.
TheCenteris interested in promoting
collaboration with researchers at
other universities through visitors
and stud ent exchange. It administers
a program for visiting students from
The Royal Institute of Technology
(KTH), Stockholm, in cooperation
with P. O. Lindberg of the KTH Divi-
sion of Optimization and Systems
Theory and E. Rune Lindgren who
has appointments at i I. .. i and
A conference in Large-Scale Optimi-
zation, hosted by Hager, Hearn and
Pardalos willbeheld Feb. 15-17,1993,
at the University of Florida. Many
leading researchers will present pa-
pers (see announcement elsewhere in
( '! i '. .., The conference has been
endorsed by the MPS, SIAM and


The Computational Optimiza-
tion Center, established with a grant
from IBM, conducts research and
education programs on the develop-
ment, implementation and applica-
tion of optimization methods.
Housed in the School of Industrial
and Systems Engineering, the
Center draws upon the diversity of
faculty with expertise in all areas of
operations research and manage-
ment science.

The principal faculty are Directors
Ellis Johnson and George Nem-
hauser, Cynthia Barnhart, Roy
Marsten and Martin Savelsbergh.
The affiliated faculty are Faiz Al-
kl ,., ,i F ii i. ,. I..- i. i.nBartholdi,
Marc Goetschalckx, John Jarvis,
Donna Llewellyn, Gary Parker, Don
Ratliff, Alex Shapiro, Mike L', ii-,
Craig Tovey and John Vande Vate.
Visitors for the academic year 1992-
1993 include Lloyd( I I.. and Ram
The research of this Center focuses on
large-scale optimization modeling
and computation and the develop-
ment of software using IBM's Opti-
mization Subroutine Library (OSL).
Recent projects include production
scheduling in a manufacturing envi-
ronment, optimization of a large dis-
tribution system, and airline crew
assignment and fleet planning prob-
lems. Funding is provided by grants
and contracts from the National Sci-
ence Foundation, Air Force Office of
Scientific Research, Army Research
Office, AT&T, IBM, American Air-
lines, Delta Airlines and Northwest
Airlines. NSF and AFORS fund basic
computational research in mixed-
integer programming, and NSF to-
gether with the airlines provide
matching funds for a project on col-
umn generation methods and their
applications to airline optimization
Workshops to increase the technical
and modeling skills of users of opti-
mization software are conducted for
executives, practitioners and re-
searchers on a regular basis.



Number Thirty-Eight



Nordic Section
E P 0 R

The Nordic Section of MPS held its second biannual
meeting in Trondheim, Norway, Aug. 14-16, 1992.
Twenty-seven people from all five countries (Norway,
Sweden, Denmark, Finland and Iceland) took part.
About one third were Ph.D. students. There was a
decision to meet again during the winter of 1993-94 in
Linkiping. A new board was elected consisting of
Stein W. Wallace (Trondheim, Norway), Jens Clausen
(Copenhagen, Denmark) and Subhash Narula
(Linkiping, Sweden).
The number of MPS members in the Nordic counties
has increased substantially over the last three years
to about 45 at this time. Most of the members can be
reached by sending e-mail to mps@iok.unit.no (auto-
matic redistribution). The leader of the section can be
reached via mps-request@iok.unit.no. All MPS mem-
bers are encouraged to use this network if they wish
to inform the Nordic members of some issue, be it a
meeting, a visit to the region or some other subject.

Enhanced Nonlinear Programming Code Available

VERSION 3.0 of FSQP has been completed recently. As was the case
for previous versions, it is available free of charge to academic users,
bu I may not be redistributed. If interested, please send e-mail to
a ndre@src.umd.edu.

The main enhancement is that FSQP now also handles nonlinear equality constraints.
"Semi-feasibility" for these constraints is maintained in the following sense: given
a scalar constraint h(x)=O, if h(xO)<=0 (resp. >=0), then h(xk)<=0 (resp. >=0) for all k.
For those not familiar with previous versions of FSQP:
FSQP (Feasible SQP, developed by J.L. Zhou and A.L. Tits at the Institute for Systems
Research at the University of Maryland, College Park) is a FORTRAN code for solv-
ing constrained optimization problems, including constrained minimax problems.
Its main feature is that all the iterates it generates satisfy the constraints except for
nonlinear equality constraints, for which 'semi-feasibility" is maintained (see above).
This is of value in many engineering-related problems. Extensive numerical tests show
that the efficiency of FSQP is comparable to that of the most popular (non-feasible)
codes. A detailed User's Manual is available.

Application for cMembership

Mail to:

c/o International Statistical Institute
428 Prinses Beatrixlaan
2270 AZ Voorburg
The Netherlands

Cheques or money orders should be made payable to
INC. in one of the currencies listed below.
Dues for 1992, including subscription to the journal
Mathematical Programming, are Dfl.115.00 (or $55.00
or DM100.00 or 32.50 or FF345.00 or Sw.Fr.86.00).
Student applications: Dues are one-half the above rates.
Have a faculty member verify your student status and
send application with dues to above address.

I wish to enroll as a member of the Society.
My subscription is for my personal use and not for the
benefit of any library or institution. I enclose payment as follows:

Dues for 1992







Number Thirty-Eight



N 38 Nov 1992
Margaret Wright (AT&T Bell Labs) has been

re-elected vice president at large of SIAM

and continues as chair of the Society's Major

Awards Committee. "i i..I 1, i r, 1 ,.., iI .i -

line for the IFORS 93 Meeting being held

in Lisbon, July 12-16, 1993, is April 1, 1993.

1ADMOD93, a Symposium on Applied

Mathematical Programming and Modeling,

will be held in Budapest, Jan. 6-8,1993. Chair-

man is IstvAn Maros. It will be preceded by a

one-day Workshop on Interior Point Meth-

ods. Contact the Secretariat, e-mail:

hl(i'.lo i, 1,, II... IE-mail address for

OPTIMA is now: optima@ise.ufl.edu. IDead-

line for the next O P T I M A is Feb. 1, 1993.

Books for review should be
sent to the Book Review Editor,
Professor Dolf Talman
Department of Econometrics
Tilburg University
P.O. Box 90153
5000 LE Tilburg

Journal contents are subject
to change by the publisher.

Donald W. Hearn, EDITOR
Elsa Drake, DESIGNER


303 WeilHall
College ofEngineering
University of Florida
Gainesville FL 32611-2083 USA



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