Title: Optima
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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: July 1994
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Bibliographic ID: UF00090046
Volume ID: VID00043
Source Institution: University of Florida
Holding Location: University of Florida
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PTIMA
MATHEMAT PROGRAM A
MATHEMATICAL PROGRAMMING SOCIETY NEWSLETTER


After three meetings,
the IPCO (Integer
Programming and
Combinatorial Optimi-
zation) coiiJlre'iccs are
establishing themselves
as important events for
the integer program-
ming community. The
following article de-
scribes the meetings.


No
43
July
1994


Fourth IPCO Conference


Copenhagen, 1995
A callforpapers currently is beingdistributed.
PAGE THREE )


History and

Scope of IPCO
BY KAREN AARDAL, RAVI KANNAN AND WILLIAM R. PULLEYBLANK

There are two key features of the IPCO conferences: FIRST, there are
no invited talks; instead, a program committee selects the contribu-
tions on the basis of extended abstracts submitted by prospective par-
ticipants. SECOND, the papers at the meeting are presented in a single
stream (no parallel sessions), and preliminary versions of all papers
are provided to participants at the time of the meeting.
PAGE TWO )


conference notes
journals
book reviews
gallimaufry


4
6
7-10
11






lA, N 3JUY19


The format of IPCO, although
new to our community, has been
used by computer scientists for many
years. It was the STOC and FOCS
meetings, organized by ACM and
IEEE, that gave Ravi Kannan and
. .! I.. .. I ,1.1 I. the idea to pro-
pose a conference with this format.
They presented their idea to the
Mathematical Programming Society
in 1987, and the Society responded
positively and agreed to be an .1,... I
sponsor. The first IPCO conference
took place May 28-30, 1990, at the
University of Waterloo, Canada, or-
ganized by Kannan and Pulleyblank.
The following two meetings were
held at Carnegie- I..11.... University
May 25-27, 1992, organized by
Kannan, Egon Balas and Gerard
Cornuejols, and at Centro Ettore
Majorana in Erice, Italy, from April
20 to May 1, 1993, organized by
Laurence Wolsey and Giovanni
Rinaldi. The meetings are held every
year in which no International Sym-
posium on Mathematical Program-
ming takes place, which means the
next ones will be held in the spring of
1995 and 1996. The location and
dates are Copenhagen, May 29-31,
1995, with Balas, Jens Clausen and
J6rgen Tind as organizers, and
Vancouver, probably in the week of
June 3, 1996, organized by ,lli h,
Cunningham and Maurice
Queyranne. More information about
the Copenhagen conference is pre-
sented on Page 3.
The two themes integer program-
ming and combinatorial optimization
- are viewed in a broad sense, to in-
clude algorithmic and structural re-
sults in topics such as geometry of
numbers, graph theory, matroids and
submodular functions, in addition to


more traditional fields. IPCO is not
restricted to theory. Computational
and practical work belongs to our
field, ,,.1 ; n,;. ,i, contributions
involving implementations and appli-
cations are most welcome.
The main acceptance criteria used by
the program committee are the qual-
ity and originality of the research,
plus its interest to people working in
the field. These acceptance criteria
have made it possible for younger,
less established researchers to present
their results in an attractive format to
a large audience of active researchers.
In the first three meetings, a substan-
tial portion of the presentations were
given by graduate students and recent
Ph.D. graduates, which is a sign of
vitality in the field.
For the first three meetings, there
were 76, 74 and 83 submissions, re-
spectively. In each case, approxi-
mately 35 were selected for
presentation.
Submission deadlines for IPCO con-
ferences have been in the late fall of
the year preceding the meeting. The
submissions are in the form of ex-
tended abstracts of at most 10 pages.
All submissions are read by the pro-
gram committee and the decisions re-
garding which papers .11 be included
in the meeting are made within about
two months.
The program committee normally
consists of established researchers
from a broad variety of fields. There-
fore, someone preparing an extended
abstract can safely assume that a large
portion of the committee will not be
experts in the topic of the paper.
These are precisely the readers to
whom the abstract should be di-
rected. Of course, correctness and
newness of the claimed results is nec-


essary, but this alone o I 11 is not
sufficient. It also is crucial that the
importance of the work be under-
stood by the committee.
Authors of accepted papers are asked
to submit a final version, which may
again be an extended abstract or a full
paper. These are printed in the Pro-
ceedings, which are provided to all
participants at the conference. These
I',..-....Jd, serve as a conference
record as well as a means of rapid dis-
semination of results, since they are
published within about six months of
submission. Most journals, including
Mathematical?.. .... '... do not
view publication of an early version
of a paper in an IPCO Proceedings as
a prior publication, which could
make the paper unacceptable.
The tight timing constraint places a
heavy demand on the Program Com-
mittee members. It is appropriate
here to remind authors that the sub-
mission of an extended abstract con-
stitutes a commitment that if the pa-
per is accepted, -I..;, il provide a
Proceedings version, and at least one
of the authors will be present at the
conference to present the paper. At
two of the three IPCOs so far, it has
been possible to provide very limited
support for some participants who
need it. This may or may not be pos-
sible at future meetings.
Presentations at the conference are 30
minutes in length. Similar guidelines
apply to them as to the extended ab-
stracts: It is generally neither neces-
sary nor desirable that presentations
give full proofs or justifications (the
proceedings serve this purpose bet-
ter); they should convey the main re-
sults, an idea of why they are true and
their relevance. -


I ~ ~


N? 43


PAGE 2


JULY 1994






~A~t 3 No43 JULY199


Fourth IPCO

Conference,

Copenhagen,

1995

By J6rgen Tind, University of
Copenhagen


S' t I ..... .I ,metotellyoualittle
about the local community surrounding
the next IPCO conference to be held in
Copenhagen May 29-31, 1995.
The scope of IPCO is integer program-
ming and combinatorial optimization. So,
. i. ,, i ,1 , .. .,, J 1 .1 ,- I .- ... -
ing to the chosen themes. However, these
two disciplines are only a part of the entire
optimization area. In fact, the area as such
contains many examples of rich interaction
between continuous and discrete optimi-
zation and receives a lot of valuable input
from, for instance, computer science and
mathematics.
This observation is from a scientific point
of view but also applies when it comes to
the role ofthe local environmentsurround-
ing the IPCO in Copenhagen. Here, it is
natural to mention the schools, where op-
timization in general plays a major role,
and names ofsenior people in some depart-
ments. This is done with no attempt to
generate a complete list of schools or
names, so please take the names mentioned
just as a kind of address for their institu-
tions.
Probably the Technical University of
Denmark has the largest tradition. Re-
cently, some of the optimization activities
have merged andcreated anew department
called the Institute for Mathematical
Modeling. This rather unusual name is
the result of a compromise, and it might
change later. This institute has research ac-
tivities in nonlinear optimization and in
model and algorithm development for a
range of optimization problems (Soeren
Kruse Jacobsen, Kaj Madsen, Oli B.G.
Madsen and R.Victor V. Vidal). In addi-
tion, at the Institute of Mathematics there
is activity around optimization and graph
theory (Martin Bendsoe, Carsten
Thomassen). Since those institutes are
located in an engineering school, the re-
search has close links to problems in engi-


, 1:1 ,; ,. 1 I I. I I" . i. I. d e al
with planning and development in general.
The University of Copenhagen has two
departments with activities in optimiza-
tion. The Department of Computer Sci-
ence has projects dealing with develop-
ment and testing of I_ .,' 1.. to solve
problems in combinatorial optimization
(Jens Clausen, Jakob Krarup and Pawel
Winter). Recently, optimization activities
have started at the Institute ofMathemat-
ic s ' I -,, I ,, ... ... ... ; -
ematics and economics that is very popu-
lar and has attracted many students. (Re-
cently I moved from the University of
Aarhus, where a similar program has ex-
isted for 25 years, to Copenhagen to take
part in this development.)
Since IPCO is in the frame of the Math-
ematical ..' .. i. _, Society, I should
mention the Nordic section ofMPS. A
series of Nordic symposia on mathemati-
cal programming has taken place. The
latest one was held May 8-10, 1994, in
Linkoping, Sweden, organized by Kaj
Holmberg, University of Linkoping, and
Stein Wallace, University of'Trondheim.
The purpose was to discuss research
projects linking togetheraspects ofinteger
and stochastic programming.
With this background, the IPCO confer-
. .n ,{{ .. . . I{,{ .. q,,i .., , . e s
from our local community to create a nice
conference in cooperation with the inter-
national program committee. We also shall
do our best for you to enjoy all other aspects
of Copenhagen. The springtime in
( ..[ .-. I ,_ .. I ... . I 1 1i. w ith aw health of
activities to enjoy inside and outside the
city and conference ...,i.li,, at the sea,
in restaurants and, of course, in Tivoli. See
you in Copenhagen.


uted. M embers oftl]. ..i..............
are: E. Balas, Carnegie-Mellon University
(chair); R. Burkard, Graz Technical Uni-


versity; V. Chvatal, i .11 University,
Montreal; J. Clausen, University of
Copenhagen; M. Fischetti, University of
Padova;W. Pulleyblank, IBMT.J. Watson
Research Center; J. Tind, University of
Copenhagen; and C. Tomassen, Techni-
cal University of Denmark.
The organizers are Jens Clausen and
Jorgen Tind, University of
Copenhagen.
Send inquiries to:
Jens Clausen
DIKU
Universitetsparken 1
DK-2100 Copenhagen 0
Denmark
e-mail: clausen@diku.dk
FAX: +45 35 32 14 01


The deadline for submis-
sion of extended abstracts
of papers is Oct. 31, 1994.


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


N? 43


JULY1994


PAGE 3





PI'll N 4J Y 9


Council

J\] LAB W


New Editors

Selected
The Mathematical Program-
ming Society Executive Com-
mittee met in Atlanta on Feb.
10, 1994, to recommend new
editors for society publications.
The full Council subsequently
approved the choices.
Don Goldfarb (Columbia Uni-
versity, New York) has been ap-
pointed to a three-year term as
Editor of Mathematical Pro-
gramming Series A, starting
Aug. 15, 1994. Goldfarb replaces
Bob Bixby of Rice University,
Houston, TX.


L 1 11V


CE


John Birge (University of Mich-
igan, Ann Arbor) has been ap-
pointed to a three-year term as
Editor of Mathematical Pro-
gramming Series B, starting
Aug. 15, 1994. Birge replaces
William Pulleyblank of the IBM
T.J. Watson Research Center.



New Nordic
Section Leaders
Elected
The Nordic Section of the Math-
ematical Programming Society held
its third meeting in Link6ping Feb.
11-13, 1994. About 25 people took
part, coming from Norway, Sweden,
Denmark and Iceland, plus Spain
Portugal and Germany. The new
group of leaders selected are:
Kaj Holmberg (Link6ping,
Sweden, leader)
kahol@math.liu.se
Kim Allan Andersen (Aarhus,
Denmark) kim@mi. aau dk
Dag Haugland (Stavanger,
Norway) -. no
It also was decided to run the fourth
meeting of Nordic MPS in Aarhus
in 1996, with Kim Allan Andersen
as the main organizer.


FORTHCOMING CONFERENCES

iL,- d'iL ,r ,,!ilidplr 'l I hefollowing conferences have been set:

'The XVI International Sym-
posium on Mathematical Pro-
gramming will be held in
Lausanne, Switzerland, in
August 1997. Tom Liebling
will chair the Organization
Committee. Dominique de
Werra will chair the Interna-
tional Program Committee.
IThe Fourth Conference on
Integer Programming and
Combinatorial Optimization
will be held in Copenhagen,
Denmark, on May 29-31,
1995. Jens Clausen and
JSrgen Tind will chair the
Organization Committee,
and Egon Balas will chair
the Program Committee.
t The Fifth Conference on Inte-
S ger Programming and Combi-
natorial Optimization will be
Held in Vancouver, Canada,
in early June 1996. Maurice
i :Queyranne will chair the Or-
ganization Committee and
, Bill Cunningham will chair
the Program Committee.


PAGE 4


N"43


JULY 1994





Ik"ri 5 N0 43 juiyl99d


0
in honor of the outstanding
contributions of James Hardy
1il. 1.. ...i to the field of numeri-
cal software, Argonne National
Laboratory, the National I'ii. .. i
Laboratory and the Numerical
Algorithms Group award a nu-
merical software prize of US
$1,000. The first prize was
awarded at the International
Conference in Industrial and Ap-
plied Mathematics (ICIAM 91)
to Linda Petzold for DASSL. The
second prize will be awarded at
ICIAM 95 in Hamburg, Ger-
many, July 3-7, 1995.




Humbolt Scholarships,

Fellowships Offered
The Alexander von Humbolt Foundation of Bonn, Germany, promotes in-
ternational scholarly cooperation through research and supporting activities.
Since 1953, the Foundation has enabled more than 3,000 highly qualified
individuals from the United States to participate in collaborative research
projects conducted in Germany. The Foundation's North American Office in
Washington, DC, provides information on collaborative research opportuni-
ties to American scholars. The Foundation is offering numerous programs and
awards to promote this cooperative research.
For more information about the Alexander von Humbolt Foundation and its
programs, please contact Bernard Stein, the Alexander von Humbolt Foun-
dation, Suite 903,1350 Connecticut Ave., NW, Washington, DC 20036;Tel:
(202) 296-2990; Fax: (202) 833-8514.


Wilkinson




Ia
SRfl


reliability, ... I ..... and usability of
the software implementation; depth
of analysis of the algorithm and the
software; importance of application
addressed in the software; and qual-
ity of the test software.


for Numerical Sofiware Software can be submitted on 3.5-
Sinch high-density (1.44 MB) dis-


Rules for Submission
Each author of an entry must be
under 40 years old on Jan. 1, 1995.
Each entry must contain the follow-
ing: A Software written in a widely
available, high-level programming
language. A A paper describing the
algorithm and the software imple-
mentation. The paper should give
an analysis of the algorithm and in-
dicate any special programming
features. A Documentation of the
software, which describes its purpose
and method of use. A Examples of
use of the software, including a test
program and data. A A one- or two-
page summary of the main features
of the algorithm and software
implementation.
Submissions must be in English. En-
tries must be received by Nov. 1, 1994.
The awards will be made to the en-
try that best addresses all phases of
the preparation of high-quality nu-
merical software, including clarity of
the paper and software implementa-
tion and documentation; portability,


kettes, one-quarter cartridge tape
(60 MB or 150 MB), 8mm cartridge
tape (2GB), or sent by e-mail. Sub-
missions should be in the form of a
tar archive with a ,''. I.' '. tl 1. de-
scribing the contents of the archive.
Makefiles for executing test pro-
grams must be included. Submis-
sions can be sent by e-mail to
wilkinsonprize@mcs. anl. gov,
or to the Board of Trustees,
. 11 ... .. Prize for Numerical
Software, at one of the following
two addresses.
Argonne National Laboratory
Mathematics and Computer
Science Division
9700 S. Cass Ave.
Argonne, IL 60439
United States
Numerical Algorithms Group Ltd.
Wilkinson House
Jordan Hill Road
Oxford, OX2 8DR
United Kingdom


---


JULY1994


No 43


I'AGiE 5





PAGL 6 N4i43 JULY 1994


Contents ofMathematical Programming





Vol. 64, No. 1


Vol. 63, No. 2

Richard H. Byrd, Jorge Nocedal
and Robert B. Schnabel, i\h I.'-
sentations of quasi-Newton matri-
ces and their use in limited
memory methods."
Michel X. Goemans, "The
Steiner tree polytope and related
polyhedra."
F. Margot, A. Prodon and
Th.M. Liebling, "Tree polytope
on 2-trees."
Aharon Ben-Tal, Gideon Eiger
and Vladimir Gershovitz, "Glo-
bal minimization by reducing the
duality gap."
Ry6hei Nozawa, "Examples of
max-flow and min-cut problems
with duality gaps in continuous
networks."
Hans Kremers and Dolf
Talman, "A new pivoting algo-
rithm for the linear
I 1, I i r,, i problem allowing
for an i ;t ,i,!, starting point."


Martin Dyer and Alan Frieze,
' i ,i:, .. walks, totally
unimodular matrices and a
randomised dual simplex algo-
rithm."
Gerald G. Brown and Michael
P. Olson, "Dynamic factorization
in large-scale optimization."
Torbj6rn Larsson and Michael
Patriksson, "A class of gap func-
tions for variational inequalities."
Gong Chen and Marc Teboulle,
"A proximal-based decomposition
method for convex minimization
problems."
Yang Dai and Yoshitsugu
Yamamoto, "A continuous defor-
mation algorithm for variational
1i, j,',l,ir, problems on polytopes."


Vol. 64, No. 2

Renato D.C. Monteiro, "A glo-
bally convergent primal-dual inte-
rior point il- .., I il., for convex
programming."
Alfredo N. lusem and B.F.
Svaiter, "A row-action method for
convex programming."
Gregory E. Coxson, "The P-ma-
trix problem is co-NP-complete."
Jean Mercenier and Phillippe
Michel, "A criterion for time ag-
gregation in intertemporal dy-
namic models."


Ali Ridha Mahjoub, "Two-edge
connected spanning subgraphs and
polyhedra."
Sunil Chopra and M.R. Rao,
"The Steiner tree problem I: For-
mulations, compositions and exten-
sion of facets."
Sunil Chopra and M.R. Rao,
"The Steiner tree problem II: Prop-
erties and classes of facets."


Vol. 64, No. 3

M. Heinkenschloss, "On the so-
lution of a !..-.- I,.;/l trust region
subproblem."
LiqunQi, ',,,1,,. I, t i.,-l conver-
gent approximate Netwon methods
for LC' optimization subproblems."
F.B. Shepherd, "Near-perfect ma-
trices."
Edith Cohen and Nimrod
Megiddo, "New ii ..', i, -: for
generalized network flows."
Rachelle S. Klein, Hanan Luss
and Uriel G. Rothblum, "Relax-
ation-based ii ..l ibi' for mini-
max optimization problems with
resource allocation applications."
Komei Fukuda and Makoto
Namiki, "On extremal behaviors
of Murty's least index method."


I- ~-------~-~


N 43


JULY 1994


PAGE 6




PAGE 7 NQ 43





,----- -__






R E V I E W S


















Nonlinear Programming: Theory

andAlgorithms
by M.S. Bazaraa, H.D. Sherali and C.M. Shetty
Interscience Series in Discrete Mathematics
and Optimization
John Wiley, Chichester, 1993
ISBN 0-471-599973-5

This book deals with topics on the foundation of optimization and computational
methods for nonlinear programming. This second edition contains new material.
It consists of 11 chapters, two appendices, a subject index and a bibliography. Each
chapter begins with an outline and terminates with extensive exercises, notes and
references. The path to be followed is discussed in the preface.
C chapter l, "Introduction," ........ .. l .. 1 ...1 1. =. ......- I,,; ... .. .. t .
some interesting real-life examples taken from different 'r. r.. '. disciplines.
Chapters 2 and 3 cover the topics of "convex sets" and "convex functions and
generalizations." As applications, Chapter 2 also reviews the I ..1. r 1 simplex
and other related methods for linear programming. Chapter 4 derives "The Fritz
John and the Karush-Kuhn-Tucker Optimality Conditions" for inequality and
equality-constrained problems, while Chapter 5, "Constraint Qualifications,"
develops the latter conditions directly without first deriving the former ones. Sec-
ond-order necessary and sufficient conditions also are derived.
Chapter 6 deals with "Lagrangian Duality and Saddle Point Optimality Condi-
tions" and briefly discusses linear and quadratic programs. Chapter 7 studies "The
ConceptofanAlgorithm ."Ui,,.. i, r n. r. i. ,i t.prl I l' ...''. .I .i. I. ..I I. pr. i
8. This chapter contains theoretical background and standard techniques such
as line search and trust region methods, Newton and quasi-Newton methods, and
conjugate direction methods. It also studies a subgradient method for nonsmooth
optimization.


jui.Y1994


_I Ib~




PAGE 8 N 43 JULY I 14


"...throughout the book,

the authors have success-

fully attempted to ensure

that relevant material is

illustrated by many

interesting examples,

graphs and extensive

exercises."


Chapters 9, 10 and I are, respectively, devoted to "Penalty and Barrier Functions,"
"Methods of Feasible Directions" and "Linear Complementary, Quadratic, Sepa-
rable, Fractional and Geometric Programming Problems." Methods for linear pro-
gramming also are discussed on the basis of the material in Chapters 9 and 10.
Appendix A (11 pages) provides some basic definitions and mathematical concepts
(related to vectors, matrices and real analysis), which frequently are used in the book.
Since several definitions and results were introduced in the text, the authors have
provided Appendix B (I I pages), which gives a summary of the relevant results on
convexity, optimality conditions and duality.
It would have been nice if the book also had an appendix containing a summary of the
notations used in the book. However, throughout the book, the authors have success-
fully attempted to ensure that relevant material is illustrated by many interesting
examples, graphs and extensive exercises. The exercises also aim to extend, material already
covered and explore new areas. For example, the well-known symmetric rank one
updating formulawas covered in an exercise. In some cases the exercises were useful
for mini-research projects, while in other cases the objective within the questions is to
provide algorithms. The book provides an impressive 50-page bibliography contain-
ingmore than 1,200 entries, which allows one to pursue special material in the original
papers. However, there are many citation misprints. With the exception of the mis-
prints, the book is quite clean of typos and errors.
As a final analysis, the book is well written and contributes significantly to its field.
It is highly recommended as a text for students and practitioners of fields related to
optimization techniques. It also is very useful as a reference for researchers in non-
linear programming.
-BY M. AL-BAALI


Proceedings of the Fifth SIAM Conference

on Parallel Processing for Scientific

Computing
J. Dongarra et al., eds.
SIAM, Philadelphia, PA, 1992
ISBN 0-89871-303-X
These excellent proceedings give wide coverage ofthe maturing area ofparallel pro-
cessing. They are divided into six sections: Matrix Computations, 22 papers spread
over Dense Linear Algebra, Sparse Direct Methods and Iterative Methods; Nonlin-
ear Equations and Optimization, nine papers; Differential Equations, 13 papers;
Applications, Modeling and Simulations, 15 papers spread over Biology, Reservoir
Simulation, and Simulation and Modeling; Performance Evaluation and Software
Tools, 31 papers spread over Performance, Parallel Software Development Tools,
ProgrammingEnvironments and NovelArchitectures; and Mathematical Software,
four papers.
As the proceedings of a specialist conference, the papers are definitely not for begin-
ners in parallel processing, as authors use terms such as BIAS and GMRES without
explanation or reference. On the other hand, most papers, though short, are clearly
written. Many have small examples and/or pseudocode. In many of the papers in
dte Matrix Computations section, the area with which I am most familiar, there is
sufficient algorithmic detail to enable the reader to implement an efficient algorithm
based on the ideas in the papers.


t




PAGE 9 NW 43 juIYl 994


Virtually all papers give numerical results. Many compared several approaches to a
problem implemented on the same machine, or alternatively, the same algorithm
or problem implemented on different machines. Both SIMD and MIMD architec-
tures are discussed and include machines with small numbers of processors, typically
the iPSC/860 arrays of transputers, some of which were quite large, more interme-
diate machines such as the nCUBE2, massivelyparallel machines, ofwhich the CM2
seems to be the most popular, and large vector machines such as the CRAYsand IBM
3090s. A number of heterogeneous networks and special-purpose architectures are
described. Almost all codes were written in FORTRAN, sometimes with parallel
additions. Now that the field ismaturing, there is an interesrin portability, andseveral
metalanguages were proposed.
The onlyuniversalconclusionwas that for the CM2, slicewise processing (using 64-
bit chips as the basic unit) gave better performance than fieldwise (single-bit pro-
cessors as the basic unit). A number of papers showed that a MIMD machine with
a modest number of processors (up to 128) or a CM2 could give equivalent perfor-
mance to a CRAY Y-MP. Just as many papers still favored the large vector
supercomputers over other architectures. It was obvious that performance on any
machine still is very much a function of the problem type, the parallelization algo-
rithms used and experience with a particular architecture.
Almost all papers were written in TeX, which gave a somewhat more uniform ap-
pearance to the volume than is often the case with proceedings. However, editing
would have reduced the authors' errors. Particularly for the type of work described
here, readerswould appreciate an e-mail address for each paper. An index ofall authors
also would, have been helpful.
There is a wealth of useful material here. The book would be a valuable addition to
the shelves of any group involved in parallel processing. For anyone wishing to enter
the field, it would, with some background reading, provide an excellent overview.
Unfortunately, as with all such proceedings, some of the material already is dated.
However, the implementarionderails and problems encounteredstill would be most
useful to anyone cackling a new area, architecture or machine.


This book gave me many stimulating ideas for my own work. I think it would do
so for others. It also is an excellent advertisement for future SIAM Conferences on
Parallel Processing.
- BY JENNY EDWARDS

Spline Functions and Multivariate

Interpolations
by B.D. Bojanov, H.A. Hakopian and A.A. Sahaldan
Kluwer Academic Publishers, Dordrecht,
The Netherlands, 1993
ISBN 0-7923-2229-0
Spline theory is a rich subject. With the benefit ofhindsight, one can find pieces of
it in papers hundreds of years old and older. One also can give an introduction to
it from many different points of view.
By all appearances, the present book serves two masters. Chapters 1-8 give a careful
introduction to splines ofone variable, with special emphasis on the topics to which
the first author has significantly contributed, such as various extremal problems for
which splines (monosplines, perfect splines and natural splines) are solutions. Also,
periodic splines get detailed treatment. Chapters 9-14 provide a view of splines of
several arguments, with special emphasis on the topics to which the second and also
the third author have contributed significantly, such as variants of Kergin interpo-


"There is a wealth of

useful material here.

The book would be a

valuable addition to the

shelves of any group

involved in parallel

processing. For anyone

wishing to enter the

field, it would ... provide

an excellent overview

of the field."


I




PAGE 10


clarion and other multivariate polynomial interpolation schemes including inter-
polation to data given on hyperplanes, and also the approximation from spaces
spanned by the integer translates of a so-called box spline.
The expert is delighted to have so readily available, in one volume, this careful pre-
sentation of recent results by the authors together with a careful telling of all the
background needed. The Western expert can pick up useful clues to the Eastern
European literature on splines.
The chapter headings are: 1. Interpolation by algebraic polynomials; 2. The space
ofsplines; 3. B-splines; 4. Interpolation by spline functions; 5. Natural spline func-
tions; 6. Perfectsplines; 7. Monosplines; 8. Periodicsplines; 9 Multivariate B-splines


Enhanced Nonlinear Programming Code Available
The CFSQP optimization software (C code) has just undergone a major upgrade (the
new feature is not available in FORTRAN FSQP). The newversion, CFSQP 2.0, in-
cludes a new scheme to efficiently handle problems with many sequentially related
objectives or constraints (e.g., discretized versions of continuous minimax problems
orofproblems involving a continuumofconstraints- i.e. ofsemi-infinite problems).
FSQP(Feasible SQP; FORTRAN; developed byJ.L. Zhou and A.L. Tits at the In-
stitute for Systems Research, University of Maryland, College Park) and CFSQP (C
version of same with enhancements; port and enhancements due to C.T. Lawrence,
also with the ISR) are software packages aimed at solving constrained optimization
problems, including constrained minimax problems (where the max is taken over a
finite number of smooth functions).
(C)FSQP's main distinguishing feature is that all the iterates it generates satisfy the
constraints, except for nonlinear equality constraints, for which mere "semi-fasibil-
ity" is maintained (given a scalar constraint h(x)=0, if h(x0)<=0 (resp. >=0), then
h(xk)<=0 (resp. >=0) for all k). This is ofvalue in manyengineering-related problems.
Extensive numerical testsshow that (C)FSQP's efficiency is comparable to that of the
most popular (non-"feasible") codes. Detailed User's Manuals are available.
(C)FSQP is available free of charge to academic and other non-profit organizations
(as well as, for an evaluation period, to for-profit organizations), but may not be re-
distributed without the authors' approval. To obtain FSQP or CFSQP, please con-
tact Andre Tits (andre@eng umd. edu).


and truncated powers; 10. Multivariare
spline functions and divided differences;
11. Box splines; 12. Multivariate mean
value interpolation; 13. Multivariate
polynomial interpolations rising by hy-
perplanes; and 14. Multivariate
pointwise interpolation.
The noveltyofthe material covered is in-
dicated by the fact that Chapter 13 is, in
essence, a paper thatwill appear in print
sometime in 1994.
The spelling of names from the West-
ern literature shows the effect of filter-
ing through some other language and al-
phabet. Thus Birkhoff and Dahmen
both often appearwithout their "h." The
fact that English is not the native tongue
of the writers expresses itself in the oc-
casional misprint. (My favorite was the
"unite cub.")
My only real complaint about the book
is that the index is only two pages long.
-BY CARL DE BOOR


"The expert is delighted

to have so readily

available, in one vol-

ume, this carefu presen-

tation of recent results

by the authors together

with a careful -lling of

all the background

needed. The Western

expert can pick up

useful clues to the

Eastern European

literature on splines."


N' 43


JULY 1994




PAGE 1 I N 43 JULY1 994

I laLnlLIL I


O P T I M A
N 43 Juy1994
OPTIMA has received a 1993
President's Award for Publication
Excellence from the University of
Florida. Congratulations to Designer
Elsa Drake and Assistant Editor
Richard Jones for this much deserved
recognition of their fine work. The
17th IFIPTC7 Conference on System
Modelling and Optimization will be
held July 10-14, 1995 in Prague.
Contact the secretariat via phone +42
6641-4554, fax: +42 2 6641-4903, or
e-mail: ifip@utia.cas. cz.
IDeadline for the next OPTIMA is
October 1, 1994.


Books for review should be
sent to the Book Reviezo 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.
Richard Jones, ASSISTANT EDITOR
Elsa Drake, DESIGNER


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