Title: Optima
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Permanent Link: http://ufdc.ufl.edu/UF00090046/00004
 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: July 1981
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Bibliographic ID: UF00090046
Volume ID: VID00004
Source Institution: University of Florida
Holding Location: University of Florida
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Robert G. Jeroslow
Georgia Institute of Technology

All OPTIMA readers are welcome to
contribute to our Society's newsletter, and
recently OPTIMA editor Don Hearn invited
me to express my views on integer program-
ming. Rather than organize a semi-scholarly
piece when my "views" tend more toward
broad speculations, I have chosen to get
down a few ideas on some of the areas
I think are very promising. I have largely
.1. !l, I lvd to seriously research these areas
myself. The pink dogwoods are budding and
as I begin to write, this city will be a park
full of flowers in two weeks. I shall attribute
any errors I make to spring fever.
Newcomers to the integer program-
ming area may get the impression that
researchers either do combinatorial optimiz-
ation and get polynominal-time algorithms,
or do group theory, cutting-planes, or
computational complexity studies, or a few
other erudite and advanced topics. In fact,
there is a high concentration of work in
relatively few subjects.
Actually, what I found refreshing,
upon returning to operations research from
the pure mathematics about ten years or so
ago, was that this area was alive. It was
motivated by problems that actually had to
be solved, and it had users. The participants
exhibited a wide variety of views as to what
the most pressing questions were, and how
to approach them. Proper discrimination was
not an issue of a correct topic or approach,
but primarily one of discerning those parts
of research which went clearly beyond
relatively pedestrian information into sub-
stantial results (in the case of theory) or
a substantial development effort (in the case
of empirical work). And with the natural
tendency to further refine those narrow
parts of our knowledge where an impetus
had built up, there were a lot of "roads not
taken" or at least, hardly taken.
For one example, I believe that the
"frontier" of empirical research on the

1 ,
mixed-integer iiIr.imIIin: probl
around 150 binary variables i.e.
be a real advance if we could fairly
expect to solve 200 binary variable
with general MIP codes. Some
it was reliably rumored that or
major computer firms has sold 100
a large-scale MIP/NLP code fo
$80,000, so there is a market here.
about developing an utterly d
general MIP code for thirty or fev
variables, and not too large of ar
either? That could certainly be don
We need a superb MIP cod
novices. The primary reason tha
organization is pushing MIP as
market thrust is the need for
make adjustments when the cod
converge. Currently any general
for 100 variables would be a he
service. The thrust in MIP industry
tions involves highly-paid technic
A general-purpose MIP corn
for novices certainly would not
range of application of the more
codes, but its market could well b
for itself and for stimulating furtl
Its use would probably be best
with heuristic, problem-based, an
theory based approaches to mode
tion. In a complex situation witl
of variables, human conceptual
identify a much smaller number
decisions, whose outcome will eit
come clu to setting, the values (



ships among these variables. If so, we should
formulate and solve the much smaller pro-
blems in the key decisions. This will get us
only an approximate solution to our actual
problem, but that is usually better than no
solution at all to the "accurate formulation."
One still needs "experts" to teach
methods for compact formulation of integer
programs. However, these skills are much
closer to the users' abilities, interests, and
personal knowledge. Minimally, we should
get stimulating and realistic technical cases
for master's students from these efforts!
lem is at So much for this point, let's move on.
it would We will not make the case either for or
regularly against this "problem-free" code for a
problems limited (but significant) set of MIP formula-
years ago, tions, because good "attorneys" can argue it
ne of the either way. The point is to find out, and I do
Copies of not think that the investment involved is
.r around excessive.
But what Several researchers are working on
ependable interactive approaches to integer program-
ver binary ming with embedded heuristics. These
n LP part, approaches differ from general MIP codes, in
ne. that extensive use is made of the particular
e for total kind of problem to get a good start and to
t no large guide the software part of the exploration.
a major To page 2
experts to i m i...
le fails to
headache to
ial applica- We are delighted to report that Dick
cal consul- Cottle, as Editor-In-Chief of the Society's
publications, has concluded arrangements
puter code with North-Holland Publishing Company for
have the printing three volumes (nine issues) of
ambitious Mathematical Programming instead of the
e adequate usual two volumes (six issues) in 1982.
her efforts. Members in good standing will receive all
combined three volumes at no additional cost.
d learning- This increased publication schedule
el formula- will reduce our backlog, thus enabling us to
i hundreds better serve the mathematical programming
izing may community through faster publication of
of major accepted papers. Of course the same high
;her set, or standards will continue to apply.
or relation- -Michael Held


In the relatively more technical business
decisions, the user typically does develop
good intuition from experience, and often
starts close in value to the optimum. These
interactive approaches are often supple-
mented by good visual displays of the
solution under current consideration, and an
ease of making changes in the solution. Very
little has been published on interactive
methods, and even technical reports are
relatively few, although many IP papers do
mention human intervention on an ad hoc
basis for the solution of some programs.
Criticisms have been made of the work
on interactive methods, to the effect that
the quality of the solutions obtained is
unknown. It is certainly true that few
mathematical theorems can be proven about
interactive procedures. However, mathe-
matics is one of several sciences of value in
the problems that occur in operations
I personally would view the recent
development of some interactive codes and
heuristic methods as "decision support
systems." The criteria for such, is that the
users are substantially aided by the algo-
rithm, whether or not their final solution is
"optimal." But if this is actually our ap-
proach, we need some empirical studies
and protocols as to how humans will try to
approach problems, by use of programming
techniques, in order to make suggestions or
simply to discern the better approaches. This
has not been done to my knowledge. The
psychologists could provide clearer scientific
standards by which to measure (and to
promote) research of this type.
Let's move on.
Within the framework of exact algo-
rithms, but still related to the previous
points, is the issue of branching conditions
in enumerative algorithms. Typically, the
branching choice is x=0 versus x=l. But if it
were felt that two projects are likely (but
not certain) to be done together, or neither
will be done, the branching choice should be
x=y versus x=l-y (with the former branch
x=y favored first to get a good "incumbent"
solution)'. The branching choices can
conform to other natural ways of grouping
the logical alternatives, as long as all the
alternatives are (implicitly) represented. An
overlap of logical alternatives is. not neces-
sarily a bad thing, particularly if the overlap
consists of unpromising alternatives. Also,
there ought to be numerous ways of taking a
large number of "unpromising" nodes in an

cnu1merative search, and "coalescing" them
into a "supernode" for further logical
subdivision (so that similar node subdivisions
do not occur repeatedly in the research)2.
Despite a ...'.in;: literature", not
ei.'tm!h has been done in sensitivity analysis
for integer programs. This is a crucial area
for applications. Some good work was done
earlier in an algorithmic setting, and Charlie
Blair and I are now finding out that a lot of
theoretical structure lies behind simple
right-hand-side changes4. But much more
remains undone. Perhaps this (admittedly
inexact) question will help put one such
open issue in focus: what is the mixed-
integer analogue of the local sensitivity
analysis of linear programming (i.e., the
sensitivity analysis from a fixed basis), and
in what essential ways is the analogous
information for IP less encompassing than
local LP sensitivity information?
The situation in multicriteria integer
programming is akin to that for sensitivity
analysis: the topic is of clear significance
from the user's perspective, and so warrants
more intensive exploration5. Let me ask a

straightforward question: with only two
criteria to trade-off against each other, what
should a master's student know about how
the integer programming efficiency frontier
is different from that for a linear program?
Surely, the "answers" to both prompt-
ing questions must involve the limitations of
local information, which occur in integer but
not linear programming. If we can phrase
fairly complete answers in accessible lan-
guage, it will indicate that we understand the
phenomena reasonably well.
The computational complexity of a
large number of problems in discrete opti-
mization has been extensively studied6,
with several surprising results regarding out-
wardly similar problems which (appear to)
have different complexity. What happens
when we study the complexity of questions
that begin, "For every value of this para-
meter, does. .?" Such questions arise

in sensitivity analysis7. What new complex-
ity heirarchies do they lead to and how
often are these heirarchies actually needed?
In the mid-60's litmu:.hj the early 70's,
a small number of integer programmers
worked on both sampling and probabilistic
approaches to integer piI ;:i.uII. By ran-
domly L'ei-.mil.- attempts at solution
and sampling the outcome, techniques were
developed for estimating the optimal value,
etc. Attempts were made to determine if the
current incumbent was optimal with a
certain probability, etc. Possibly not all
these attempts were properly modelled.
There are a lot of variations possible on
these ideas, and they are not (conceptually
or mathematically) equivalent.
Rumors have it, that these -.n,.i.lilli,
probabilistic methods lost interest when the
state of the art for exact solutions went
beyond what these methods were then
capable of for linear integer programs (as
opposed to nonlinear ones). 1, for one, am
unconvinced that enough of the alternatives
in this approach were considered. For one
thing, these methods were never adopted to
*"';.'. lh Ir I1111 problems. In recent
years, some interesting probabilistic results
have been established which iii i. structure.
I think it likely that the Shapley-
Folkman-Starr Theorem9 has a certain
relevance to integer programming. This
result has been interpreted as saying that the
sum of a large number of (possibly noncon-
vex) sets is "more convex" than the sets, in
the sense that the size of the "holes" is less,
relative to the total size of the set. An
immediate application is to any integer
programming constraint set, where the
individual sets are doubletons < ,ii-iilln, of
zero and a column of the constraints, but
there are less obvious applications.
Now Cassel's proof9 reveals even
more, for he shows implicitly that a sam-
pling technique can be used to get approx-
imate solutions to any point in the convex
span of the sum set. Is this about as close as
a discrete problem has approximate solu-
tions for its linear relaxation? For which
special structures, and for which conditions,
are approximations of this type satisfactory?
I would be only guessing if I were to
project future trends in integer programming
research. My sole expectation is that it will
prosper, as will operations research generally.
'.l.ii directions would 1, personally,
like to see? I would like to see an enlarge-
ment of the focus of research interests
that is more in line with the diversity of
users' needs. Our field, as a collective entity,
could support a broader range of serious
To page 3

J .. -

research efforts than it now does. Such
effortss would, for the most part, represent
substantiall concentration on issues that are
already of interest.

r TF L.;
,ciu E r-_.

. Several years ago 1 made a very modest
start in this direction. See "Cross-branching
in Bivalent Programming," MSRR no. 331,
GSIA, Camegie-Mellon University, March

2. Some of the types of phenomena
which occur in this setting were noted in
"Treeless Searches," by C.E. Blair and the
author, MSRR no. 396, CSIA, Carnegie-
Mellon University, October 1976.

3. A few representative papers are: C. Piper
and A.A. Zoltners, "-..,,. Easy Postopti-
mality Analysis for Zero-one Programming,"
Management Science 22 (1976), pp.
759-765; A.M. Geoffnon and R. Nauss,
"Parametric and Postoptimality Analysis in
Integer Linear Programming," Management
Science 23 (1977), pp. 453-466; and L.A.
.'1...-, "Integer Programming Duality:
Price Functions and Sensitivity Analysis,"
Mathematical Programming 20 (1981), pp.

4. See our paper, "The Value Function of
an Integer Program," to appear in Mathe-
matical Pr ,r.;.iiniiii. W -i. 's article refer-
enced in footnote 3 also has an emphasis on
conceptual structure.

5. See, for example, the paper by S.
Zionts, "Integer Linear Programming with
Multiple Objectives," July 1975, State
University of New York, Buffalo, N.Y.

6. The "bible" for this area is the book by
M.R. Garey and D.S. Johnson, "Computers
and Intractibility: A Guide to the Theory of
/ '"-Completeness," W.H. Freeman and Com-
pany, San Francisco, 1979 (paperback).
The P versus NP classifications are very
significant for conceptual analysis, although
they do not seem to conform to our intu-
itive concepts of "tractible" and "intract-
ible" problems. The Simplex Method, the
mainstay of mathematical programming, has
no polynominal bounds. Khachian's recent
polynominal algorithm appears to be much
worse than the Simplex. While the classifica-
tion of P versus NP (versus all other heir-
archies as well!) is one of the problem and

not a specific algorithm for it, the view
which equates I.. ...1 ..... ,. 1 (worst-case)
hounds to intractibility is clearly tied to the
assertion that a nonpolynomial algorithm is
bad (or, in any case, worse than a poly-
nomial one). That assertion is false and
based on an a priori analysis that is far
removed from actual experience.

7. In my paper, "Bracketing Discrete
Problems by Two Problems of Linear
Optimization," (Operations Research Verfa-
hren, XXV, 1977, pp. 205-216, Anton
Hain publisher), I showed that a natural
question of linear programming sensitivity
analysis could be I'-hard. The NP sets are
usually associated with integer .r.. r.ii Ii",.
More recently, in an A \ '; abstract with
( I.ih.r Blair, "Computational Complexity
of Parametric Programming," we will an-
nounce several more results, including
parametric linear problems which are poly-
nominal, parametric linear problems which
are exactly as hard as their integer counter-
parts, and parametric integer problems
which do not leave NP. Moreover, the
classification of a parametric problem can
depend on how it is presented. There are
also parametric problems that require
exponential space. These are initial results in
a problem area which, I believe, merits a
systematic development.

8. A paper from that period is "Discrete
Optimizing Solution Procedures for Linear
and .-WIn. r Integer Programming Prob-
lems," by S. Reiter and D.B. Rice, Manage-
ment Science 12 (1966), pp. 829-850. A use
of this approach for purposes of conceputal
analysis occurs in "Allocating Indivisible
Resources Affording External Economics or
Diseconomices," by S. Reiter and G.R.
Sherman, International Economic Review 3
(1962), pp. 108-134; and there are more
recent related economics papers as well (see
e.g., 1976 Econometrica).

9. "Measures of the Nonconvexity of Sets
and the Shapley-Folkman-Starr Theorem,"
Mathematical Proceedings of the Cambridge
Philosophical Society 78 (1975), pp. 443-
436. The "implicit" sampling technique is
simply to generate points in accordance with
the probabilistic processes studied by
Cassel, since random points will realize the
expected values or do better. Incidentally,
Cassel's proof is also the most economical
one available in terms of exposition and
contains some sharpening of the original
result as well. O

.,A ir'i I. .; 41CAL PROGRA "i P. NG
The Council of the Mathematical
P .1...' .inIM Society has unanimously de-
cided that it will be desirable for the Society
to obtain the benefits that are uniquely
available to professional societies organized
as tax-exempt not-I.,, l-r.lii corporations.
Some of these are: (1) The ability to solicit
institutional :. !iiir ,ili from Universities
and Corporations throughout the world, and
the ability to carry on other fund raising
activities; (2) Limitation of the Society's
legal liability to the assets of Society, rather
than being unlimited as is now the case; (3)
Better .,r .,.ii .,li.... of the Society's internal
operating procedures.
\1,,-! international scientific societies
comparable to ours are incorporated entities,
for these reasons.)
Consequently, under the Councils
direction the Mathematical Programming
Society, Inc. has been organized under the
laws of the state of Delaware in the U.S.A.
It is anticipated that the final steps of this
re-organization will take place in the Fall of
This re-organization will in no way
affect the Society's professional activities
nor its Constitution. It is, however, required
by law that the Constitution be supple-
mented by a set of By-Laws which spell out
internal operating procedures, primarily with
regard to disbursements by the Society.
Members of the Society who wish to
comment on this re-organization or obtain
a copy of the Articles of Incorporation and
By-Laws may do so by writing, prior to
August 31, 1981 to the Chairman of the
Society, Professor Jean Abadie at 29,
Boulevard Edgar-Quinet, Paris 14 FRANCE.

This public document was promulgated at a cost of
$426.15 or $0.61 per copy to inform researchers in
mathematical programming of recent research

Newsletter of the Mathematical Program-
ming Society
Donald W. Hearn, Editor
Achim Bachem, Associate Editor
Published by the Mathematical Programming
Society and Information Services of the
College of Engineering, University of Florida.
Composition by Lessie McKoy, and Mech-
anical Production by Dick Dale.


Puy-de-D8me, France

Seventy-two participants, mainly from
France and West Germany but also from
nine other countries, attended the Confer-
ence, "Optimization: Theory and Algo-
rithms" held in CONFOLANT, March
The Scientific organization was direct-
ed by J.-B. Hiriart-Urruty (Clermont-Ferrand
II), W. Oettli ,'l.ioII ,in) and J. Stoer
(" ,',,,,h ,r..'
Thirty-five papers on theoretical and
applied topics were presented in eight half-
day sessions. A proceedings will he published
in an international series which is, as yet, not
definitely fixed.
-J.-B. Hiriart-Urruty


Approximately sixty participants re-
presenting nine countries attended the
Third Symposium on .\.Iil, 111.1,1ti Program-
ming with Data Perturbations held in Wash-
in,-i.to D.C. in May. The meeting was
directed by A.V. Fiacco, George Wash-
tington University.
Topics covered included parametric
programming, stability and sensitivity anal-
ysis in mathematical programming and
related problems. Contributions to the
theory were complimented by papers on
applications in business and economics. The
conference was technically rewarding and
socially pleasant. There will be a conference
proceedings of refereed papers edited by
A.V. Fiacco. A similar meeting is planned in
1982 in Washington, D.C.
Direct inquiries to A.V. Fiacco,
Operations Research Dept., The George
Washington University, Washington, D.C.
-S. Schaible


The Sixth Mathematical Programming
conference organized at Mftrafiired (Hun-
gary) took place between January 18-22,
1981. The Conference was organized and
sponsored by the Computer and Auto-
mation Institute of the Hungarian Academy
of Sciences (Chairman: A. Prekopa, Secre-
tary: Mrs. P. Turchanyi) and its site was the
Summer House of the Academy. The five

former meetings in this series t(
1973, 1974, 1975, 1977, 1979.
known mathematical program
participated and given talks at t
ences and everybody enjoys
atmosphere that one can expe
from the scientific and the soc
view. This time there were 80
of which 60 were from Hung;
from other countries. The .. .I
consisted of 27 lectures; and one
discussion on the problems of
practice. Many participants exp
views with great devotion and

A recent report, "Integer P
with a Fixed Number of Va
H.W. Lenstra, Jr., University of
(see Technical Report Sectio
address) has been cited in the A
issue of Science.
According to the article
Kolata, Lenstra's result represent
major advance in integer pr
Kolata quotes both Herbert S
and Richard Karp (Berkeley)
favorably impressed by the result
In response to an inquiry
Lenstra has provided OPTIMA
following abstract of his paper:
"It is shown in the paper
fixed natural number n there
nominal algorithm for the in
programming problem with n va
degree of the polynominal that
running time is an exponential fu

ook place in
Many well-
imers have
these confer-
the good
rience both
ial noint of

It appears that the practical, value of the
result is limited to small values of n. The
basic i ._1. l, of the method is a reduction
process for lattices in n-dimensional space."

Zeitschrift fiir Operations Research

participants, ZOR is a journal of Operations 1..
ary, and 20 search consisting of Series A: Theory, and
II. program Series B: Applications.
round table ZOR Theory publishes quality papers
theory and in operations research and related optimiza-
ressed their tion theory, including works on mathe-
enthusiasm. maticald : -r.-, .I ;,,_ dynamic programming
and optimal control, stochastic program-
A. Prekopa ming, discrete 1.1 -..I.,..,; graphs and
6,,,,,-6i4 network problems, game theory, stochastic
decision processes, inventory, ; -I.I.i.. and
reliability. ZOR Theory also welcomes
CE theoretical papers in economics and com-
rogramming puter science that are relevant to operations
riables" by research. ZOR Theory is published in En-
Amsterdam glish. All papers in the journal are refereed
n for full to ensure high quality. The waiting list for
pril 3, 1981 accepted papers is much shorter than in
most other operations research journals;
e by Gina most accepted papers are published within
ts a possible twelve months of their submission dates.
ogramming. Editor-in-Chief:
eart (Yale) Klaus Neumann, Karlsruhe
as being Institut fiir Wirtschaftstheorie und
t. Operations Research
y, Professor University of Karlsruhe
I with the D-7500 Karlsruhe 1, West Germany

that for any Editorial Board:
is a poly- E. Balas, R.E. Burkard, W. Dinkelbach,
teger linear K. Hinderer, P. Kall, B. Korte, W. Krabs,
riables. The EJ. Muth, H. Noltemeier, Q. Oettli, U.
bounds the Rieder, K. Ritter, J. Rosenmuller, S.
nation of n. Schaible, R. Schassberger, N. Schmitz.


(PRINT) Name
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This subscription is for my own use only.

The dues for 1981 are:
42 Dollars (U.S.A.)
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69 Francs (Switzerland)
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82 Guilders (Netherlands)

Please send this application with your dues to:
The Mathematical Programming Society
The International Statistical Institute
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--~--~-s`- I-
I----------- ------~





This Calendar lists meetings specializing in mathematical programming or one of its subfields in the
general area of optimization and applications, whether or not the Society is involved in the meeting.
(These meetings are not necessarily "open".) Any one knowing of a forthcoming meeting not listed here
is urged to inform the Vice Chairman of the Society, Dr. Philip Wolfe, IBM Research 33-221, POB 218,
Yorktown Heights, NY 10598, U.S.A; Telephone 914-945-1642, Telex 137456. *


July 6-17: Deterministic & Stochastic Scheduling: A study institute", Durham, England. Contact:
Prof. A. H. G. Rinnooy Kan, Econometric Institute, Erasmus University, P.O. Box 1738,
3000 DR Rotterdam, The Netherlands.
July 13-24: "NATO Advanced Research Institute on Nonlinear Optimization", Cambridge, England.
Contact: Professor M.J.D. Powell, Department of Applied Mathematics and Theoretical
Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, England. Sponsored
by the MPS.
July 20-24: "Eighth British Combinatorial Conference", Swansea, England. Contact: A.D. Keedwell,
Department of Mathematics, University of Surrey, Guildford, Surrey GU2 5XH, U.K.
August 24-28: "C081: Conference on Combinatorial Optimization", Stirling, Scotland. Contact:
Professor L. Wilson (C081), Department of Computing, Stirling University, Scotland, U.K.
August 24-28: "International Colloquium on Stochastic Programming", Koszeg, Hungary. Contact:
Bolyai Janos Mathematical Society, Budapest VI, Anker kov 1-3, H-1061, Hungary.
August 31-September 4: "Tenth IFIP Conference on System Modeling and Optimization", New York
City, U.S.A. Deadline for submission of abstracts, 15 February. Contact: 10th IFIP Confer-
ence, Polytechnic Institute of New York, 333 Jay Street, Brooklyn, NY 11201, U.S.A.;
telephone 212-643-2305.
September 8-10: "International Symposium on Semi-infinite programming and Applications", Austin,
Texas, U.S.A. Contact: K.O. Kortanek, Department of Mathematics, Carnegie-Mellon
University, Pittsburgh, PA 15213, U.S.A.
October 19-20: Second Mathematical Programming Symposium Japan, Kyoto, Japan. Contact:
Professor Toshihide Ibaraki, Department of Applied Mathematics and Physics, Faculty of
Engineering, Kyoto University, Sakyo-ku, Kyoto, Japan 606.
October 19-22: "International Symposium on Optimum Structural Design" (Eleventh Naval Structural
Mechanics Symposium), Tucson, Arizona, U.S.A. Contact: Dr. Erdal Atrek, Dept. of Civil
Engineering, Building 72, University of Arizona, Tucson, AZ 85721, U.S.A.


August 23-28: Eleventh International Symposium on Mathematical Programming in Bonn, Federal
Republic of Germany. Contact: Institut fuir Okonometrie und Operations Research Universitat
Bonn, NassestraBe 2, 5300 Bonn 1, Federal Republic of Germany; Telex 886657 unibo b,
Telephone (02221) 739285. Official triennial meeting of the MPS. (Note: The International
Congress of Mathematicians will be held August 11-19 in Warsaw, Poland.)

Substantial portions of regular meetings of other societies such as SIAM, TIMS, and the many
national OR societies are devoted to mathematical programming, and their schedules should be

-~~~B-~ *.; :i.r


College of Business and "'lanpur ir.".
University of Maryland
College Park, Maryland 20742

Assau and Golden, "A Categorized Bibliography of Survey Articles
in Management Science and Operations Research," 81-001.
Provan and Ball, "The Complexity of Counting Cuts and of Com-
I.!,i. ii, i Probability that a Graph is Connected," 81-002.
Golden, Assad, Bodin, Ball and Dahl, "Listings and Documentation
for Selected Network Optimization Computer Codes," 81-003.
Gass and Joel, "Concepts of Model Confidence," 81-005.
Ball, Bodin, Golden, Assad and Stathes, "A Stratgic Truck Fleet
...., Problem Analyzed By a Routing Heuristic," 81-006.
Ball, Bodin and Dial, "A Matching Based Heuristic for Scheduling
Mass Transit Crews and Vehicles," 81-007.
Gass, "Validation and Assessment Issues of Energy Models," 81-008.
Stewart, "New Algorithms for Deterministic and Stochastic Vehicle
Routing Problems," 81-009.
Golden and Wasil, "A Curve-Fitting Experiment in Estimating
Optimal Solution Values to Traveling Salesman Problems," 81-011.
Ball and Provan, "Calculating Bounds on Reachability and Connect-
edness in Stochastic Networks," 81-012.
Ball and Provan, "Bounds on the Reliability Polynominal for Shell-
able Independence Systems," 81-013.
Ball, Bodin and Golden, "Large Scale Network ., .n'raln. and
Applications," 81-015.
Golden and Keating, "Network Techniques for Solving Asset
Diversification Problems in Finance," 81-017.
Golden and Keating, "On Simplifying a Network Model for Cash
Flow Management," 81-019.
Assad and Golden, "PERT," 81-021.

Department of Mathematics
Mathematisch Institut
Roetersstraat 15
1018 WB Amsterdam

H.W. Lenstra, Jr., "Integer Programming with a Fixed Number of
Variables," Report 81-03.

Department of Mathematics
D-5000 Cologne, West Germany

H.Hamacher, "On a Class of Easily Solvable Optimal Co-Circuit
Problems in Regular Matroids," 80-15.
R. Euler, "Augmenting Paths and a Class of Independence Sys-
tems, 80-16.
B. Neng, "Zur Erstellung von Optimalen Triebfahrzeuglauf-
planen," 80-17.
R. Burkard and U. Fincke, "On Random Quadratic Bottleneck
Assignment Problems," 81-2.
R. Burkard and U. Fincke, "Probabilistic Asymptotic Properties of
Quadratic Assignment Problems," 81-3.
R. Burkard, H. Hamacher and J. Tind, "An Abstract Duality
Theory in Mathematical Programming," 81-4.

Mathematics Research Center
610 Walnut Street
Madison, WI 53706

Roland Zielke, "Elementary Proofs of an Inequality for r..
Functions for n 5," No. 2113.
C. Conley, "The Behavior of: ril,. ...il Symmetric .. .'.1,.,] Near
Infinity," No. 211.7.
Emmanuele 1)iBenedetto, "Continuity of Weak Solutions to Certain
,,.,. l Parabolic Equations,"No. 2124.
George Miel, "An Updated Version of the Kantorovich Theorem for
Newton's Method," No. 2125.
Nira Dyn and Warren Ferguson, "Numerical Construction of
Smooth Surfaces From Aggregated Data," No. 2129.
Ronald J. DiPerna, "Finite Difference Schemes for Conservation
Laws," No. 2139.
S. -P. Han, "Least-Squares Solution of Linear Inequalities," No.
Dan Amir and Zvi Ziegler, "Relative Chebyshev Centers in Normed
Linear Spaces, Part II," No. 2143.
Peter A. Markowich, "A Theory for the Approximation .i ..l I... i-
of Boundary Value Problems on Infinite Intervals," No. 2146.
O.L. Mangasarian, "Least-Norm Linear Programming Solution as an
Unconstrained Minimization Problem," No. 2147.
Guang-Chang Dong, "Data Smoothing," No. 2151.
Peter A. Markowich, 'i ,..n'ii', Problems on li,,.,.' Intervals,"
No. 2157.
Carl de Boor, S. Friedland and A. Pinkus, "Inverses of Infinite ..
Regular Matrices," No. 2159.
Carl de Boor and Allen Pinkus, "A Factorization of Totally Positive
Band Matrices," No. 2163.
II i....I-, Fujiwara, "Morse Programs: A Topological Approach to
Smooth Constrained Optimization," No. 2169.
C.W. Cryer, P.M. Flanders, D.J. Hunt, S.F. Reddaway and J. Stans-
bury, "The Solution of Linear Complementarity Problems on an Array
Processor," No. 2170.
Cu Duong Ha, "A Decomposition Method and its Application to
Block Angular Linear Programs," No. 2174.
Okitsugu Fujiwara, "Morse Programs: A Topological Approach to
Smooth Constrained Optimization II," No. 2176.
Shih-Ping Han, "Solving Quadratic Programs by an Exact Penalty
Function," No. 2180.

Faculty of Mathematics
Department of Combinatorics and Optimization
Waterloo, Ontario, Canada N2L 3G1

Mustafa Akgul, "Ellipsoidal Algorithm: Khachiyan's I i... '
Mustafa Akgill, "Solving Convex-Concave Games via Ellipsoidal
Algorithm," CORR 81-16.
Mustafa Akgiil, "On Convex Programming via Ellipsoidal Algo-
rithms," CORR 81-17.
Mustafa Akgiil, "On the Work of Judin-Nemirovskii on the
Ellipsoidal Algorithm and a Proof of Khachiyan's Result," CORR 81-8.
Mustafa Akguil, "On the Shor-Khachiyan Algorithm," CORR 80-50,
Rev. 12/80.
Mustafa Akgiil, "An Ellipsoidal Algorithm Solves Some Well-known
Hard LP and LCP Problems Almost Instantly," CORR 80-51.



---- ---------



Department of Operations Research
D-5300 Bonn, West Germany

J. Araoz and E.L. Johnson, "Polyhedra of Additive System Prob-
lems," WP 80160-OR.
L. Butz, "Connectivity in General Designs with two Blocking
Factors, "(extended abstract) WP 80162-OR.
E.L. Johnson, "Characterization of Facets for Multiple Right-hand
Choice Linear Programs," WP 80162-OR.
B. Korte and R. Schrader, "On the Existence of Fast Approxima-
tion Schemes, "WP 80163-OR.
W.R. Pulleyblank, "The Matching Rank of Halin Graphs," WP
A. Bachem and M. Grotschel, "Homogenization of Polyhedra,"
WP 80166-OR.
E.L. Johnson and M.W. Padberg, "Degree-two Inequalities, Clique
Facets, and Biperfect Graphs," WP 80167-OR.
A. Bachem and B. Kdrte, "Primal and Dual Methods for Updating
Input-Output Matrices," WP 80168-OR.
D.A. Holton and M.D. Plummer, "Cycles Through Prescribed and
Forbidden Point Sets," WP 80170-OR.
D. Naddef and W.R. Pulleyblank, "Ear Decompositions of Elemen-
tary Graphs and G (F2)-rank of Perfect Matchings," WP 80171-OR.
G. Cornuejols and W.R. Pulleyblank, "The Travelling Salesman
Polytope and [0,2 -Matchings, "WP 80172-OR.
Institute fur Okonometric und Operations Research: "Annual
Report 1980" WP 81173-OR.
R. Schrader, "Ellipsoid Methods," WP 81174-OR.
L. Lovasz, "Bounding the Independence Number of a Graph,"
WP 81175-OR.
M. Grotschel, L. Lovasz and A. Schrijver, "Polynomial Algorithms
for Perfect Graphs, "WP 81176-OR.
B. Ki'rte and R. Schrader, "Can the Ellipsoid Method be Effi.
cient?" WP 81177-08.
L. Butz, "Uber die Zusammenhangseigenschaft in Versuchsplanen
mit Mehrfacher li.. lit Inl Eine Kombinatorische Analyses," WP

Department of Operations Research
Budapest IX, Hungary III

P. Kas and J. Mayer, "A Reduced Gradient Approach to the Non-
linear Network Problem," MO/1.
I. Deak and B. Bene, "Random Number Generation: A Bibliog-
raphy," MO/5.
M.Bir6, "Efficient Method Applying Incomplete Ordering for
Solving the Binary Knapsack Problem," MO/7.
W.F.A. Aighe, "Quasi Barrier Method and Optimality," MO/12.
G. Keri, "On the Minimization of the General Entropy Function on
a Convex Set," MO/16.
E. Boros and A. Sebo, "Approximative Solution of Linear Program-
ming Problems with the Modification of Khachian's Algorithm," MO/19.
G. Meszaros and B. Vizvari, "Production Control in One of the
Hungarian Iron Works," MO/19.
I. De'ak, J. Hoffer, J. Mayer, A. Nnmeth, B. Potecz, A. Prekopa and
B. Strazicky, "A Short Description of the Optimal Daily Scheduling of the
Electricity Production in Hungary," MO/20.
H. Bernau and E. Halmos, "Dimensioning of Statistically Indeter-
minate Lightweight Strucutres of Complex Stress on the Basis of Min-
imum-Weight Conditions," MO/21.
P. Kelle, "Safety Stock for Random Delivery Process," MO/22.

1 Journal/ & /tudiei

Volume 20 No. 3

M. Christofides, A. Mingozzi and P. Toth, "Exact Algorithms for the
Vehicle Routing Problem, Based on Spanning Tree.and Shortest Path
M. Frank, "The Braess Paradox."
J.K. Ho and E. Loute, "An Advanced Implementation of the
Dantzig-Wolfe Decomposition Algorithm for Linear Programming."
J. Flachs, "Global Saddle-Point Duality for Quasi-Concave Pro-
grams. "
J.-S. Pang, "A Unification of Two Classes of Q-Matrics."
M.J.D. Powell, "An Example of Cycling in A Feasible Point Algo-

VOI.IA1L 21 No. 1

D. Granot and G. Huberman, "Minimum Cost Spanning Tree
E. Balas and N. Christofides, "A Restricted Lagrangean Approach to
the Traveling Salesman Problem."
A.H. Wright, "The Octahedral Algorithm, a New Simplicial Fixed
Point Algorithm."
V.P. Grishuhin, "Polyhedra Related to a Lattice."
G. Gunawardane, S. Hoff and L. Schrage, "Identification of Special
Structure Constraints in Linear Programs."
K.H. Haskell and R.J. Hanson, "An Algorithm for Linear Least
Squares Problems with Equality and Nonnegativity Constraints."

VOLUME 21 No. 2

J.F. Maurras, K. Truemper and M. Agkul, "Polynomial Algorithms
for a Class of Linear Programs."
S. Erlander, "Entropy in Linear Programs."
D.P. Bertsekas, "A New Algorithm for the Assignment Problem."
Ph. Toint, "A Note About Sparsity Exploiting Quasi-Newton
R.B. Myerson, "An Algorithm for Computing Equilibria in a Linear
Monetary Economy."
M. Kojima and R. Saigal, "On the Number of Solutions to a Class
of Complementarity Problems."
B. Villarreal and M.H. Karwan, "Multicriterion Integer Programming:
A (Hybrid) Dynamic Programming Recursive Approach."
B. Benveniste, "One Way to Solve the Parametric Quadratic Pro-
gramming Problem."
L. Brosius, "Comment on a Paper by M.C. Cheng."
V. Von Hohenbalken, "Finding Simplicial Subdivisions of Poly-
G.W. Stewart, "Constrained Definite Hessians Tend to be Well

VOLUME 21 No. 3

J.Tind and L.A. Wolsey, "An Elementary Survey of General Duality
Theory in Mathematical Programming."
W.I. Zangwill and C.B. Garcia, "Equilibrium Programming; The Path
Following Approach and Dynamics."
U.M. Garcia-Palornares and A. Restuccia, "A Global Quadratic
Algorithm for Solving a System of Mixed Equalities and Inequalities."
J.M. Borwein, "Direct Theorems in Semi-Infinite Convex Program-
E. Rosenberg, "On Solving a Primal Geormetric Program by Partial
Dual Enumeriation."
D.M. Murray and S.J. Yakowitz, "The Application of Optimal
Control Methodology to Nonlinear Programming Problems."
R. Zielinski, "A Statistical Estimate of the Structure of Multi-
Extremal Problems."


Bill Cunningham (Carleton University) will spend the year 1981-82 at the Institute for
Operations Research, University of Bonn. .Siegfried Schaible was awarded a McCalla
Research Professorship by the University of Alberta for 1981-82.. .Henri Theil, formerly of
the University of Chicago, will become McKethan-Matherly Professor of Econometrics and
Decision Sciences at the University of Florida starting Fall 1981 .Horst W. Hammacher,
formerly of Cologne, and Suleyman Tufekci formerly of Syracuse, have joined the Industrial
and Systems Engineering Department, University of Florida. .The June, 1981 issue of
Scientific American contains a feature article, The Allocation of Resources by Linear Pro-
gramming," by Robert G. Bland (Cornell). This amply illustrated article covers both applica-
tions and computational aspects of LP, including the ellipsoid algorithm, at an introductory
level. .From Madison, Wisconsin, we have the following items: S.-P. Han (Illinois) will
spend a second year at MRC, Steve Robinson will be Chairman of Industrial Engineering,
and Bob Meyer will be Chairman of Computer Science. Academic Press has indicated that
Nonlinear Programming 4, consisting of papers presented at the July, 1980 NLP 4 Sympo-
sium, will be published by July 29, 1981.. .A.C. Williams (Mobil) is the new MPS liaison
representative to ORSA. .Mike Todd (Cornell) has been awarded one of twenty Sloan
Research Fellowships in Mathematics for 1981. The award is for two years. Deadline
for the next OPTIMA is October 15, 1981. *


In accordance with the Constitution of
the Society, the triennial elections of offi-
cers will be held in March, 1982. All offices
will be on the ballot: Chairman, Treasurer,
and four Council members-at-large. The
Nominating Committee (Jean Abadie, Chair-
man) welcomes suggestions for consideration
from the membership. Naturally, before
anyone is proposed it should be determined,
if possible, that the potential candidate is a
member in good standing of the Society and
is willing to run. It is perfectly appropriate
for a member to propose himself as a candi-
The Nominating Committee will circu-
late the proposed names among the Council
of the Society, which will choose the candi-
dates. In addition, any person nominated in
writing by at least six members of the
Society, and who agrees to stand, will
be placed on the ballot.
Suggestions should he sent to the
Chairman of the Society (Professor Jean
Abadie, 29 Boulevard Edger-Quinet, Paris
14, France) or to the Chairman of the
Executive Committee (Dr. A.C. Williams,
Mobil Oil Corpoaration 150 East 42nd
Street, New York, N.Y. 10017) by January
31, 1982. 0

303 Weil Hall
College of Engineering
University of Florida
Gainesville, Florida 32611

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