P
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No32
MATHEMATICAL PROGRAMMING SOCIETY NEWSLETTER March 1991
'0
Beyond the bounds of
the conference, visitors
will be rewarded by
a sampling from
Amsterdam's over
flowing agenda.
Tls YEAR'S International Symposium on Mathematical
Programming is being held in Amsterdam, the capital
of the Netherlands. The meeting runs from August 5 to
9,1991 and is being jointly organized by CWI, the University of
Amsterdam, Eindhoven University of Technology, Erasmus
University Rotterdam, Free University Amsterdam, and
Tilburg University.
The opening session is on Monday August 5 at 10 a.m. Here
the Mathematical Programming Society will award the
Fulkerson Prizes for outstanding papers in discrete mathemat
ics (jointly with AMS), the George B. Dantzig Prize for original
research with a major impact on mathematical programming
(jointly with SIAM), the BealeOrchardHayes Prize for
excellence in computational mathematical programming, and
the A.W. Tucker Prize for an outstanding paper by a student.
The session will be completed with a plenary opening address
by W.R. Pulleyblank (Yorktown Heights/Waterloo).
The remainder of the meeting is comprised of invited onehour
lectures as well as invited and contributed thirtyminute
presentations. These will focus on theoretical, computational
and practical aspects of mathematical programming. The
committee has selected June 1, 1991 as the deadline for
submission of abstracts so as to facilitate the presentation of
current and ongoing research. In addition, there will be two
special sessions in memory of Robert G. Jeroslow and Darwin
Klingman.
The series of invited onehour lectures will include E.H.L.
Aarts (Eindhoven), R.E. Bixby (Houston), V. Chvytal (New
Brunswick), A.R. Conn (Yorktown Heights/Waterloo), T.M.
Cook (Dallas), J.E. Dennis, Jr. (Houston), C.C. Gonzaga (Rio de
Janeiro), M. Gr6tschel (Augsburg), R.M. Karp (Berkeley), A.V.
Karzanov (Moscow), K. Kennedy (Houston), LG. Khachiyan
(Moscow/New Brunswick), C. Lemar&chal (Rocquencourt),
C.H. Papadimitriou (San Diego), D.E Shanno (New
Brunswick), and R.E. Tarjan (Princeton).
The official activities of the symposium take place in the heart
of the city and thus enjoy as a backdrop the charm of its canals.
Although the first settlements in Amsterdam date back to the
13th century, most of the early (wood) buildings have been
CONTINUES, PAGE TWO
w Nominations
 invited for
0 1991Elections
The Constitution of the Mathematical
Programming Society sets the term of
office for all officers of the Society at
three years. Elections for all offices
(Chairman, Treasurer, and four atlarge
members of the Council) are to be held
four months prior to each triennial
International Symposium. The four
teenth Symposium will be held in
Amsterdam, August 59,1991, so the
next election will be held in April 1991.
The new membersatlarge of the
Council will take office at the time of
the Symposium, while the Chairman
elect and Treasurerelect will take office
one year later. CONTINUES, PAGE TWO
Ih P T I MA
ISH NUMBER 32
ON NOTATION FOR
QUASINEWTON METHODS 3
CONFERENCE NOTES 5
TR&WP 6
BOOK REVIEWS 89
JOURNALS 10
GALLIMAUFRY 12
~ ~ ~
P 2nmbethrytw MARCH9
Amsterdam 1991
CONTINUED
destroyed by fire. What exists
now is a living museum of well
preserved 17th century architec
ture. This period of Dutch history
was known as the Golden Age
and witnessed the growing
importance of Amsterdam as a
center of international trade. The
best mode of sightseeing is the
stroll. Though firsttime visitors
can easily become lost (the streets
and canals shift between polar
and rectangular coordinates), this
can also provide an interesting
strategy for getting to know the
environment. Along with being
home to much of the business
sector, the center also houses
300,000 inhabitants, and
Amsterdam is rare in that first
level dwellers are eager to give
the passerby a glimpse of their
residences. A different perspec
tive of the city is gained from one
of the several boat tours (includ
ing an evening dinner cruise). The
boats meander through the canals
while a guide divulges an
impressive amount of information
in a handful of languages.
The Symposium, apart from the
lectures themselves, has always
been a time for informal discus
sions amongst colleagues and
potentially for beginning new
research directions. The meeting
rooms of Amsterdam are its caf6s
and pubs, varying from the
intimate twotable Belgian
caf6 to the art deco splendor of
Caf6 Americain. The facilities are
extensiveapproximately one
establishment to each participant.
There is also an admirable
selection of restaurants for the
evening meal. Depending on the
mood, dinner may be the
traditional Indonesian rijsttafel,
French cuisine served in a post
moder atmosphere, or a meal at
one of several vegetarian
restaurants.
Beyond the bounds of the
conference, visitors will be
rewarded by sampling from
Amsterdam's overflowing
agenda. Possibilities range from
the chaotic Waterlooplein flea
market to the English theater or
an evening in arguably the
world's most famous concert hall,
the Concertgebouw. Jazz aficiona
dos will also not be disappointed,
with a variety of venues that
includes the reputed Bimhuis
which has hosted such greats as
Charles Mingus and Dexter
Gordon. This is not to imply that
pop, reggae, African, salsa or
blues are overlooked. One need
only check the local paper De
Uitkrant for a list of performances,
many of which are free.
Amsterdammers are understand
ably proud of their many
museums, and a visit to the city
should at least include time to
enjoy the work of the Dutch
Masters in the Rijksmuseum
(home of Rembrandt's Night
watch) and the collection in the
Van Gogh Museum The
Rijksmuseum is also of interest in
that the works on display provide
a pictorial history of the streets
through which you will wander.
Today, the rich tradition of visual
art in the Netherlands is contin
ued by its many living artists,
whose work can be viewed in a
staggering abundance of small
galleries located throughout the
city. A high density of these is
found in the Kerkstraat and
Spiegelstraat where galleries are
interspersed with exclusive
antique shops.
For those extending their visit or
travelling with family, there are a
number of worthwhile day trips
near Amsterdam. Destinations
include Delft, Gouda, the
medieval wall surrounding
Naarden, as well as the coast,
which is a thirtyminute journey
by train. Another popular outing is
to the Kr6llerMiiller museum. This
is located in a wildlife reserve
outside Arnhem and is well suited
to being explored as a biking and
picnic trip. The museum itself has a
fine collection of many styles; two
of the highlights are its sculpture
garden and Theo Van Gogh's
collection of his brother's work.
Flights to Amsterdam arrive at
Schiphol Airport. Taxis to the
center cost about fifty gulden, but
there are also frequent connections
to the Centraal Station using the
excellent national train system. The
train costs about five gulden and
takes approximately twenty
minutes; from Centraal Station one
may then take a taxi or tram, or
walk to the hotel. There is no need
for a car during the conference as
everything is within walking
distance.
R REGISTRATION MATERIAL FOR
THE CONFERENCE CAN BE OBTAINED
BY WRITING TO:
14th International Symposium on
Mathematical Programming
do NOVEP, Paulus Potterstraat 40
1071 Amsterdam, The Netherlands
Telephone +31206752120
fax +31206628136
email ismp@swi.psy.uva.n 1.
The deadline for early
registration is April 1.
Registration fees for members and
nonmembers are, respectively,
NLG 240 and NLG 300. These
increase by NLG 100 after the
deadline. The feesfor nonmembers
also include membership to the
Mathematical Programming
Society. Student fees are one half of
the above rates.
On behalfof the organizers, I
cordially invite you to attend the
Symposium. lam certain that the
participants willfind the meeting
productive and memorable.
BRUCE SHEPHERD
1991 Nominations
CONTINUED
It further states that the
Chairman is to invite nomina
tions. Candidates must be
members of the Society. They
may be proposed either by
Council or by any six members
of the Society. No proper
nomination may be refused,
provided the candidate agrees
to stand. The Chairman decides
the form of the ballot. It also
states that the Council shall
pass bylaws governing
elections designed to promote
international representation on
the Council.
Accordingly, the Council has
agreed to the following
procedure:
(1) Nomination to any office is to
be submitted to me by April 1,
1991.
Such nomination is to be supported
in writing by the nominator and at
least five other members of the
Society.
(2) In keeping with what seems to
have become a tradition, the
membership is asked to give
preference to nominees who are not
from North America.
(3) When the ballots are counted,
the four atlarge candidates for
Council receiving the highest
number of votes will be elected,
except that not more than two
members having permanent
residence in the same country may
be elected.
G. L. Nemhauser
Chairman 19891991
Department of Industrial and
Systems Engineering
Georgia Institute of Technology
Atlanta, GA 303320205, U.S.A.
Fax: 4048942301
_ ~ _I~ ~I~ _1_~ 111. ~~
MARCH 1991
I
PAGE 2
number thirtytwo
Some Comments on Notation for QuasiNewton Methods
W.C. Davidon," R.B. Mifflin and J.L. Nazareth'
Abstract
In this informal note, we propose a
notation and terminology for quasi
Newton methods for nonlinear
minimization. We do not intend that
our proposed notation be definitive.
Rather, our aim is to provide a starting
point for discussion by other researchers
in the field in the hope that a more
usable notation will evolve.
Introduction
A recent visit to Washington State Univer
sity by Bill Davidon provided the opportu
nity for us to discuss the conflicting and
sometimes confusing notation used to
describe quasiNewton methods for
nonlinear minimization. For example, the
symbol H is often used in the literature to
denote the true Hessian matrix of second
partial derivatives; at other times H is used
to denote a quasiNewton approximation to
the Hessian, and on yet other occasions it is
used to denote a quasiNewton approxima
tion to the inverse Hessian matrix. The
symbol B is used by many to denote a quasi
Newton approximation to the Hessian
matrix. This conflicts with H, and it also
seems inappropriate to use an unsymmetric
letter to denote a symmetric matrix. The
terminology of quasiNewton updates, for
example, DFPupdate, BFGSupdate, PSB
update, has grown haphazardly to the point
that Dennis and Schnabel [3] call it a form of
"alphabetsoup" in the preface of their book.
Various authors, for example, Dennis and
Tapia [4], Dennis and Schnabel [3], have
tried to propose remedies for this unfortu
nate state of affairs. However, since their
suggestions have not fully taken root, we
begin afresh. We do not intend for our
proposed notation to be definitive. Rather,
we hope to provide a starting point for
discussion in the hope that a more usable
notation will evolve. In order to better the
chances of acceptance, we have also focused
on a few items and not sought to be compre
hensive.
Proposed Terminology and
Notation
We suggest the term quasiNewton be used
as a generic name for the entire class of
methods that rely on the quasiNewton (or
secant) relation. The subset of methods for
which positive definite approximations to the
Hessian are made will be termed variable
metric methods, because they provide a
natural choice of preconditioner or metric.
When the approximations are permitted to
be indefinite, then the associated methods
will be called secant methods. Thus, variable
metric methods [2] are a subset of secant
methods, and, collectively, variable metric
and secant methods may be termed quasi
Newton methods.
Denote the step from the iterate x to the next
iterate x+ by s, i.e., s = x+ x. Denote the
gradients at the points x and x. of the
function f(x) being minimized by g and g.,
respectively. Denote the change of gradient
corresponding to the step s by y, i.e.,
y = +g g. Thus, for example, when the line
search that determines step s is exact, we
have g' s = 0.
Denote the approximation to the Hessian
matrix by M, and the approximation to the
inverse Hessian matrix by W. Note that M is
natural for Matrix and that the letter W is
close to the symbol M inverted. Also, both
M and W are symmetric letters, which is
appropriate, because they denote symmetric
matrices.
Define the three scalars,
a = s'Ms, b = yTs, c = yTWy. (1)
Assuming a, b and c are nonzero, define the
two vectors,
y Ms
m b a (2)
b a
s Wy
c
so that m's = 0 = wry.
Define the two matrices
MssTM yy
M+() = M M + (4)
a b
WyyTW ssT
W+()= W + (5)
c b
For each value of the parameters t and v,
define the Broyden [1] family of updates,
M,(u) = M+(O) + pa mmT, (6)
W,(v) = W(0) + vcwwT. (7)
Note that the matrices M.(p) and W+(v)
satisfy the quasiNewton equations
MK(A)s = y and W+(v)y = s for all values of p
and v.
The symbol m for the vector in (6) is very
natural in association with M and the
symbol p is Greek for 'm'. The symbol w for
the vector in (7) again goes naturally with
W. The letter v follows y in the Greek
alphabet and is, therefore, a natural and
easily remembered choice for the parameter
in the family of inverse updates (7). (So
many conflicting symbols have been used in
the literature for these two parameters that
we feel a fresh choice is required.)
Note that the BFGSupdate of M and W
yields M+(0) and W+(1), respectively, and
that the DFPupdate of M and W yields
M+(1) and WV(0), respectively. The foregoing
notation makes it possible to dispense
entirely with names that are mainly of
historical interest. For instance, the BFGS
and DFP updates could be termed the "M
zero" and "Wzero" updates, respectively.
Also, based on personal taste, a researcher
may prefer variants that retain some of the
historical terminology, but remain within
the general guidelines of the notation
CONTINUES
"Department of Mathematics, Haverford
College, Haverford, PA 19041.
*Department of Pure and Applied Mathematics,
Washington State University, Pullman, WA
99164.
MARCH 1991
number thirtytwo
PAGE 3
PAGEIC 4 number thrytoMRH19
proposed here. For example, one could
substitute M8 for M+(O) and WD for W(O).
The inverses of these quantities can then be
denoted by WB and MD, respectively. If
M+Y() and W+(v) are found to be cumber
some, one could substitute M and W+,
respectively. An iteration subscript can be
attached to all symbols as needed, for
example, Mk, wk, a, Mk+,(), Mk+(0), MA,.
(Note that k+1 replaces + and k is used
otherwise.) We have used boldface letters
in this note to distinguish vectors from
scalars and matrices, but this convention can
easily be dropped. It can prove to be a
nusiance when wordprocessing an article,
and some may not care for the appearance
of boldface letters in formulae. In addition
to the commonly used symbols x (or x),
g (or g), s (or s) and y (or y), the symbols
M, W, m (or m), w (or w) t, v, a, b, and c
form the mainstay of the notation proposed
here, and it is these symbols that we hope
researchers will choose to adopt.
We now give a few useful identities that
also serve to illustrate the notation.
IfM is positive definite with inverse W, then
b < ac if and only if y and Ms are linearly
independent. If acb2, then m = 0 and the
entire Broyden family for approximating the
Hessian reduces to MK(O). Similarly, w = 0,
and the entire Broyden family for approxi
mating the inverse Hessian matrix reduces
to W,(0).
If WM = I, then
mrw = (b/ac) (1/b), (8)
M,(i)w = (p (a/b)+(lgi)(b/c)) m,
W,(v) m= (v (c/b)+(1v)(b/a)) w,
W,(v)M(u) = I+((1p)(1v)b lwc/b) wm'. (11)
Thus, if WM = I, and wm' is nonzero,
W,(v)MK ) = I if and only if
(1pI)(1v) b2 = wc. (12)
Also, under the same assumptions, the value of
p which makes M,(u) singular equals the value
of v which makes W,(v) singular, namely,
2/(b2 ac).
Finally, we have the following two results concerning determinants:
det(M,(i))/ det(M) = p(c/b)+(1j)(b/a), (13)
det(W+(v))/det(W) = v(a/b)+(lv)(b/c). (14)
The following chart gives specializations of these results:
Update t v det(M,(p))/det(M) det(W,(v))/det(W)
DFP 1 0 c/b b/c
BFGS 0 1 b/a a/b
SR1 b/(ba) b/(bc) (cb)/(ba) (ba)/(cb)
where SRI denotes the symmetric rank1 update.
For a further illustration of the use of our proposed notation, see Nazareth and Mifflin (5].
References
[11 Broyden, C.G (1970), "The conver
gence of a class of doublerank
minimization algorithms," Parts I and
II, J.I.M.A., Vol 6, pp. 7690, 222236.
12] Davidon, W.C. (1959), "Variable
metric methods for minimization,"
Research and Development Report
ANL5990 (Rev.), Argonne National
Laboratory, Argonne, Illinois. (re
printed in SIAM J. Optimization, Vol. 1,
No. 1, to appear, February, 1991).
[31 Dennis, J.E. and Schnabel, RB.
(1983), Numerical Methods for
Unconstrained Optimization and
Nonlinear Equations, PrenticeHall,
New Jersey.
[4] Dennis, J.E. and Tapia, R.A. (1976),
"Supplementary terminology for
nonlinear iterative methods," SIGNUM
Newsletter, Vol. 11, No 4, pp. 46.
15] Nazareth, J.L. and Mifflin, RB.
(1991), 'The least prior deviation quasi
Newton update," Technical Report 91
2, Department of Pure and Applied
Mathematics, Washington State
University, Pullman, WA.
New Code for Constrained
Optimization
FSQP (Feasible SQP) Version 2.0, developed
by J. Zhou and A. L. Tits, at the Systems Re
search Center at the University of Maryland,
College Park, MD 20742, is now available.
FSQP is a FORTRAN code for solving con
strained optimization problems, including
constrained minimax problems (but
nonlinear equality constraints are not al
lowed). Its mainfeatureis thatall theiterates
generated satisfy the constraints. This is of
valuein many engineering related problems.
Extensive numerical tests show that FSQP's
efficiency is comparable to that of the most
popular (nonfeasible) codes. A detailed
User's Manual has been completed. FSQP is
available free of charge to academic users but
maynotbe redistributed without the author's
approval. To obtain the code, please contact:
Andre Tits
Department of Electrical Engineering
and Systems Research Center
University of Maryland
College Park, MD 20742
Email: (andre@src.umd.edu)
ANDR I. Trrs
   m~p~s~`
MARCH 1991
PAGE 4
number thirtytwo
number thirtytwo
MARCH 1991
^tI
Thirteenth Symposium on
Mathematical Programming
with Data Perturbations
May 2324, 1991
A Thirteenth Symposium on Mathematical Pro
gramming with Data Perturbations will be held at
George Washington University'sMarvin Center on
May 2324, 1991. This symposium is designed to
bring practitioners, who use mathematical pro
gramming optimization models and who deal with
questions of sensitivity analysis, together with re
searchers who are developing techniques applicable
to these problems.
Contributed papers in mathematical program
ming are solicited in the following areas:
(1) Sensitivity and stability analysis results and
their applications.
(2) Solution methods for problems involving
implicitly defined problem functions.
(3) Solution methods for problems involving
deterministic or stochastic parameter changes.
(4) Solution approximation techniques and error
analysis.
"CLINICAL" presentations that describe problems
in sensitivity or stability analysis encountered in
applications are also invited.
ABSTRACTSof papers intendedfor presentation at
the Symposium should provide a good technical
summary of key results, avoid the use of math
ematical symbols and references, not exceed 500
words, and include a title and the name and full
mailing address of each author. The deadline for
submission of abstracts is March 9,1991. Abstracts
should be sent in triplicate to:
PROFESSOR ANTHONY V. FIACCO
INSTITUTE FOR MANAGEMENT SCIENCE
AND ENGINEERING
SCHOOL OF ENGINEERING AND APPLIED
SCIENCE
THE GEORGE WASHINGTON UNIVERSITY
WASHINGTON, DC 20052
TELEPHONE: (202) 9947511.
APPROXIMATELY 30 minutes will be allocated
for the presentation of each paper. A blackboard
and overhead projector will be available.
ANTHONY V.FIACCO,ORGANIZER
Integer Programming/Combina
torial Optimization Conference
May 2830, 1990
The University of Waterloo
The Mathematical Programming Society was a
principal sponsor of a three day conference on
integer programming and combinatorial optimiza
tion held at the University of Waterloo in May of
1990. Approximately 100 people participated in the
meeting, the formal portion of which consisted of
thirtysix papers, selected by a program committee
on the basis of extended abstracts. The proceedings
of the conference, consisting of full versions of all
the papers presented, were provided to all
participants at the meeting and may be ordered as
described below.
In view of the success of the conference, the Society
has decided to make it a regular event. It will be held
the two out of every three years that there is not an
International Mathematical Programming Sympo
sium. The next IPCO conference will be held in 1992
at Carnegie Mellon University.
The proceedings (535 pages) are published by the
University of Waterloo Press and may be ordered
from them directly at the address below:
THE UNIVERSITY OF WATERLOO PRESS
UNIVERSITY OF WATERLOO
WATERLOO, ONTARIO, CANADA N2L 3G1
TELEPHONE (519) 8851211 EXT. 3369
FAX (519) 7474606
The purchase price is $48.00 (CDN) for orders within
Canada and $48.00 (US) for nonCanadian sales.
BILL PULLEYLANK
FIRSTCAL FR PA
2" Stockholm Optimization Days
August 1213, 1991, KTH
Stockholm, Sweden
A Workshop on Optimization is to be held in
Stockholm, August 1213, the week after the
Mathematical Programming Symposium. The
workshop will take place at KTH (the Royal
Institute of Technology), Stockholm, and is
organized by the Optimization Laboratory at
the Division of Optimization and Systems
Theory with financial support by the Goran
Gustafsson Foundation and the Swedish
National Board for Technical Development.
The main themes of the workshop will be dual
optimization and nonlinear optimization
respectively. We also welcome papers in other
areas of mathematical programming as well as
applications, however.
At present, the following invited speakers have
agreed to participate in the workshop:
Don Hearn, U Florida, Gainesville
Philip Gill, UC San Diego
Jean Louis Coffin, McGill U, Montreal
Walter Murray, Stanford University
Panos Pardalos, Penn State U.
We have some limited funds for partial
coverage of transportation and housing of
participants.
Abstracts, not exceeding 200 words, should be
sent by email to P 0 Lindberg at the address
pol@math.kth.se (on internet) or at
pol@sekth.bitnet (on bitnet). Please use the
format given below. Deadline for abstracts is
June 1,1991.
Applications for support as well as requests for
additional information may also be sent to the
above address.
FOR THE ORGANIZING COMMITTEE P LINDBERG
Abstract format:
(If you use mathematical formulas, please write them so that they can be processed by LaTeX directly.)
AUTHORS) AND AFFILIATIONS)
TITLE:
ABSTRACT (NOT EXCEEDING 200 WORDS):
Ib~ik ISb~jl
 ~~
PAGR c
MARCH 1991
PAGE 6 numrber tirtytw
Mathematical Sciences
Clemson University
Clemson, SC 296341907
R. Ringeisen and S. Stueckle, "Crossing
Unique Graphs and Other Range Properties of
Drawings," #580.
M.C. Golumbic and R.C. Laskar,
"Irredundancy in Circular Arc Graphs," #582.
E. Bibelnieks and P.M. Dearing, "Neighbor
hood Subtree Tolerance Graphs," #585.
M. Kostreva and K.B. Jennings, "Nurse
Scheduling on a Microcomputer," #587.
J. Boland and R. Ringeisen, "Inclusive
Connectivity: An Introduction to a Local
Parameter," #588.
R.D. Ringeisen, S.K. Stueckle and B.L. Piazza,
"Subgraphs and Bounds on Maximum Cross
ings," #589.
R. Laskar and J. Dunbar, "Universal and
Global Irredundancy in Graphs," #591.
R.D. Ringeisen, B.L. Piazza and S.K. Stueckle,
"Subthrackleable Graphs and Four Graphs,"
#592.
R.D. Ringeisen and J.W. Boland, "Relation
ships Between iConnectivity Parameters," #593.
K.L. Dunlap and M.M. Kostreva, "More with
Murty's BardType Algorithm," #594.
A.A. Ebiefung and M.M. Kostreva, "Global
Solvability of Generalized Linear Complementar
ity Problems and a Related Class of Polynomial
Complementarity Problems," #595.
Technical
Reports
WORKING
PAPERS
Technische Universitit Graz
Institute fiir Mathematik B
Kopernikusgasse 24
8010 Graz, Austria
F. Rendl and G. Woeginger, "Reconstructing
Sets of Orthogonal Line Segments in the Plane,"
No. 160.
R.E. Burkard and J.A.A. van der Veen,
"Universal Conditions for Algebraic Traveling
Salesman Problems to be Efficiently Solvable,"
No. 163.
H.A. Eiselt and R.E. Burkard, "Reshipments
and Overshipments in Transportation Problems
with Minmax Objective," No. 165.
H. Kellerer and G. Woeginger, "On the
Euclidean Two Paths Problem," No. 166 (a).
G. Woeginger, "A Simple Solution to the Two
Paths Problem in Planar Graphs," No. 166 (b).
H. Tuy, "The Complementary Convex Structure
in Global Optimization," No. 167.
F. Rendl and H. Wolkowicz, "A Projection
Technique for Partitioning the Nodes of a
Graph," No. 169.
H. Kellerer and G. Woeginger, "A Tight
Bound for ThreePartitioning," No. 170.
System Optimization Laboratory
Operations Research Department
Stanford University
Stanford, CA 943054022
A.L. Forsgren and W. Murray, "Newton
Methods for LargeScale Linear Equality
Constrained Minimization," SOL 906.
JC. Yao, "A Monotone Complementarity
Problem in Hilbert Space," SOL 907.
P.E. Gill, W. Murray, D.B. Poncele6n and
M.A. Saunders, "Preconditioners for Indefinite
Systems Arising in Optimization," SOL 908.
R.W. Cottle and YY. Chang, "LeastIndex
Resolution of Degeneracy in Linear Complemen
tarity Problems with Sufficient Matrices," SOL
909.
R.W. Cottle and JC. Yao, "Pseudomonotone
Complementarity Problems in Hilbert Space,"
SOL 9010.
E. Schweitzer, "Modifying MINOS for Solving
the Dual of a Linear Program," SOL 9011.
W. Murray and F.J. Prieto, "A Sequential
Quadratic Programming Algorithm Using an
Incomplete Solution of the Subproblem," SOL 90
12.
W. Murray and F.J. Prieto, "A Second
Derivative Method for Nonlinearly Constrained
Optimization," SOL 9013.
B.C. Eaves and A.J. Hoffman, "Covers by
Polars of Arrangements," SOL 9014.
B.C. Eaves and U.G. Rothblum, "A Dis
countedCost ContinuousTime Flexible
Manufacturing and Operator Scheduling Model
Solved by Deconvexification Over Time," SOL
9015.
F. Jarre, "InteriorPoint Methods for Convex
Programming," SOL 9016.
R.W. Cottle and SM. Guu, "Two Character
izations of Sufficient Matrices," SOL 9017.
      II
PAGE 6
number thirtytwo
HANDBOOKS IN OPERATIONS RESEARCH
AND MANAGEMENT SCIENCE
General Editors:
G.L. Nemhauser, Georgia Institute of Technology, USA and
A.H.G. Rinnooy Kan, Erasmus University, Rotterdam, The Netherlands
Optimization
editedby G.L. Nemhauser, A.H.G. Rinnooy Kan
and M.J. Todd
(Volume 1)
Collected together in this book are ten stateoftheart
expository articles on the most important topics in
optimization, written by leading experts in the field.
The book therefore provides a primary reference for
those performing research in some area of
optimization or for those who have some basic
knowledge of optimization techniques but wish to
learn the most uptodate and efficient algorithms for
particular classes of problems.
1989 xiv + 710 pages
ISBN 0444872841
Stochastic Models
edited by D.P. Heyman and M.J. Sobel
(Volume 2)
One of the central problems in operations research is
how to quantify the effects of uncertainty about the
future. This, the second volume in a series of
handbooks, is devoted to models where chance
events play a major role. The thirteen chapters survey
topics in applied probability that have been particularly
useful in operations research and management
science. Each chapter was written by an expert (both
in subject matter and in its exposition), and most are
intended to be accessible at an introductory level. By
this is meant a calculusbased probability course and
the rudiments of matrix algebra.
1990 x + 726 pages
ISBN 0444874739
Special price for members of ORSA/TIMS/MP Society
Price per volume: US$ 69.00
Use this form (or a photocopy) for your order.
Send to:
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PAGl8n
Applications of
Discrete Mathematics
Edited by
Richard D. Ringeisen
and Fred S. Roberts
SIAM Philadelphia 1988
ISBN 089871219x
This book forms Proceedings of the Third Confer
ence on Discrete Mathematics, held at Clemson University,
Clemson, South Carolina, May 1416,1986.
As the firstsuch conference under the direct sponsorship of the ,_
SIAM Activity Group (SIAG) on Discrete Mathematics, the confer
ence brought together mathematicians from business, industry and gov
ernment with those from academia to express their common interest in
discrete mathematics and its applications.
This volume consists of papers from invited speakers at the plenary sessions
and the minisymposia. The last part of the volume is a summary of the
problems presented in the problem session. The papers reflect the wide range
of topics covered at the meeting, and they are grouped by type of presen
tation at the conference rather than by topic.
The reader finds articles by invited speakers in cryptography (Ernest F.
Brickell, Don Coppersmith), combinatorial geometry (Paul Erd6s), prob
ability (Peter Winkler) and perfect graphs (W.T. Trotter Jr.), as well as ap
plications such as the useofdiscrete mathematics in airline scheduling (Kevin
K. Gillette).
IThe Part II (Minisymposia) contains research articles on combinatorial as
Spects of network reliability (Daniel Bienstock, WilliamT. McCullers and R.
Kevin Wood,J. Scott Provan and Michael O. Ball, Douglas R. Shier), chemi
cal graph theory (Gerry Ray Rias, R. Bruce King, Dennis H. Rouvay) and
topics on domination in graphs (D.W. Bange, A.E. Barkauskas and P.J.Slater,
C. Berge and P. Duchet, S.T. Hedetniemi and R. Laskar).
The selected papers are clearly written, providing both surveys of research
areas and the new achievements.
The volume focusesonintensivelygrowingbranches of discrete mathematics
with the aim to contribute to interaction between pure discrete mathemat
ics and users of discrete mathematics. The reader also gets an impression
about the spirit governing the SIAM conferences on Discrete Mathematics.
The volume is recommended to researchers and graduate students in dis
crete mathematics and computer science.
MARTIN LOEBL
V I S kw S
Introduction to the
Mathematics of
Operations Research
by Kevin J. Hastings
Dekker, 1989
Operations Research (in short,O.R.) is
a recent but fastgrowing branch of applied math
f ematics and has become an important part of so
called industrial mathematics. Models and methods of O.R.
are the core of many industrial processes. Some of these, in
cluding production, inventory, transportation, and telecom
munications, are now classical applications. However, in the last
two decades, methods of O.R. have been shown to be instrumental in
several fields whichseemed far away whenO.R. was young. Some instances
are design problems, which come especially from elastoplasticity and struc
tural engineering, computer networks, and aerospace engineering, just to
mention a few.
Rapid growth of a discipline requires continuous renovation of the teach
ing. The present book can be considered in this category. It is addressed to
students of O.R. at the university or postgraduate level, as well as to those
scientists who want to become familiar with the basic methods of O.R The
exposition aims to acquaint them with the basic ideas.
The book begins appropriately with Graph Theory and Network Analysis.
In fact, this topic has become one of the most essential parts of the math
ematical machinery of computer science, of the language of discrete math
ematics, and of the organization of ideas. The penetration of mathematical
methods into science and technology takes place to a significant degree by
means of graph theory.
Then the book is concerned with Linear Programming, the study of optimi
zation of linear functions of several variables subject to linear constraints.
The importance of this topic goes beyond O.R.; it has become a fundamental
tool in most mathematical applications.
Special attention is then devoted to the study of systems moving in a
nondeterministic way as time progresses, by analyzing some stochastic
processes, like Markov Chains. Deterministic and stochastic Dynamic Pro
gramming, the study of optimization of randomly evolving systems, con
cludes this part, which is becoming more and more important.
A good mixture of exercises of several levels of difficulty and problems il
lustrating possible applications complete the book.
F.GIANNESSI
M a~
t)O)
a ~ bl. I~I,&.r
I
MARCH 1991
PAGE
number thirtytwo
MARCH 1991
PAGE 9 numb r thrt
Theory of Vector Optimization
by Dinh The Luc
Springer Verlag, Berlin
optimization, have been restudied and recognized to have
a vector nature. As a consequence, in the last two decades
there has been a rapid growth of both theory and methods
for vector optimization.
Monograph 319 R K I I The book presents a study of the most important topics in
the field. The reader, even if unfamiliar with vector optimi
The book is concerned with the important field of vector zation, is brought quickly and smoothly to the most ad
optimization, namely constrained extremum problems vanced topics, such as nondifferentiable problems and du
where the objective function is vectorvalued. In the finite di ality. This has been made possible by the successfulattempt of the
mensional case such problems are referred to as multiobjective pro authorto givea unified approach to vector optimization byexploiting
ramming. theorems of the alternative and an axiomatic theory of duality, as well as
classical arguments such as Lagrangian and conjugate duality.
Great progress in optimization techniques has made multiobjective pro . GIANNE
gramming a reality. Several problems, which had been formulated as scalar
Newfromw
A quarterly journal for:
M Aeronautical, chemical, civil, electrical, environmental, and mechanical engineers engaged in optimal design U Modelers
concerned with optimal parameter selection such as chemists, geophysicists, physicists, and statisticians U Software and algorithm
developers in computer science, mathematics, and operations research U Mathematical scientists concerned with the existence of
solutions and with the design and analysis of continuous and discrete algorithms.
* CONTENTS / February 1991, Volume 1, Number 1
Variable Metric Methodfor Minimization; William C. Davidon; A New Variational Result for
QuasiNewton Formulae, Roger Fletcher; On the Performance of Karmarkar's Algorithm
Over a Sequence of Iterations, Kurt M. Anstreicher; Composite Nonsmooth Programming
with Gateaux Differentiability, V. Jeyakumar; Local and Superlinear'Convergence for Par
tially Known QuasiNewton Methods, John R. Engels and H6ctor J. Martinez; Minimization of
Locally Lipschitzian Functions, JongShi Pang, ShihPing Han, and Narayan Rangaraj; A
PolynomialTime PredictorCorrector Algorithm for a Class of Linear Complementarity
Problems, Jiu Ding and TienYien Li; A New Proof of Superlinear Convergence forBroyden's
Method in Hilbert Space, C.T. Kelley and Ekkehard W. Sachs; On the Solution ofLarge Quad
ratic Programming Problems with Bound Constraints, Jorge J. Mor6 and Gerardo Toraldo;
Convergence of Iterates of an Inexact Matrix Splitting Algorithm for the Symmetric Monotone
Linear Complementarity Problem, O. L. Mangasarian, On the Convergence of the Multidirec
tional Search Algorithm, Virginia Torczon.
* MANAGING EDITOR
John E. Dennis, Jr., Rice University
To subscribe to SIAM Journal on Optimization, please contact:
SIAM Customer Service Department
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* SUBMITTING A PAPER
Submissions are invited on algorithms, applications, and existence and
uniqueness theory of: linear and quadratic programming, mixed integer
programming, large scale optimization, nonsmooth optimization, stochastic
optimization, convex analysis, and combinatorial optimization.
To contribute a paper to SIAM Journal on Optimization,
send submissions to:
SIAM Publications
Attention: John E. Dennis, Jr.
Box 7541, Philadelphia, PA 19101
New from ,
  
~~
number thirtytwo
PAGE 9
PAE 0 ume tiryw MRC 19
0
Journals
MPBIER
R.H. Byrd and J. Nocedal, "An Analysis of
Reduced Hessian Methods for Constrained
Optimization."
D. Goldfarb and S. Liu, "An O(n`L)
Primal Interior Point Algorithm for
Convex Quadratic Programming."
F. Jarre, "On the Convergence of the
Method of Analytic Centers when Applied
to Convex Quadratic Programs."
S. Kim, H.S. Ahn and S.C. Cho, "Vari
able Target Value Subgradient Method."
C. Herrero and J.A. Silva, "On the
Equivalence between Strong Solvability
and Strict Semimononicity for Some
Systems."
H.D. Sherali, "Capacitated, Balanced,
Sequential LocationAllocation Problems
on Chains and Trees."
J.J. More and S.A. Vavasis, "On the
Solution of Concave Knapsack Problems."
R.H.F. Jackson, P.T. Boggs, S.G. Nash and
S. Powell, "Guidelines for Reporting
Results of Computational Experiments.
Report of the AdHoc Committee."
F.E. Torres, "Linearization of Mixed
Integer Products."
V B.5
J.C. Gilbert, "Maintaining the Positive
Definiteness of the Matrices in Reduced
Secant Methods for Equality Constrained
Optimization."
I. Adler and R.D.C. Monteiro, "Limiting
Behavior of the Affine Scaling Continuous
Trajectories for Linear Programming
Problems."
A.B. Gamble, A.R. Conn and W.R.
Pulleyblank, "A Network Penalty Prob
lem."
S. Kim and H. Ahn, "Convergence of a
Generalized Subgradient Method for
Nondifferentiable Convex Optimization."
S. Mehrotra and J. Sun, "On Computing
the Center of a Convex Quadratically
Constrained Set."
C.C.Y. Dorea, "Effort Associated with a
Class of Random Optimization Methods."
D.T. Luc, "Contingent Derivatives of Set
Valued Maps and Applications to Vector
Optimization."
U. Derigs and A. Metz, "Solving (large
scale) Matching Problems Combinatori
ally."
A. Tamir, "On the Core of Network
Synthesis Games."
Lllr"llClssl~SILTII"~~IC~IIBClal
 ~ ~
PAGE 10
number thirtytwo
MARCH 1991
MARCH 1991
Editorial Board: N BpC.rck. I ninkring. I C
%1 G(jj.3 Zara02a: ( H.A b 'I .ui 'r)h
'i rkro%n Ge.h' \1Munlr3.h, li.r e
1. Vines. Flaris: M, kedi%?..i114 PaCIL
Fiffl.her, ALIck[lid: P.C. r[c. Par[: I Ditla Dinr, (Irrnotblc:
'.H ZU eu urkit'. P. J Launrent. Circnioe: NI*hI.
S. Pa'.ci .\rocl..: K. Tau ._, T4 : R>.\ r.ca. vnt 1iH.
Volume i in .4 i 1u99. 1991. 4S i'i, 1, l ,J H 1.i. iiIJ ;. iSS\ lIrl3' ... Lrt: iu' M\ : h I'l
The journal is intended t c' er al l al pv .1 n m rical ,lorih'.hms from lth or, de nti,. ani d u'ifulne tiC. ques[ior
dealing A it h their .omplei'.l: a J their implrn.mn: ['ir n .ariu. t:,pes A ot comn puters Ip;rallel... . r. mlrn urc r algr bra
in relation to the ataiiimenit :f num ci ai r ul ... ilil adl. be n diered it i aku ch, pirpc.e *'.. journal H.? pu li.h
computer progranis and s:ub'lr.',u[ne
Actually, no other journal is entire. Je.'te.j to numneri. l algiornrhm and appli.an : a. .el!.
The journal i. of parucular interest to numerical analit'. applied m.ithematicit n co'. ompru r , eie i:d all fhlio
performing nuirerical calculations.
Authors are cordially invited to submrn papers, r tlhe editors.
Please request a free specimen copy
In the United States please send your order to:
J.C. Baltzer AG, Scientific Publishing Co., P.O. Box 8577, Red Bank NJ 07"'0185"7.
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A ne%% journal covering all aspect,; (if nunmrical algorihhm%;. theoretical results. implementalion. numerical
i1abilil). coniplexiI.. subroutineN and applications.
Editorin(hief: C Brr iii4;.i Lii' J n.'flr Numeriqiic !L'rt:lit,'n LJR El. ni .JEE VNii.. I :
Tec:hniqi,:7 Ie [_iN. lairdro~ \r. 'w \ IhI::!;u CI XA'.q ( C F'. ? ri~e.
PAGE 12 number lllthirtt MAC 19
Stein W. Wallace has moved to The
University of Trondheim (Norway) to
become a professor of Operations
Research. IThe Wall Street Journal, Oct.
19, 1990, featured a story on Ron
Dembo's development of algorithms for
trading "synthetic" securities. IAIRO
'91 will be held Sept. 1819,1991, at Riva
del Garda, Italy. Contact Prof. Franco
Molinari, Universita Delgi Studi di
Trento, Phone +39 461 882118,
Fax +39 461 882144, Email
molinari@itncisti.bitnet. TDeadline for
the next OPTIMA is June 1,1991.
Mathematical Program
ming Backlog Crisis Over
I am happy to report that Math
ematical Programming Series A
backlog, which had grown to an al
most three year waiting period, has
now been substantially reduced. Pa
pers currently accepted can expect to
wait about one year before being
published.The waitingperiod should
be reduced even further in 1991.
Several measures were undertaken
to achieve the backlog reduction. The
most significant was to renegotiate
the Journal's contract with North
Holland, increasing the number of
issuesperyearfrom 6 to9, effective in
1991. That increased the number of
pages peryearfrom 720 to1080. In ad
dition, the sizes of the volumes pub
lished in 1990 were increased and one
issue from 1991, volume 49, was
shifted back into 1990. The result is
that over 1300 pages were published
in 1990.
ROBERT E BIXBY
Books for review should be
sent to the Book Review Editor,
Prof. Dr. Achim Bachem,
Mathematiches Institute der
Universitfit zu Kiln,
Weyertal 8690, D5000 Kiln,
West Germany.
Journal contents are subject
to change by the publisher.
Donald W. Hearn, EDITOR
Achim Bachem, ASSOCIATE EDITOR
PUBLISHED BY THE MATHEMATICAL
PROGRAMMING SOCIETY AND
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UNIVERSITY OF FLORIDA.
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