M
A
NQ
38
Nov
1992
MATHEMATICAL PROGRAMMING SOCIETY NEWSLETTER
SCORNELL ,
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 postdoctoral 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 interiorpoint methods; largescale boundconstrained
nonlinear optimization; complexity in nonlinear optimization; and
parallel optimization and linear algebra.
6FLORIDA 1
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,
CY 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 codirectors of the Center, and
Panos Pardalos is currently visiting the ISE Department and the
Center.
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 
New
Optimization
Centers at
Conell,
Florida and
Georgia Tech
; .. i l.. 1. : : .
CONFERENCE NOTES 23
TR&WP 4
BOOK REVIEWS 59
JOURNALS 10
GALLIMAUFRY 12
P
T
I
IllllllICllr"~""sl~'~
PAGE 2
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
JeanLouis 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
JongShi 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 email 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: 9043926254), Don Hearn (email:
hearn@ise.ufl.edu), and Panos Pardalos (phone: 9043929011).
3RD TWENTE WORKSHOP
ON GRAPHS AND
COMBINATORIAL
OPTIMIZATION
University of Twente
Enschede, The Netherlands
June 24, 1993
The 3RD TX\ F NTE WORKSHOP on
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
TWENTE WORKSHOP is planned.
Prospective participants are asked to
register before Dec. 18,1992. There is no
registration fee.
For more information contact:
Prof. U. Faigle (003153893462) or
Prof. C. Hoede (003153893429:
Faculty of Applied Mathematics
University of Twente
P.O. Box 217
7500 AE Enschede
The Netherlands.
Number ThirtyEight NOVEMBER 19C
CONFERENCE ON LARGE SCALE OPTIMIZATION
University of Florida
Gainesville, Florida /Feb. 1517, 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
OPTI93
COMPUTER AIDED
OPTIMUM DESIGN OF
STRUCTURES
3rd International Conference
July 79, 1993
Zaragoza, Spain
Structural optimization is wellestablished 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.
Topics
Design Optimization;
Shape Optimization;
Knowledge Based and Heuristic
Optimization;
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 Reliabilitybased 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 cameraready manuscript of the
final fulllength 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 30minute
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;
EMail: CMI@uk.ac.rl.ib;
International EMail: 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;
EMail: CMI@uk.ac.rl.ib;
International EMail: CMI@ib.rl.ac.uk.
STRUCTURAL
OPTIMIZATION 93
The World Congress on Optimal
Design of Structural Systems
Rio de Janeiro, Brazil
Aug. 26, 1993
The purpose of this meeting is to bring together
designers and researchers to present the latest
advancements in Structural Optimization and
ComputerAided 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.
Stateoftheart 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
participants.
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
oneday 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
Program
COPPE, Federal University of Rio de Janeiro
Caixa Postal 68503, 21945970
Rio de Janeiro, Brazil
Phone: (55) 21 280 7043;
Fax: (55) 21 290 6626.

Number ThirtyEight
NOVEMBER 1992
PAGE 3
PAGE 4
RUTCOR Rutgers
Center for Operations
Research
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 192.
L. Eeckhoudt and P. Hansen,
SI,.,. i .. ',.. ,, Changes in Risk
with TailDominance," RRR 292.
P. Hansen and B. Jaumard,
"Reduction of Indefinite Quadratic
"'i. '' i to Bilinear Programs,"
RRR 392.
I. Maros, "A Practical Anti
D. .. ; .. i. i Row Selection
Technique in Network Linear
... ,,,"i.;.'.." RRR 492.
J.M. Bourjolly, P.L. Hammer,
W.R. Pulleyblank and B.
Simeone, I'. ..I.,,.Combinatorial
Bounding of Maximum 2
Satisfiability," RRR 592.
P.L. Hammer and A. Kogan,
"Horn Functions and their DNFs,"
RRR 692.
E. Boros, P.L. Hammer, M.E.
Hartmann and R. Shamir,
i'.), '. l, j Problems in Acyclic
Networks," RRR 792.
P.L. Hammer and A. Kogan,
"Horn Function Minimization and
Knowledge Compression in
Production Rule Bases (Extended
Abstract)," RRR 892.
E. Boros, Y. Crama, P.L. Ham
mer and M. Saks, "A Complexity
Index for P...,,.;,',.i",h!' Problems,"
RRR 992.
P.C. Chen, P. Hansen and B.
Jaumard, "Partial Yi ..I;. in
Vertex Enumeration," RRR 1092.
I. Maros, "Performance Evaluation
of MINET Minimum Cost Netflow
Solver," RRR 1192.
P. Hansen, B. Jaumard and G.
Savard, "New Branch and Bound
Rules for Linear Bilevel Program
ming," RRR 1292.
P.C. Chen, P. Hansen, B.
Jaumard and H. Tuy, "Weber's
Problem with Attraction and
Repulsion," RRR 1392.
P.L. Hammer and A.K. Kelmans,
"On Universal Threshold Graphs,"
RRR 1492.
Y. Crama and A.G. Oerlemans,
"A Column Generation Approach
to Job Grouping for Flexible
Manufacturing Systems," RRR 15
92.
E. Boros, P.L. Hammer and X.
Sun, "i:'. .,, '.", of QHorn
Formulae in Linear Time," RRR
1992.
E. Boros and P.L. Hammer, "A
Generalization of the Pure Literal
Rule for Satisfiability Problems,"
RRR 2092.
N.V.R. Mahadev and F.S.
Roberts, "Amenable Colorings,"
RRR 2192.
CENTRUM VOOR
WISKUNDE EN
INFORMATICA
LIBRARY
CWI Department of
Operations Research,
Statistics and System
Theory Reports
Postbus 4079
1009 AB Amsterdam, The
Netherlands
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, BSR 9101.
O.J. Boxma, "Analysis and
Optimization of Polling Systems,"
BSR 9102.
M. Kuijper, "Descriptor Represen
tations without Direct i ... li ,, i,
Term," BSR 9103.
H.J.A.M. Heijmans, J. Serra,
"Convergence, Continuity and
Iteration in Mathematical Morphol
ogy," BSR 9104.
H.J.A.M. Heijmans, .l., I. ,... 
cal Discretization," BSR 9105.
C. MacDiarmid, B. Reed, A.
Schrijver,' il,'... I Circuits in
Planar Graphs," BSR 9106.
A.L.M. Dekkers, L. de Haan,
"Optimal Choice of Sample
Fraction in ExtremeValue
Estimation," BSR 9107.
M. Kuijper, J.M. Schumacher,
"State Space Formulas for Transfer
Poles at i'.,:. i, "BSR 9108.
A.J. Baddeley, M.N.M. van
Lieshout, i .... ,gt ...: of
0:. 1,; ..',i Objects using Markov
Spatial Processes," BSR 9109.
B. Gamble, W. Pulleyblank, and
B. Reed, "Right Angle Free
Subsets in the Plane," BSR 9110.
O.J. Boxma, H. Levy, J.A.
Weststrate, "Efficient Visit
Frequencies for '. 'I, ,, Tables:
Minimization of I\,iatr, Cost,"
BSR 9111.
~ 1~1~ ~
Number ThirtyEight
NOVEMBER 1992
NOVEMBER 1992
R E V I E W S
Evolution ofRandom
Search Trees
Hosam M. Mahmoud
Wiley and Sons
Chichester
1992
ISBN 0471532882
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 wellserved 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 selfcontained
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
Devroye.
Chapter 3 generalizes these results to mary 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 kd trees. The distribu
tions of random variables considered appear to be
identical to their binary search tree equivalents.
PAGE 5
rFi_
PAGE 6
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
chapters.
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).
 D.C. VAN LFITENHORST
Parametric Optimization:
Singularities,
Pathfollowing and Jumps
J. Guddat, F Guerra Vasquez and
H. Th. Jongen
Teubner and John Wiley & Sons
Chichester
1990
ISBN 0471928070
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 (AkademieVerlag, 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 multiobjective) 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 reallife 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 predictorcorrector 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 GarciaPalomares 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 coauthors.
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 socalled
I I I I.,, tI i, I. I ..., L r I, thechapterremindsthe
reader about general important facts, such as the
role of the MangasarianFromovitz 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.
~sl~
Numbgpi;J 1, i I i 1, 1
NOVEMBER 1992
NOVEMBER 1992
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 KarushKuhnTucker
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.
S. ZLOBEC
Handbooks in Operations
Research and
Management Science
Volume 2, Stochastic Models
Edited by D.P. Heyman and M.J.
Sobel
North Holland, Amsterdam
1990
ISBN 0444874739
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 nontechnical 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 calculusbased probabil
ity course and the rudiments of matrix algebra."
For example, the concept of conditional expecta
tion given a oalgebra 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
11).
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.
 L. MATTER
". ..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."
IIAGF 7
~
Numbe~iThirtyEight
NOVEMBER 1992
Structural Complexity
Theory
Vol. Iand Vol. II
EATCS Monographs on
Theoretical Computer Science, 11
and 22
J. L. Balcizar, J. Diaz and J.
Gabarr6
Springer Verlag
Berlin
1988 and 1990
ISBN 3540186220 (VOL. I)
ISBN 3540520791 (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
timization.
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 timebounded 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 nondetermin
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
NPcompleteness.
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 NPcompleteness, 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 NPcomplete turn out to be even more simi
lar than what is expressed by the fact that they are
interreducible by polynomial time manyone 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 NPcomplete problems
in fact extends to all possible NPcomplete prob
lems. Having observed that this is a hardtoprove
conjecture (its truth would el, 1 i  ',, they set
out to disprove it by constructing an NPcomplete
problem which could not be isomorphic to a stan
dard NPcomplete problem like SATISFIABILITY,
on behalf of its structural properties. Thus the quest
for a sparse NPcomplete 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
Numt
PAGE 8
NOVEMBER 1992
Numb(
study into machine models and the combinatorial
study of characterizing their finite computations
in terms of circuit models or descriptive
complexity.
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 NPcomplete
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 wellknown 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: nonuniform 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 nonexistence of a sparse
complete set) can be found in Chapter 5. The struc
tu .,ri I t p r, i. ..t. 'Liin ,.,!. 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 nonexistence results on con
crete problems mentioned in the introduction of
this review.
The final chapters on resourcebounded
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 wellwritten 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 uptodate.
Thebooks are suitable for use in a graduate course,
but the course should include more recent mate
rial from journals and conference proceedings as
well.
P. VAN EMDE BOAS
PAGE 9
~
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: Cliqueweb
Inequalities."
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
Functions."
K. Yokoyama, "eC', "',"I,,t
Criteria for Convex Programming
1' ', N m Via Exact ,,, ii ;
Functions."
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
tion."
M.C. Ferris and A.B. Philpott,
"On Affine Scaling and Semi
Infinite! ,i'.,', ,m .."
CONTINUED
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
KTH.
A conference in LargeScale Optimi
zation, hosted by Hager, Hearn and
Pardalos willbeheld Feb. 1517,1993,
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
ORSA.
&GEORGIA TECH
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
Pandit.
The research of this Center focuses on
largescale 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
problems.
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.
"
PAGE 10
Number ThirtyEight
NOVEMBER 1992
III
MPS
Nordic Section
E P 0 R
The Nordic Section of MPS held its second biannual
meeting in Trondheim, Norway, Aug. 1416, 1992.
Twentyseven 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 199394 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 email to mps@iok.unit.no (auto
matic redistribution). The leader of the section can be
reached via mpsrequest@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.
STEIN W. WALLACE
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 email to
a ndre@src.umd.edu.
The main enhancement is that FSQP now also handles nonlinear equality constraints.
"Semifeasibility" 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 'semifeasibility" is maintained (see above).
This is of value in many engineeringrelated problems. Extensive numerical tests show
that the efficiency of FSQP is comparable to that of the most popular (nonfeasible)
codes. A detailed User's Manual is available.
Application for cMembership
Mail to:
THE MATHEMATICAL PROGRAMMING SOCIETY, INC.
c/o International Statistical Institute
428 Prinses Beatrixlaan
2270 AZ Voorburg
The Netherlands
Cheques or money orders should be made payable to
THE MATHEMATICAL PROGRAMMING SOCIETY,
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 onehalf 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
NAME (PLEASE PRINT)
MAILING ADDRESS (PLEASE PRINT)
SIGNATURE
FACULTY VERIFYING STATUS
INSTITUTION
PAGE II
Number ThirtyEight
NOVEMBER 1992
OPTIMA
N 38 Nov 1992
Margaret Wright (AT&T Bell Labs) has been
reelected 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 1216, 1993, is April 1, 1993.
1ADMOD93, a Symposium on Applied
Mathematical Programming and Modeling,
will be held in Budapest, Jan. 68,1993. Chair
man is IstvAn Maros. It will be preceded by a
oneday Workshop on Interior Point Meth
ods. Contact the Secretariat, email:
hl(i'.lo i, 1,, II... IEmail 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
Netherlands
Journal contents are subject
to change by the publisher.
Donald W. Hearn, EDITOR
Dolf Talman, ASSOCIATE EDITOR
PUBLISHED BY THE MATHEMATICAL
PROGRAMMING SOCIETY AND
PUBLICATION SERVICES OF THE
COLLEGE OF ENGINEERING,
UNIVERSITY OF FLORIDA.
Elsa Drake, DESIGNER
P T I M A
MATHEMATICAL PROGRAMMING SOCIETY
303 WeilHall
College ofEngineering
University of Florida
Gainesville FL 326112083 USA
FIRST CLASS MAIL
818111~~
