Title: Optima
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Permanent Link: http://ufdc.ufl.edu/UF00090046/00032
 Material Information
Title: Optima
Series Title: Optima
Physical Description: Serial
Language: English
Creator: Mathematical Programming Society, University of Florida
Publisher: Mathematical Programming Society, University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: March 1991
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Bibliographic ID: UF00090046
Volume ID: VID00032
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.


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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 Beale-Orchard-Hayes 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 one-hour
lectures as well as invited and contributed thirty-minute
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
The series of invited one-hour 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

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 at-large
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 5-9,1991, so the
next election will be held in April 1991.
The new members-at-large of the
Council will take office at the time of
the Symposium, while the Chairman-
elect and Treasurer-elect will take office
one year later. CONTINUES, PAGE TWO



~ ~ ~

P 2nmbethrytw MARCH9

Amsterdam 1991

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 first-time 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 two-table Belgian
caf6 to the art deco splendor of
Caf6 Americain. The facilities are
extensive-approximately 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

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 thirty-minute journey

by train. Another popular outing is
to the Kr6ller-Miiller 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

14th International Symposium on
Mathematical Programming
do NOVEP, Paulus Potterstraat 40
1071 Amsterdam, The Netherlands
Telephone +31-20-6752120
fax +31-20-6628136
e-mail ismp@swi.psy.uva.n 1.
The deadline for early
registration is April 1.
Registration fees for members and
non-members are, respectively,
NLG 240 and NLG 300. These
increase by NLG 100 after the
deadline. The feesfor non-members
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.

1991 Nominations

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 by-laws governing
elections designed to promote
international representation on
the Council.
Accordingly, the Council has
agreed to the following
(1) Nomination to any office is to
be submitted to me by April 1,
Such nomination is to be supported
in writing by the nominator and at
least five other members of the
(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 at-large 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 1989-1991
Department of Industrial and
Systems Engineering
Georgia Institute of Technology
Atlanta, GA 30332-0205, U.S.A.
Fax: 404-894-2301

_ ~ _I~ ~I~ _1_-~ 111-. -~---~

MARCH 1991



number thirty-two

Some Comments on Notation for Quasi-Newton Methods
W.C. Davidon," R.B. Mifflin and J.L. Nazareth'

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.

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 quasi-Newton 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 quasi-Newton approximation to
the Hessian, and on yet other occasions it is
used to denote a quasi-Newton 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 quasi-Newton updates, for
example, DFP-update, BFGS-update, PSB-
update, has grown haphazardly to the point
that Dennis and Schnabel [3] call it a form of
"alphabet-soup" 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-

Proposed Terminology and
We suggest the term quasi-Newton be used
as a generic name for the entire class of
methods that rely on the quasi-Newton (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
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

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 quasi-Newton 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 BFGS-update of M and W
yields M+(0) and W+(1), respectively, and
that the DFP-update 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 "W-zero" 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

"Department of Mathematics, Haverford
College, Haverford, PA 19041.
*Department of Pure and Applied Mathematics,
Washington State University, Pullman, WA

MARCH 1991

number thirty-two


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 bold-face 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 word-processing an article,
and some may not care for the appearance
of bold-face 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 ac-b2, 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)+(l-gi)(b/c)) m,

W,(v) m= -(v (c/b)+(1-v)(b/a)) w,

W,(v)M(u) = I+((1-p)(1-v)b lwc/b) wm'. (11)
Thus, if WM = I, and wm' is nonzero,
W,(v)MK ) = I if and only if
(1-pI)(1-v) 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)+(1-j)(b/a), (13)

det(W+(v))/det(W) = v(a/b)+(l-v)(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/(b-a) b/(b-c) (c-b)/(b-a) (b-a)/(c-b)

where SRI denotes the symmetric rank-1 update.
For a further illustration of the use of our proposed notation, see Nazareth and Mifflin (5].

[11 Broyden, C.G (1970), "The conver-
gence of a class of double-rank
minimization algorithms," Parts I and
II, J.I.M.A., Vol 6, pp. 76-90, 222-236.
12] Davidon, W.C. (1959), "Variable
metric methods for minimization,"
Research and Development Report
ANL-5990 (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, Prentice-Hall,
New Jersey.
[4] Dennis, J.E. and Tapia, R.A. (1976),
"Supplementary terminology for
nonlinear iterative methods," SIGNUM
Newsletter, Vol. 11, No 4, pp. 4-6.
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

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 (non-feasible) 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
E-mail: (andre@src.umd.edu)
-ANDR I. Trrs

------ -- ----- m~p~s~--`-

MARCH 1991


number thirty-two

number thirty-two

MARCH 1991


Thirteenth Symposium on
Mathematical Programming
with Data Perturbations
May 23-24, 1991
A Thirteenth Symposium on Mathematical Pro-
gramming with Data Perturbations will be held at
George Washington University'sMarvin Center on
May 23-24, 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
"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:
TELEPHONE: (202) 994-7511.
APPROXIMATELY 30 minutes will be allocated
for the presentation of each paper. A blackboard
and overhead projector will be available.

Integer Programming/Combina-
torial Optimization Conference
May 28-30, 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
thirty-six 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:
TELEPHONE (519) 885-1211 EXT. 3369
FAX (519) 747-4606
The purchase price is $48.00 (CDN) for orders within
Canada and $48.00 (US) for non-Canadian sales.


2" Stockholm Optimization Days
August 12-13, 1991, KTH
Stockholm, Sweden
A Workshop on Optimization is to be held in
Stockholm, August 12-13, 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
Abstracts, not exceeding 200 words, should be
sent by e-mail 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.

Abstract format:

(If you use mathematical formulas, please write them so that they can be processed by LaTeX directly.)




Ib~ik ISb~jl

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


MARCH 1991

PAGE 6 numrber tirty-tw

Mathematical Sciences
Clemson University
Clemson, SC 29634-1907
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,"
R.D. Ringeisen and J.W. Boland, "Relation-
ships Between i-Connectivity Parameters," #593.
K.L. Dunlap and M.M. Kostreva, "More with
Murty's Bard-Type 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.





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 Three-Partitioning," No. 170.

System Optimization Laboratory
Operations Research Department
Stanford University
Stanford, CA 94305-4022
A.L. Forsgren and W. Murray, "Newton
Methods for Large-Scale Linear Equality-
Constrained Minimization," SOL 90-6.
J-C. Yao, "A Monotone Complementarity
Problem in Hilbert Space," SOL 90-7.
P.E. Gill, W. Murray, D.B. Poncele6n and
M.A. Saunders, "Preconditioners for Indefinite
Systems Arising in Optimization," SOL 90-8.
R.W. Cottle and Y-Y. Chang, "Least-Index
Resolution of Degeneracy in Linear Complemen-
tarity Problems with Sufficient Matrices," SOL
R.W. Cottle and J-C. Yao, "Pseudo-monotone
Complementarity Problems in Hilbert Space,"
SOL 90-10.
E. Schweitzer, "Modifying MINOS for Solving
the Dual of a Linear Program," SOL 90-11.
W. Murray and F.J. Prieto, "A Sequential
Quadratic Programming Algorithm Using an
Incomplete Solution of the Subproblem," SOL 90-
W. Murray and F.J. Prieto, "A Second-
Derivative Method for Nonlinearly Constrained
Optimization," SOL 90-13.
B.C. Eaves and A.J. Hoffman, "Covers by
Polars of Arrangements," SOL 90-14.
B.C. Eaves and U.G. Rothblum, "A Dis-
counted-Cost Continuous-Time Flexible
Manufacturing and Operator Scheduling Model
Solved by Deconvexification Over Time," SOL
F. Jarre, "Interior-Point Methods for Convex
Programming," SOL 90-16.
R.W. Cottle and S-M. Guu, "Two Character-
izations of Sufficient Matrices," SOL 90-17.

- -- -- - -- -- II


number thirty-two



General Editors:
G.L. Nemhauser, Georgia Institute of Technology, USA and
A.H.G. Rinnooy Kan, Erasmus University, Rotterdam, The Netherlands

editedby G.L. Nemhauser, A.H.G. Rinnooy Kan
and M.J. Todd
(Volume 1)
Collected together in this book are ten state-of-the-art
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 up-to-date and efficient algorithms for
particular classes of problems.
1989 xiv + 710 pages
ISBN 0-444-87284-1

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 calculus-based probability course and
the rudiments of matrix algebra.
1990 x + 726 pages
ISBN 0-444-87473-9

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:
Attn: H.A.C. Gierveld
P.O. Box 1991
1000 BZ Amsterdam, The Netherlands

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Applications of
Discrete Mathematics
Edited by
Richard D. Ringeisen
and Fred S. Roberts
SIAM Philadelphia 1988
ISBN 0-89871-219-x

This book forms Proceedings of the Third Confer-
ence on Discrete Mathematics, held at Clemson University,
Clemson, South Carolina, May 14-16,1986.

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.

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 fast-growing 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.

M a~

a ~ bl. I~I,&.r


MARCH 1991


number thirty-two

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 vector-valued. 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


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
Quasi-Newton 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 Quasi-Newton Methods, John R. Engels and H6ctor J. Martinez; Minimization of
Locally Lipschitzian Functions, Jong-Shi Pang, Shih-Ping Han, and Narayan Rangaraj; A
Polynomial-Time Predictor-Corrector Algorithm for a Class of Linear Complementarity
Problems, Jiu Ding and Tien-Yien 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.

John E. Dennis, Jr., Rice University

To subscribe to SIAM Journal on Optimization, please contact:
SIAM Customer Service Department
3600 University City Science Center
Philadelphia, PA 19104-2688

SIANI Member Rates

Non-member Rates
i'l/7 sr(Xdjir I 75 c- .,r t
Pflrk are in I *S dollars

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 thirty-two


PAE 0 ume tiry-w MRC 19



R.H. Byrd and J. Nocedal, "An Analysis of
Reduced Hessian Methods for Constrained
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
H.D. Sherali, "Capacitated, Balanced,
Sequential Location-Allocation 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 Ad-Hoc 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
I. Adler and R.D.C. Monteiro, "Limiting
Behavior of the Affine Scaling Continuous
Trajectories for Linear Programming
A.B. Gamble, A.R. Conn and W.R.
Pulleyblank, "A Network Penalty Prob-
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
U. Derigs and A. Metz, "Solving (large
scale) Matching Problems Combinatori-
A. Tamir, "On the Core of Network
Synthesis Games."


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


number thirty-two

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 G-e.h' \1Munlr-3.h, l-i.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. Circnio-e: 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\ lIr-l3' ... 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 i-mplrn.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"'01-85"7.
From all other countries please send >our order to:
J.C. Balizer AG, Scientific Publishing Co., Wettsteinplatz 10, CH-4058 Basel, Switzerland.

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Cheques or money orders should be made payable to
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number thirty-two


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A ne%% journal covering all aspect,; (if nunmrical algorihhm%;. theoretical results. implementalion. numerical
i1abilil). coniplexiI.. subroutineN and applications.

Editor-in-(hief: C Brr iii4;.i Lii' J -n.'fl-r 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 lllthirt-t 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. 18-19,1991, 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.

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

Journal contents are subject
to change by the publisher.

Donald W. Hearn, EDITOR
Elsa Drake, DESIGNER


303 Weil Hall
College of Engineering
University of Florida
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- -- -- -- ~ --- ~-------

MARCH 1991


number thirty-two

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