Title: Optima
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00090046/00002
 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: October 1980
 Record Information
Bibliographic ID: UF00090046
Volume ID: VID00002
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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OCTOI'- ,11- 1980


Walt-er Mt-rray

Algo!i ~i ~ l-" The Influornice of Flinite
F.-i a -I at." T
~yr I ac

Almost all substantive problems in
appalled lmathellatics require the use of a
co(lllputer for their solution. An article in1
the April 1980 edition of the SIAMl News-
letter likenedl the introduction of the co(m-
puter into applied imatlhicmatics with thei
discovery of relativity and q(uantumin mech-
anics in theoretical physics. Modern co-
pulting l .....e .. has had the revolutionary
effect of changing the einphasis of mauchl
applied tiat.hcin alics from transforining a
problems into its most compact fomple to
expressing a problem in its moist comlputablet

In theoretical physics, ti e process of
change lasted some forty years about the
length of time to retirement ol of a Ph.D.
graduating prior to Einstein's work. On such
a time scale, the computer revolution,
although advanced, is still not complete. In
this article, mny intention is to illustrate
where, in my opinion, improvements are
still necessary in recognizing the role of the
computer in the study of mathematical
....: .miinii : algorith ll s.
Since computers will obviously be,
lsed to inmpleient any algorithm, it would
-cicn tllhalt those who devise and studv
algorithms could not fail to consider thei
coipu national aspects. however, such ne-
glect is sufficiently cornllni to cause some
onlceriI. Curiously, even algorithmis pre-
sented in a pseudo-progralnoing style
often fail to take full account of t11 basic
limitations of computers.
The explanation for this situation is
not entirely clear. Possibly the effects of
Ill-iiiI.-lini.. an algorithmn on a computer
are considered ni. !l(ii.I', or the work
required to .1,'.li.p an implementation is
i'i' as routine. In my view, both these
altitudes are erroneous, and often lead to
unsound algorithmls. In fact, many believe
that implementation of an algorithm is any-
ii.'- but routine; for example, Watts and
Shanipine I i'. i state that "...how a
method is implemented may be more
important than the method itself". The

purpose of this article is not to argue the
merits of devising algorithms as i'.I....'- to
implementing them. Rather, I believe that
the two processes should he conceived as a
whole. In some cases, advantage can be
taken of finite-precision arithmetic to tlhe
extent that it is p..-- .Ii to define algorithms
that have no mathematical counterpart for
example, inverse iteration in tlie determtina-
tion of eigenvectors.
Because almost all algorithms for
nonlinear optimization are iterative, it is
often supposed tllat alny errors introduced
by computation arc somehow sell-correcting.
However, tile conjugate gradient algorithmn
clearly ill'- i, .i.. the fallacy of, this view-
point. Tle ....in I. gradient lumethod was
first proposed for solving positive definite
linear systems in I I at a time when it was
believed that. computational errors in direct
methods such as Gaussian elimination would
necessarily he overwhelming. By contrastt.
the ..n i l.1 method proceeds bV coiln-
puting a sequence of "inlprovillng estimates
of tlhe solution, and is thus iterative in
nature. Witi exact aritlimetic, lthe algorithin
will terminlate- with tlih exact solution in a
finite nuntmber of' iterations. However, in
practice it, is not difficult to construicl
exaImples for which the ..-iP... I. gradient
method requires rany tirnes the lnumlber of
iterations that would bei taken v the exact
procedure. Moreover, the difficulty dots nlot
arise purely from thle iterative nature of (ith
algorithmn. Certain quasi-Newton methods
are iathemnatically equivalent to the con-
jugate gradient algorithn, yet will convetrge
to the solution in the expected number ofd
The computational steps of algorithms
as d..-- ,l,.,- in research papers are rarely
defined completely or even unambiguously.
This olnission in itself is not necessarily
cause for concern, since the authors may
intend to study properties of the algorithms
that are unaffected by the miissing parts.
Many authors undoubtedly believe that the
trappings associated with clearly defined
To page 3


The Constitution of the Mathematical
!',, .,ii, ,,i:. Society requires the retir-
ing Chairman to write an account of the
activities of the Society during his term.
While this requirement has not always
heen observed as carefully as others, it is
a good one, and our ., I-. I. ,- is the
right place for it.
My term of office ended on August
3 \; e are all pleased to welcome the
new Chairman, Jean Abadie, who will
serve through August, 1983, and Man-
fred P..li. . who will serve as Treasur-
er for the same term, replacing Freerk
Lootsma. (The members-at-large of the
Council, Mordecai Avriel, Michael Held,
Ailsa Land, and Alex Orden, hold office
1'17'I .:., and the retiring ( lI i ii l.,
serves as Vice-Chairman until 1982. Al
Williams continues as ( l i, n.i.,i of the
Executive Committee.)
Rv its own definition, the Mathemati-
cal Programming Society is an interna-
tional organization dedicated to the pro-
motion and the maintenance of high pro-
fessional standards in the subject of
mathematical programming. The last se-
veral years' activities of the Society show
a number of accomplishments to that
end. New projects have been undertaken
and some traditional tasks have been re-
organized as a result of what has been
learned during the Society's first ten
This Newsletter is one of the new
things. Michael Held, ( l..... i- i i, of the
Society's Publications Committee told the
story of its founding in the first issue.
We know it will be of real service to the
mathematical programming community.
Last year the Society inaugurated the
first Prize to be given in the broad field
of mathematical programming: the Fulk-
erson prize, for outstanding papers in the
area of discrete mathematics. It is spon-
sored jointly by the Mathematical Pro-
gramming Society and the American
Mathematical Society. The first awards
To page 2

I.: I '. !', : T . .

were made in Montreal in 1979 at the
Tenth International Symposium on Math-
ematical Programming.
This Spring the Society concluded ar-
rangements with the Society for Industri-
al and Applied Mathematics for the
George B. I nI I ., Prize in mathematical
programming 'for original work, which
by its breadth and scope, constitutes an
outstanding contribution to the field.'
We expect the first award of the Prize to
take place at the Eleventh Symposium in
mathematical programming in r,,,, n in
1982. The Prize is fully described in the
first issue of this Newsletter.
Every year there are important meet-
ings around the world dedicated to math-
ematical ,... i-,. ,, ,._ The Society be-
gan offering sponsorship to any properly
constituted conference related to mathe-
matical .,'. ,ihnl i or one of its sub-
fields. The Society requires only that
the meeting have a scientific or educa-
tional purpose, rather than that. of profit-
,,I..,,. that it be open to all members of
the Society so far as available space or
resources allow, and that there be oppor-
tunity to solicit membership in the Socie-
ty at the --. ii'.. We can provide mail-
ing lists or labels of the Society member-
ship, space in its publications for an-
nouncements, facilities for publicity at
other sponsored meetings, and the loan
of some money. Any one interested in
such sponsorship should contact the
Chairman of the Society or the Chairman
of the Executive Committee. -;.:. -i.ii,.
for other modes of support of mathemati-
cal programming are also welcome.
Under this program the Society spon-
sored these meetings in 1980: 'Workshop
on polynomial-time algorithms for linear
programming', New York City, February;
'Workshop on Large-scale Linear
Programming', Laxenburg, Austria, June;
'', workshop in Numerical Methods for
System Engineering Problems', Lexing-
ton, Kentucky, June; and 'Nonlinear Pro-
gramming Symposium 4', Madison, Wis-
consin, July. In 1981 it will sponsor the
four meetings so listed in the MPS Cal-
endar in this issue.
The Membership Committee was
formed in 1979 with R.W. Cottle as
( i 1.iaii.' (now John Mulvey). Having a
substantial membership benefits the Soci-
ety not only in enabling it to speak with
To page 4

1"AW '.. k.-,, U n:

The Coummittee on Algorithms has
heen quite active the last few months. The
latest issue of the COAL Newsletter was
mailed in August to all members of tlhe
Mathematical PI, ... ..p,,t Society and all
1I,.. ..- of COAL"'. If, for sonim reason, you
do not receive this newsletter within thel
next month, please contact me, so that this
error can he corrected. Also, proceedings of
t.he special session jointly sponsored by
(COAL and the (Coplluter Science Technical
Section of ORSA was published in the April,
1980 issue of I' 1\P. The proceedings
entitled "Rece'nt and Future Advances ill
lathemltatical PIrograntmming Software" in-
clude papers written by all major mathe-
matical programlming system developers.
(Copies of this issue are available to "friends"
of COALI, free oif charge, wlile supplies last.
Any requests for this issue should be sent to
Hichard P. ('N'ill, I)epartment of ncergy,
Division of (il and Gas Analysis, Wash-
ington, D.C. _("' -I I .
In tle near future, all members of the
MPS and .. ...I.'" of COAL will he receiv-
ing a survey requesting information about
M'P Codes. This survey will be used to
compile a list completee with characteristics)
of the mathematical program ing software
available throughout the world. TheI Cotm-
mittee intends to sort and .11,o. all informa-
tion received and to update this inform matiion
regularly. We believe this information is
useful to a wide cross-section of the sci-
entific community and( intend to maintain
this information service in the future. The
results of such an effort can only be success-
ful if we liave the cooperation of the entire
nlathematical programming community. So
please help us by completing and returning
thllis survey form.
At lthe ORSA/TIMS meeting in Col-
orado Springs, COAL will sponsor a session
chaired by Patsy B. Saunderrs in which the
following talks will be presented:
"Tlesting mathematical software which

solves nonlinear systems of equations," K.L.
"FT'..l.iiii:. new data structures for
I,,.-.,ll/il. network optimization," Ired
(;lover and anldv (;lover
"A study of redundancy in Linear
P,,.i: iii.. ii.Ii,," M/ark Karwan, Vahitd Lotfi,
Jan Telgen and Stanley Zionts
"Computational experience with the
ellipsoidal algorithm for Linear :i.....
in ol.." John Barrer and an Telgen
This session will take place in the
Academy Room of the Broadmoor Hotel
at 9 10:45 on Monday Nov. 10.
On January 5 6, 1981, a conference
sponsored ly C(OAL on Testing and Valid-
atinlg MP Algorithms and Software will
he held in Boulder, Colorado. Ir. ,,i,.
1.'...11. and Prof. Darwin Klingman will
present keynote addresses. Elleven sessions
have been scheduled. This conference ill
bring together both developers and users of
optinization software as well as researchers
from a variety of other disciplines who have
performed computational analysis in order
to further develop Inmethodologies for con-
ducting software evaluation. I'Tose inter-
ested in attending this meeting should
contact Prof. Jolin NM. Mulvey, Princeton
University, Princetonl, .New Jersey i,-.40.
Finally, Doug : I .. ha s been invited to
chair a session on computational testing of
mathematical programoning software at the
"Optiimation Days, 1981" meeting to be
held in Montreal on May 13 -14, 1981. Any-
one interested in presenting recent computa-
tional results should contact Doug Shier,
National Biureau of Stanidards, (Center
for Applied M'athcmatics, Washington, ).C.

In I...,,. I encourage each of you to
inlform me of research being done bv you or
your colleagues in the area of development
andl testing of optimization software that
might be highlighted il the C)OA News-
letter. The I'. i..i for the next issue is
November 15, 1980.

K-arla Hoffnlan
Editor, COAL Newsletter

Winter -.. j.,nai.ry 1
ipin Issue March I

procedures are -1'.' il, '1 to the theme of
their work. 1' ii!h. I .riili. ii is a noble goal,
it should not be achieved at the price of
l;ii i. I ; ,Iti; im portant detail.
To illustrated this point, consider tlie
study of the asymptotic rate of convergence
of Ne wton's iretho( d when lte matrix oft
second derivatives is approximated by
forward differences of tlhe gradient, It is
important to note first that the eventual
rate of covergeit c of any iterative algorithmll
oni a computer is at best linear, ,,,II. -- of'
the properties of its exact malleniaticalI
counterpart. In fact. a limit is inevitably
reached beyond which the solution cannot
be further refined (otherwise, solutions ofl
arbitrarily high accuracy could be obtained).
A superliniar rate of convergence is typically
exhiitited in a seqluece of cormputed iterates
or only a few ilterations before .'1 .11..
In the case of tlie feis t illl r in,,i
Newton method, it can ie shown iathe-
matically that the convergence rate is linear,
with the factor of improvelenlt ... [ ...I i,, ,I
to tle size of the finite-difference interval.
'' has led to the suggestion that a super-
S rate of IIr mi;.,ii .ii can be acliieved
by reducing the fi,.-i..-lil. -I,, interval to
zero as the solution is approached.
Despite its theoretical justification, use,
of this strategy in ai implemented algonitini
is danigerous, and( fortluinately unnecessary.
II the finite-differencle interval is chosen
sensibly, the predicted linear rate of tonver-
sein1ce occurs only after improvement iln the
iolilion lias reached the level of ...... 1:,,
error. Moreover, prior to this stage, thle
finite-differencee algoritllin exhibits a quad-
ratic rate. of converlgence almost identical to
t.lhat of' Newton's method will analytic:
-second derivatives. It. is thus important to
establish tile effects of' rounding errors on a
rate of convergenc:e that is derived under the
assutlption of exact arithinetic.
,lil... I: L niuIch attention is devoted to
S, iir: convergence of algorithms, such
results are not always wui .... ,,, in practice.
example, global convergence can be
.I.... for the steepest descent algorithm
for unconstrained optimization under very
,ihi assumptions. However, it is well known
That this is a very inefficient algorithm.
Almost all proofs of convergence are based
on I ..ii i-- that some reduction in tile
function value occurs at each iteration. What
can h Tpi-,' inl practice with the steepest
descent and other methods is that the step
taken or the subsequent decrease in the
function value becomes i..:li:.,ill. with
respect to the machine precision, even at
points remote from the solution. Conse-
quently, tle change cannot be recognized
and the =.ilrr.l', sequence terminates.

The itctlre existence of a con vetrgence
proof' of' standard theoretical forili does n1ot
necessarily assure that the algorithm will
succeed. (Convergence proofs are oftell
extended by generalizing the (class of funlc-
tions or situations for which they apply.
It would be useful for research to lbe carried
out on extending proofs to lake account of'
the comillputational environment ill which tlih
algorithm il be applied. In essence, tile gap
between theory and practice needs to be
narrowed by developing a more sophis-
ticated theory.
Difficulty with the implemented ver-
sions of algorithms takes three distinct
formts: the algorithms may be inherently
unstable, instability may be induced, or the
conditioning of the problem may be exac-
erbated. The last two difficulties can lbe
avoided, although it is often far from obvi-
ous how to do so. The reader may wonder
why anyone would choose to implement anl
algorithm in other than the most stable
form. Unfortunately, unstable fornis of an
algorithm are usually more common than
stable forms; moreover, instability is often
related to closed-forli expressions.
An algorithm is said to be inherently
unstable, if tlhe steps ol' the procedure arei
prone 1o overwhelming computational error,
irrespective( of how they are implemented.
The error does not occur due to ill-condi-
tioning of the problem l or the solution,
but rather because of( the manner in which
the iterates are defined. Inherent instability
takes two forms: the errors may he inev-
itable, or they may occur by chance.
An example of inevitable error is
provided by some cutting-plane methods.
These .ii., oillns. solve a nonlinearly con-
strained optimization problem by trans-
f.] in: it into a sequence of linear i.l.... i ..,
ming sub-problems. As the method proceeds,
the solution of the linear program contains
at least two linearizations of the same
nonlinear constraint, unless thle number of
binding nonlinear constraints is equal to the
number of variables. Al,1111..!' the LP
constraints retain linear independence imath-
ematically, in practice there is ..-i..i!;
overwhelming computational errors ill com-
puting the LP solution.
The occurrence of chance error is
JIli-1i I. ..i byv an algorithm that requires the
determination of the ( I...I .I y factoriza-
tiol of an arbitrary symmetric niatrix.
The Cliolesky factorizatioln mayN= not even
exist unless tlie matrix is positive definite.
iMoreover, even if the factorization exists
for an indefinite matrix, there may be
catastrophic error in its computation. /I,,
error is not, however, inevitable because it
may happen that the relevant matrices are
always positive definite, or that no signif-
icant errors occur in forming the factoriza-
tion. Although such anl algorithms is inher-
To page 4

--i -

Since this is just tlli second issue of
OPTIMA. it might he 11 to repeal, some of
the ilnformilation about theli newsletter. Our
purpose is to make information about
progress in mathematical programming avail-
able to the wide-sprlad II' member-
ship. Toward tliat end we will publish a
calendar, technical report titles, ineeting
announcements, news from COAL, II lor
papers, etc. as well as brief items about tlle
activities of individuals and theiJr where-
abouts. Brief position announcement and
short course, anniouncemients will lbe included
for anominial fee ( 1).
In each issue of CIl'l I I\ we hope to
feature ani article of broad interest. In tlie
rirst issue w e had I inI ", ..ItI 's i. 1111 -...
. i-I... iiu, and in this issue we have Walter
"itrray's article. Contributions are invited.
Thle feature articles mav be historical, offer
perspectives on our field, .,_ .. i directions
for research, alld, ,_ il, be onl anlly topic
likely to be of interest to the membership.
Such articles will be edited, but not refereed.
If these articles, or others, provoke Letters to
the I'(ditor, we can start sulih a co(unn.
I'i very pleased to announce that
Professor Acbim In !... i-i,.. of thle universityy
of >onn,) will be (;!' I I'\'s Associate klditor.
He iI particularly be involved with reporl-
illg news rom ll I'urope. Items for Professor
Blachem should Ibe sent to:

Institute fiir Okonomniehrie und
Operations Research
liniversilv of Bonlli
Nassestrasse 2
L: .i, Bonlll I H D
Professor Bac:lien's contributions will
do much to enhance )OP'TIM1\A. ad they H 11
undoubtedly prove v apl'lroach thie Bonn rmeetlig in I'i _'.

-D)on Hlearn

J7,'," ,-'. a..--, "_-E" :=- ^-- -'-f -- iF$a,

Newsletter of lthe Mathematical Progranm-
rning Society
D)onald W. learn, Fditor
Acllim Bachiem,, Associate Editor
Published by the Mathematical Programmning
Society) and Information Services of the
College of l'n. ..... h 11. lniversitN of I .
Composition by Lessie McKloy, anld Mleclh-
anical Production iv byDick D)ale.

i LGCiL, iT. ,. .

enttly unstable, it. may elljov some: success onil
selected problems.
Induced instability may occur because
of the incomplete '.11 .m! ii.,i .li definition
of an algorilthm. For example, in some
methods the search direction is defined as
lie solution of a set of linear equations. This
calculation may be performed in various
ways, some of which are iunI.I-.I .II l unsta-
ble even for a well-conditioned system.
If a poor technique is used to solve the linear
system, the instability has been induced into
the I .,.;il,, because an alternative, num-
, ,ii. stable method could have been
used. Even when the author of an algorithm
specifies an unstable procedure for -..ilh .
a siub-probleni induced instability can be
avoided by substituting a numerically sound
,Exacrbation of tihe condition of a
Iiprobile can occur ill two foInrms. lOne is
illustrated by the i l I ..'wn iexalple of
formiill llhe "'normal' equations wt ll'
solving linear least-squares problems, which
occur in their own right and as sub-prolblemsi
withi methods for nonlinear 1east-squarcs.
ti'li e1 rro in tile sol ution of tlie normal
(eqiltios depends on tlhe square of tlh
condition number of thle Jacobian matrix. l'
tie i. i ...... 1 i ll ( uivalent solution 1is
o tiaiied instead via tlhe ()I factorization,
ithei tl I.e e irror in the solution depends on
lhe condi tion number of t he Jaoobian-
provided that the residual is zero. Even if llihe
residuals are pot zerot, t b accuracy of thie
solution obtained using (lte Q1 factorization
is close to that which would be obtained if
tile solution wiere computed inl infinite
'pr'ision after representing tihe original
problem itn finite precision. Tlalt is, tle
el'ffiec of tle error il rtlde solution due ati
error- inilroduiced ib computation is of tlse
-lesia order as tihe, ivitabl error introduced
b\ representing tle problem onl thle machine.
c A -il..rl, kind of error is not, strictly
i ;i,... all exacerbation of the condi-
tioning of the problem, but rather tile
introduction ofd error based liltheu codi-
lioning that could be entirely avoided.
This kind of error is illustrated by an early
technique for i- .t I ,... a qu., i .' l ....1
method for unconstrained i iforini..iili, to
problems with linear equality constraints.
The-idea is to choose a rank-deficient matrix
as tlhe initial approximation to the inverse
Hessian. /,ilh,,.1 i the null fi., of tlhe
constraint normnials does not change, at each
iteration the inverse Hlessian approximation
imust be updated in order to build lup curva-
ture information. Thus, thlie represenfa-
tion of a constant piece of information is
,1.,,io. ,. because it has been combined willth
the .1' "l.,.ii.. of another piece of

information tliat does vary. The conse-
quence is that unnecessary error is intro-
duced into the c.Inmit1' 1 search direction,
and here can be a substantial loss of 1.-.,-d.li
ity in the iterates. This type of error is not
the same as induced instability because the
error would be small if every part of the
problem were well conditioned. Ii ..... -,
this case dI .... froni the normal equation
example because the error that causes a loss
of feasibility can be made independent of
the conditioning of other parts of the
problem for example, by -i.. ir. separate
representations of the information concern-
ing curvature of the function and orthlog-
onality to the constraint normal.
Tlis article has presented only a brief
overview of one aspect of how til collputer
: ... tire suldy of algorithli s. A coni-
pjlte treratlmcint of thi s subject would require
consideration of many other complicated
areas, includill data structures and t(le
design of software.

cf rencie
I1 .A W atts and I. : I .....).... 1975 1, Th ,
/Art of JI ..o... a R~unge-KuIa cod: RK45,
paper presented at SIAV1 National meeting.
june 1975).

-r."'- \

Si; PORT. .. .

a louder voice on behalf of its members.
but in lowering the cost of services to the
membership. The work of the member-
ship Committee has increased the num-
her of members from 408 to almost 5(0,
the figure at which we will lie able to
purchase our journal at a reduced price
(see below).
A new agreement has been negotiated
with North-HIolland Publishing Compa-
ny, publisher of Mathematical Program-
ming and the Studies. It provides for
reductions of the member's price for the
journal when membership of the Society
exceeds 500, and a novel feature: sub-
stantially increased royalties to the Socie-
ty for new institutional subscriptions
which have come about as a result of the
Society's efforts. Thus, if your institu-
tion does not subscribe to Mathematical
-'; yo. i.,,,l;1,I.. you think it should, and
are successful in getting it to do so,
please inform Michael Held (IBM Sys-

teams .: .. ceh Institute, 205 East 42
Street, New York, NY 10017) so that the
Society can claim credit for it and ex-
press its gratitude to you.
Michel Balinski, founding Editor-in-
Chief. announced his plans in mid-1979
to resign his post as soon as a suitable
replacement could he found. We were
delighted to find Richard W. Cottle will-
ing to serve in this key position, which
he has done since January. He has im-
plemented a reorganization of the Edito-
rial Board aimed at reducing the editori-
al workload and speeding the handling of
manuscripts: Collaborating with the
Editor-in-Chief, Co-editors (presently
L.C.W. Dixon, B. Korte, and M.J. Todd)
can accept submissions and conduct all
dealings with authors.
Of course, the major regular event
was the Tenth International Symposium
o n .. I I I l .. 1, .i !' I ,,. ,,,l in I,. ,,
real in August last year, where 4.50 pa-
pers on all aspects of mathematical pro-
gramming were presented to 700 regis-
tered attendees. A new, successful fea-
ture of the program were the minicourses
in combinatorial algorithms, in pivotal
exchange methods, and multiple criteria
decision making. Organization of the
Symposium was assisted to a modest de-
gree by the newly formed Symposium
Advisor) Committee (Alex Orden, Chair-
man; now Jean-Louis Goffin). The Com-
mittee is charged with encouraging pro-
posals for sites for the International Sym-
posia, advising the Council on the choice
of site, assisting their hosts where possi-
ble, and setting guidelines for the
Society's role in these official meetings.
The Society will continue its practice of
giving the host committee charge of the
whole affair, but will arrange, at least,
for a reduced registration fee for mem-
hers of the Society.

After considering several proposals,
the Council of the Society chose Bonn,
Federal Republic of Germany, as the site
of the Eleventh International Symposium
August 23-28, 1982. It is not too soon to
begin the study of possible sites for the
Twelfth Symposium, which should be
held at a like time in 1985. The Sympo-
sium Advisory Committee welcomes all
suggestions about possible sites for future
meetings. Please address the Chairman
(Professor Jean-Louis Coffin, Faculty of
Management, McGill University, 1001
'-h r1.....I e Street West, Montreal, Que-
bee H3A 1GS, Canada). To page 5

,. ,, r )3RT . .

The fourth issue (August, 1980) of
the Newsletter of the Society's Commit-
tee on Algorithms has just appeared. As
editor Karla Hoffman says, 'The Commit-
tee on Algorithms has been rather active
the past six months...' Indeed, this valua-
ble group has been very active since its
formation. Please see its Newsletter, as
well as the Committee's column in this
and the previous issue of OPTIMA, for
more information.
it seems that the year will end with
the Society healthy financially as well as
morally. Projections of the state of the
treasury have encouraged the Council to
set the dues for 1981 at the same level
(in dollars) as for 1980, and in other cur-
rencies the dues should he about the
same, or lower. Of course this represents
a reduction of dues in real terms, We
i"'1" it will encourage members cheerful-
ly to pay when they receive their notices
in the near future, and, if you are not a
member, encourage you to make applica-
tion for 1981 -- if you have read this far,
then you should join us.

:'i,.li W olfe


Two research rolups oil inath' iatiali
progralinilnii ill Japall (onle inl the Toklyo
area chaired lvy iProfessor K. lone of Sait-
ania nlliversit alnd to l other inll te Kansai
area chaired by Professor T. lbaraki of
Kvoto L[IliversilJ[) lhave agreed to start
the annual Symnposia onl Mathemnatical
111 -_ to prollote research in, and
applications of, millnahelatical programminglii
in Japanl. The symposia will be lield in the
aultumnl of every year. inll tieTokyo area and
in thie K\ansai area alternately. Tutorial
lectures on recent advalices illn mlatihemiatical
prog-ralnliill II e11 delivered and contri-
buted ... on participants' original
works 11i be presented. Participation fromn
abroad is ilso, we(lcomlle.
Tlie first sympoil siulm 11 i l e ield
November 6-7, I'i at the Institutlle oil'
Statistical Mathematics in Tokyo. LecturTes,
and tutorials will be given iln tLe. following

sessions: Linear and ,,,iln,'u ii, -'. .i .1...,11.1-
claired by 11. IKonno, Cornbinational Opti-
inizationl cellired by T. i ... ', Applica-
tions chaired by S. Suzuki.
S;1.. interested are requested to
olltact Ithe oranilzin Ccommittee I' !i .... .. ,
Professor Mlasao Iri, University of Tokyo,
Bunkyo-ku, Tokyo, Japian 113) or tihe
Programnlne Committee, 1.......... Professor
Kaoru Tone,, graduatee Institute for IPolicy
Science, Saitama University, I- !n.. .. kubo,
U[rawa-shi, Saitama-ken, japan ).

VI. Iri

Conference ont
ALGOCii !!')I1
March 16- '* 1981

Tlet (Conlf'rellncl will ie heldl at Con-
folalli ( n i... I. i Ply-dc-l) i o i) Fra lnce
about ,'0 knil froi (JC ;ln lll.-werraid. It hlias
been organized by J.-B. Hiriarl-Urruty,
Uliiiversity of (lern-ont-'errand II,
Oettli, l iversilt Mannhlllcim, and J. Stoer,
Uiniversitit W.irzhurg. Forty rcsearcihers'
mllainly froill ]'1rance alndt \\cst (;e'tll er a y,
have been invited to speak oiln the latest
de velopments inll t the eory, algorithmls and
applications of optimization. lThe official
languages ofl the conference arc French alnd
For lllore in formnatioll and reoistratioi,
prospective participants should conltacl one
of tihe oranilizei's.

.-3I. Iliriat-lrrutys

IFOi: ;'81 HA'.i:URG, Gi IL ', \NY
JULY 20-24, 1981

Thel international F:ederation of Oper-
ational Research Societies (IFOiS) .,I
hold its 9thli INTE{NATI)\AI] T1'II AI,
(O)NI'lI I ( l in lanllburg, (nerllialny, oil
July 20-24. 1981.
'T1hio aimlls o IFORIS are the' develop-
inentl of Operational Researcll as a unified
science allnd its advancement in all nations of

the world. 1p) to now, 31 national (O
societies have becolle Member Societies of
IF'O)RS. In addition, 6 )O. societies, such as
the M them atical '. . ........... Society, are
associated will IFOR.S as Kindred Societies.
One series of sessions along several
others l, hle dedicated to tite theme of
F()ORS '81 which reads: Operational Re-
search in the Interest of International
Cooperation. in addition tohe mainstream
Sessions which are dedicated to ihe theme,
there .11 be Technical Sessions, National
Contributions Sessions, Contributcd p1.,
Sessions, .', ...I 1. '... and a special t;xibition
of colmlputer hardware allnd soft are.
Authors who would like to contriibutll
a paper shouhl subilmlit all abstract no later
than DecemblIer 15, 1i-'r to the ( 1
of the roIgraillne Comlnllittee: Prof. Dr.
Mlarce Roubens, Faculte' polyteclinique, Hlue
de lioudain 9, R-7000 MVons, Belgiumll.

H teiner lull. ,-Merl)aehli
I FOHS' 81 : Public Relations
Amn Loweniter I I


U.S. Department of Energy

The Mid-Ter Elnergy Market Model
(MEIMM) forecasts energy silllulies and prices for
the period 1985-1995. In addition to making a
l..11 ilandated annual forecast, we are
using the niodel for a comprehensive assessmentl olf
government interventions in tile energy market.
Thie model is also used for special studies of
proposed ..1 I ..... alt(] regulatory programs.

We are looking ior good analysts with at
background in operations research, economllics or
collmputler science whio would like to work in a
demlandiig atmosphere. Two types of people
would liav tllhe highest priority a fresli graduate
witli a bachelor's or master's degree, extensive
computer progranunlling experience, and some
knowledge of economics or programming; or
someone who lias received a Ph'i) within tlie last
five years, preferably i ll mathematical program-
ming, lias excellent analytic capability, anld a
II..... i to do some computer. prograillllming.
Somel other combination of talents Ilian tliose
stated above might be acceptable. The most
important requirelllcits are excellent analytic
Il il', II and a il-i; .1 to w ork hard.
For more informnatiol., contact:

Juilic II. Zalkind
Midterm Analysis Division
EInergy Inftoralition Administration
121h & Pennsylvania Ave., N,\V. Hn. 44.33
i,,,, ... I. D C 20461
(202) 633-8505

School of Operations Research
Industrial i ......... .....
Upson Hall
Ithaca, NY 14853

J.J. Billera and 1). lHath, "A Unique Procedure fir ':, ..
location of Shared Costs," 'T 4.30.
W-L. Ifsu and (.L Nemhauiser, "'A Polynominal Algorithm for thei
Itinimum I., i.,. I Clique C(over Problem on Claw-free Perlfict Graphs,"
TR 43i4.
W-L. Ilsu, "Hlow to Color Claw free Perfect Graphs,"THI 4'35.
M.J. Todd. "Approximate Labelling for Simplicial .t- .. and
Two Classes of Special Subsets of the Sphere," TR 4.12.
M.J. Todd, "A Constructive Proof f f Sonnenschein 's Lemnma," TR
I). Goldfarb and M.]. Todd, Il i,. and Implementation of
the Shor-Khachiain I'.. ti ii. for Linear .i .* .......... TI 446.
R.G(. Bland, "Linear Programming Duality andil inty's eninma, T' '
W.I. Iucas, "Game i "T 4 ,"TR 450.
M.,J. Todd, "Pl,.AIGO: A FORTRAN Implementation of a PIiecewiise-
Linear !' ..... ., Algorithm bfor Solving Systems of Nonlinear Equations, "
ll 452.
M.J. Todd, "An Implementtation of the *', i Method for linear
r......o. obleims with Variable Upper Bounds, "'' 46 1.

Department of Mathematics
Weyertal 86-90, D-5000 Koln 41, West Germany

R.E. Burkard, II. Hamacher, "Minimum Cost Flows in Regular
latroids," 79-12.
*. Ziinmmermann, "Linear Optimization for Linear anld Bottleneck
w ith One Nonlinear Parameter." 79-15.
U. Zimmerimann, "A Primal Dual Method for Algebraic Linear
.. ...... 79-16.
R. I Euler, "On a Classificatiol of Independence Systems," 80-7.
IH. llamacher, "Optimal Cuis, 80(8.
R.E. Burkard, J. Krarup, P.M. Pruzan, "Efficiency and Optimality inl
Minisumr Minimax 0-1 :', .. .........' Problems," 80-9.
R.E. Burkard, II. I .I,. J. Krarup, P.M. Pruzan, "A Relationship
!letIeen Optimality and rEfficiency in Multicriteria 0-1 Programming
Problems," 80-10.
)R. E. Burkard, U. Zimmermann, "Combinatorial Optimization inl
Linearly Ordered Semimodules: A Study," 8012.

Mathematics Research Center
610 Walnut Street
Madison, Wisconsin 53706

Stephen M. Robinson, "Generalized 'Equations and ITheir Solutions,
Part II: Applications to Nonlinear Programming, "TR 30418.

Electronics Research Laboratory
College of Engineering
Berkeley, CA 94720

E. Polak and S. T i .1 ...I.... "New Coinvergence Theorems for a
Class of Feasible Directions II... .11.... '" LUCl/ERL M78/25, 1980.
E.Polak and A. Satngiovaiiii-Vinccentelli, "Theoretical atnd Compula-
tional Aspects of the Optimal Design C(entlering, Tolerancing and
Tuning Problems," UCB/ER 1, M/79/6. 1979.
R. Trahan and E. Polak, "A )erivative-Freet Algorithm for a Class of
Infinitely Constrained Problemts, UCB/El L M78/75, 1977.
C. onaga E.Gonaga Polak and Polak and Trahan, "An improved for
Optimization Problems Wilh Functional Inequality Constraints."
UCB/ERfL M78/56, 1977.

System and Decision Sciences Area
2361 Laxenburg

A. Propoi, "Iterative Methods for Structured Linear .t
WP 79-013.
M. Kallio, "On the ...... MAethod Using an io ...' Basis," WP
K. Tone, ...' ... Benders' Decomposition Applied to Multi-
period, Multicommliodlity Production, Distribution and Inventory System,"
WP 79-045.
E. Nurmiinski, "Conceptual Newton Mlethod for Solving lMulti-
valued Inclusions: Scalar Case," WP\ 79-050.
A. Wierzlicki, "7The Use of Reference (I ', i.. in Multiobjective
Optintization-- ''leoretical Implications andl Practical 'Experience," WP
M. Kallio, W. Orchard-Hays, A,. i ,.i- "linklage of Optimization
Models, NW 79-083.
NM. Kallio, W. Orchard-Hlays, '" ...... .. with the Reduced
Gradient tMethod for Linear Progranmming, "' P 79-0841.
J. .. "Some Conditions for Optimal Deterministic Solutions to
Slochastic Dynamic Linear Programs, 'WP 79-10 i.
E. Nurminski, "Some Theoretical Considerations on Linkage Prob.
lems, WP 79-117.
A. Wierzbicki, "A Methodological Guide to ii. ';.; ,. Opti-
mization," WI' 79-122.
A. Wierzictki, "The Use of i.. 0. i. L ('' n..' Levels in Group
lAssessmentl of Solution of MAltiobjective Optimization," WP 79-124.
M. Pescliel, J. Ester, Nguyen ThIe ILoan, .' .. Preference,
Convexity and '1 t --Basic Notions in Mdultiobjective Decision
nalking,"WP 80-022.
M. Kallio, A. Lewandowski, W. Orchard-H lays, "An ImplemIentatiion
of the .... Point Approach for i- '.'. .t Optimization,' WP
C. Lemiarechal, "Nonsmooth Optimization: Use of the Code
DYIN/EPS," WP 80-036.
E. Nurmninski. "Numerical Experiments with Decomposition of LP
on a Small Comnputer," 1W 80-037.
A. ierzbic ki, "A Mathematical Basis fotr i . .. Decision
i;,' ,, "WP 80-090.
C. Lemarechal, E. Nurtiinski, "i'.,.... .,'. ,t' of a Support
Function of ian Ei-Subgradient," WP 80-101.
Y. Ermnolev, "Some Problems of Linkagi e Systems," WP 80-102.

i ~. ...
ii; i I,i ~ r j; I I

II ~~
1 .il 1.I: i


t 4 7;%-- r !-
'r- ' c" r- " .

Systems Optimization Laboratory
Department of Operations Research

George 13. D)antzig, I ,..' Number of Steps of the Simplex
icethod for a Linear ....,... with a Coi exit Covey nstraint," SOL 80-3.
Walter Murray, Michael L. Overton, "/I Projected l,agrangian
tlgorithm for Nonlinear I Optimization," SOL 80-4.
Zachary I'. Lansdowne, "Network Forrmulation of the Miderm
l Market Model," SOl, 80-5.
Philip E. (ill, Waller Murray, Michael A. Saunders, Margaret 1.
', 1l,. "Computing I ..'. II ', ... Approximations to )Derivatives for
tNumterical Optimization," SOL 80-6.
Philip E. Gill. Walter Murray, Michael A. Saunders, Margaret II.
I -i "'spects of Mlathemactical Modeling Relatedl to Optimization," SOL
Philip E'. Gill, Walter Murray, Michael A. Saunders, Margaret IH.
Wrighl, "Miethods for Large-Scale Nonlinear Optimization," SOL 80-8.
Iobert M. Freund, "A Constructive Proof of the Borsuk-Ulam
intipodal Point lTheorem," SOL I80-9.
Iobert M. Freund. "Variable-Dimension Complex with Applica-
tions," SOL, 80-11.
Robert M. Freund, Michael J. Todd, "A Constructive Proof of Tucker's
Comrbinational LIeoma, SOL, 80-12.
lBruce A. Murtagh. Michael A. Saunders, "Minos/Augmented User's
manual," SOL 80-14.
R.W. Cottle, J.S. Pang, "On theeConvergece of a Block Successive
Over-Relaxation Melthod for a Class of Linear Complemen arity Problems,"
01L 80-17.
George B. Dantzig, "Time-Staged Methods in Linear Programming;
Cornments and Early History," SOL 80-1 8.
Philip G. Abralhamson, "A Nested-Decomposition Approach for
Solving Stair-Case-Structured Linear Programs, SOL 80-20.

Department of Operations Research
Nassestr. 2, D-5300 Bonn, West Germany

Animal Report 1979, WP 801 50-OR
M. (Grotschel L. LovAis, A. Schrijver, "The Ellipsoid Method and its
Consequences in Combinatorial Optimization," WP 80151 -0R.
L.lutz, ". I.. I i.i .. .. . Zusammenhtngender Zweifacher Block-
..i... "WP 80152-OR.
I.. Btz, "Characterizations of Connectivity in Row-Column Designs,"
WP 80153-0OR.
A. Bachen, "Anwendungen der Komplexitiitstheorie im Operations
Research: Eirn Uberblick," WP' 80154-OR.
A. Bachem, R. Schrader, "Einfuhrung in des Operations Research,",
WPI 10155-OR.
IB. Korte, R. Schrader. "A Note on Convergence Proofs for Shor-
Khachian Methods,"WP 80156-O0R.
V. Klee, "A Note on Convexs Cones anid Constraints Qualifications int
Infinite-Dimensional Vector Spaces," WP 80157-OR.
M.A. FIrtumkini, G.\. Gens, Ju. 1. lhnelevakii, E.V. lcvne.r, "Onl
Computational Complexity of Optimization Comnbinatorial Problems, "'WP
"IV Bonn Workshop on Combinatorial Optimization, August 28-30,
1980, Abstracts, WP 801 59-O1.

1jichard W. Cottle, 'lditor-In-( I.. 1, has announced their
following contents of' Mathematical P .'... !',IIIII,. Volume 19,
Numbers 2 and 3:
Volume 19 No. 2
I.G(. Rothbluin and II. Schneider. "Characterizations of Optimal
Scaliags of Matrices."
W.(Goeiet and Y. Simeers,"A I t,' I Reduced Gradient Method for
a Class of Nondifferentiable Problems.
P.11. Zipkin, "Bounds for Aggregating Nodes in Network Problems.
T.F. Coleman and A.R. Conn, "Second-Order Cotnditions for an Exact
Penalty Iunction."
{.D). Armstrong and D.S. Kung, "A Dual Method sfor Discrete
(Chebycetev Curve r '....
O.L. Malngasarian, "locally Unique Solutions of Quadratic Programs,
Linear and Nonlinear Complementarity Problems. "
K.G. Murty, "Computational Complexity of Parametric Linear

A. luszczynski, "l'ea'csibile Direction Mlethods for Stochastic Program-
rming Problems."
M.C. (I .. "New Criteria for the Simplex Algorithm."
1. Ilorst, "A Note on lthe Convergence of anit .nI . for Noncon-
vex Programming Problems."

Volume 19 No. 3
A.F Perold, "A Degeneracy Exploiting 1,1 Factorization for the
Simplex Me thod."
M.E. Dyer, "Calculating Surrogate Constraints."
R.D. Wolliher, "The Two-Stage Linear Prograrmming Model inder
Uncertainty with 0-1 First Stage Variables."
S. SchaiblIle and 1. Zang. "On the .... ,. d ,i, of Pseudonconveta
C" -Functions.
J. Gauvin, "Shadow Prices in Nonconvex Mathematical Program-
ming. "
P1.S. Brooks. "..n,,,,.: Retrogression in thet Eaves-Saigal Algorithm."
,.Van der IHyden, "A Variable Dimension Algorithm for the Linear
Complementarity Problem."
It. W. Cottle, "Completely-Q Matrices.
J. Ch. Ponerol, "About a Minimax Theorem of Mattheis, Strang, and
Mathematical P' .1.nl.,iI'l' ,-,i. l: 13, Combinational Opti-
mization II, Edited by V.J. Rayward-Smhith i1 ble published
in the near future. In addition, the following studies are in prepar-
Network Models and Applications, Edited by D.W. Klingnan andl J.M.
Mathematical Programming at Oberwolfach, Edited by 11. Konig, B.
Korte and K. Bitter.
('pt.in.idi., Duality and Stability, Edited by M. Guignard-Spielberg.
Constrained Optimization, Edited beyV.G. Buckley and J.-L. (offin.
Applications, Edited by J.-L. Goffin and J.M. Rousseau
Mathematical Programming with Data Perturbations, Edited by A.\.
Matrix generation Report Writing and Computer-Assisted Analysis,
Edited by 1I.1. (;reenberg.
Numerical Methods for System I mirit,.. 111, Edited by R.J.B. Wetts.

A 1,

70 PA Tq, T's...


November 6-7: . Japan Mathematical ,~,i l,- Symposium", Tokyo, Japan. Contact:
Masao Iri, University of Tokyo, .i .-ku, Tokyo, Japan 113.

November 6-8: Fall meeting of SIAM, Houston, Texas, U.S.A. Theme: Mathematical applications in
energy production, mathematical modeling in medical science, advances in mathematical
optimization. Contact: H.B. Hair, Society for .ii1. I.i11 and ,A .1l;-,' Mathematics, 1405
Architects i.I.i i.ii 117 South 17 Street, !'i l.,,i II.i... PA 19103, U

December 10-12: "19th -' Conference on Decision and Control", All .1..... New Mexico,
U.S.A. (Submission ii... llini was 31 March 1 I. ') Contact: '..i. Michael K. Sain, i.,
I l. .:al Fr ,:; U. .-;,in Notre Dame University, t..!n I n.., IN 46556, U.S.A.


January 5-6: i ..... . I ... i...i.i Testing and .I .....n Algorithms and 'tware".
National Bureau of Standards, Boulder, Colorado. Organized by the Committee on Algor-
ithms of the MPS, the ';m ..-; of ,.I -, and the -,i.n .ill iil of i n., ..-. Contact: Dr.
i.!'.III H. F. Jackson, Center for A1 lii.. Mathematics, National Bureau of Standards,
Washington, D.C. : '. .4, U.S.A.; telephone ;'.1-921-`:' '15.
T .in:. 26-31: 'I ...ii ..i .'-ih. Optimierung", Mathematisches Forschungsinstitut Oberwolfach,
ii. ,... I, ... i -..l : .,,i. of Germany. Contact: Institut fOr Okonometrie und Opera-
tions Research (see 1982, August 23-28).
A ..i i : .11. i.,i Congress on Mathematical '* .11 1...", Rio de Janeiro, Brazil. (Abstract
deadline 1 December 1'' r,. i l! forms .. I11:. Ii Contact: i ... Milton Kelmanson,
Caixa Postal 1507 CEP 20100, Rio de Janeiro, I' i., Brazil. "!...-. ~.i by Sociedade
1.1 .*il de Ti u,,., Operacional and the MPS.

May 13-14: "Optimization Days", Universit6 du Queb6c A Montr6al. Contact: :-',..... Efim
Galperin, Departement de math6matiques, Universit6 du Qu6bec A Montreal, C.P. .' Succ.
"A", Montr6al, Ou6bec, Canada H3C 31" telephone 514-282-3221. 'p..n ...... by the MPS.

July 13-24: -'TO Advanced Research Institute on Nonlinear Optimization", Cambridge, I Ill.iiu
Contact: Professor M.J.D. Powell, D. i. ..in .' of A .,ii' .' Mathematics and Theoretical
ih, .' University of Cambridge, Silver Street, Cambridge C' 9EW, England. Sponsored
by the .

r. 20-24: ':-B:11 British Combinatorial Conference", Swansea, England. Contact: A.D. i...-!
"1.'.'" '. of Mathematics, University of Surrey, Guildford, Surrey GU2 .. ,-: U.K.

i ,.... I., : Programming", i.-.i.- ,. iii"-. I Contact: I .1 M athematical Society,
;l ....i.., VI, Anker kov 1-3, I. 1 1. III, Hungary.

August 24-. : "CO81: Conference on Combinatorial Ci ';l,. ..i ..", I1 .Ii:. Scotland. Contact:
Professor L. Wilson (CO81), Department of C. il.i.ii.. Stirling University, Scotland, 1 I-


August 23- : Eleventh International Symposium on Mathematical Programming in Bonn, Federal
i. Ii of Germany. Contact: 1,1 'n fiir Okonometrie und Operations Research Universitit
Bonn, ... i -..I. 2, I. ,,, 1, .- .al -. ..li of Germany; Telex :':,,..:7 unibo b,
Telephone (02221) 739' .. CIOm...I triennial meeting of the i' (' The !i .,i .
Congress of Mathematicians will be held August 11-19 in Warsaw, Poland.)

I -:
IP~ '.~~ CIh

VA (:: 1 i

ApproximateV si~i ixty-five revarch~lc~is
''i }Hn 14 nltrie's atitetdediicl fliii' NAMl)
i;jloisonIi NhxAvanced'xi Researx'chii in. titxnce oil
M(,'n Iahiicx'xi (Conici'axity in Opiitinataoni anid
iNnoinix s," bell!i iin Vancouver in early
Aigilt. Ile n'etin)2 wasdiri'ted by Sim
dickii \vrix' (1 x'xhIroii), Siegftried Sc'haibiie'
(University of ih and Biiilll Zim

m~rbI xWrtx ilii'luio. Sess)x'~xion x itop
'xin tx'x'ix C h a r al ei z ai' a nd, -,'~ i l xl ,i 1 i o f

Gee;dve aled t( inc ae (,eneriikied

(l~llllProbie ~lffisCI1; 4.1;1 for
-it ,11 Conerave "'. .. ; ,onvexixty
'actionWa In ..
of' (Generalizedi Con-
eavity in x Analyisi
aud Stodiastic ii.. and Coxicax-
ifiableaiIi -, ; '. 'cadx'inic i'Pc ss .1I
pub"lishi thce con ferejjc~: ~ c I..~ (cdtitedt

cstinla~tod .111, p~agies, a l sf h o ixdli bex availaile
by ilate Spring, I .
'T he hx'iiiiiicka irogirnlli xas cwas lljli
inclae'd y a 11- _..- soccial prcgrainr
V0llsistinxx' of' hikes. fours,' lunch'ieoxns and
rieceipt iois.

Monii lIwln

The IV Bonn Workshop on Combina-
tional Gr !l.... .i;- was organized by theL
Institute of Operations ilesearch, University
of Boii, August 28-30. Fifty-four partici-
pants from 17 cnitries attended and
presented 39 papers. There ,li be a special
issue of Discrete Mathematics where some of
thie material will appear. A list of he paIrti-
cipants as well as abstracts of presented
papers ,I; appear as report number
80154-(-O of tle institute. Copies are
available on request
-A Bachen

CC .C. ,-E

lainer Burlard and Thesdor I I ,,i
were local organizers of tI.h V [' ... .... of
O,. '- -, ich hlied at the university
of (Cologine, Auguist -. -27. The mieting was
arIrailged iv ( .I I 11 fi ir Matiheinatik,
)konomnic Iund Operations Research, ;Ger.
many. Thure were 'i participants of
whoIm I I1 cami from (;ermianlv and 220
from, foreign countries. I ,, lectures.
were given by C. i (Paris) L. ovasz
( ), 1, I .1 (Seattle) and
Vogei (B1onn). In seven parallel contributed
paper sessions. 2f50 papers 'were re sented.

A very successful '1,, ,. on
Scale Linear ,' ....... was liel at the
International Institute for Applied Systems
Analysis, Laxeniurg, Austria, on June 2-6,
.1 i .', Tihe workshop was co-sqponsored by
thel Systemns ()ptinization Laboratory of
Stanford Iniversity as .' as lby II' The
approximately 40 participants were mainly
invited Eastern and I t scientists who
actively contribute to ith research in tihe
field. A proiee(diis is being edited by
(;eorge .)anitzig, Michael )Deipster and
arklku i. alnd it will be published by
IHASA during Fall, 1" . in the form of two
volumes e Kallio and A. Wierzbicki

An Inlernational i ... .'.. on Ad-
vances in Linear I .,... ...... Algorithms
and Software was lield ii mid-sunmner.
Fifteen papers, were presented on linear
. ......... network flows, and combina-
loral optimization. The workshop was
sponsored by Centro Seientifieo '1. I di Pisa,
Institute di MatLemaltia, I. Tonelli, Univer-
sity of' '' and I ,,i,, di Flabrazione dell'
liinorlmaione ( i Pisn. Local arrange-
iments were well taken care of by C. Snadi.

A. Bachiem


Edited by:
Dr. Hlarvey J. ( reenh'erg
F . infrmatio n A ildinistrationi
1200 .... .. Avenue, N.W.

........ D .C. 20461J
( ) 633-' ..

This special study on MlG/i /'CAA
considers computer aides for model manage-
rmelnt in mathematical programmin g. Paters
aire heirebi solicited, which conform to tihe
standards of Mathematical ..
that pertain to these support flnetions,



apart firo)I optimization. Topics include:
i tornmation structures
Language design
,, ..111 :evaluation
In-depth surveys;
Diagnostic analysis
Interactive: processing.
I'1. send 3 copies of vour imainu-
script, to Harvey (;renberg (see address
above and 1 copy to othe, Editor-x-C(hief of
Mati henat ical ' i....... I'Pro essor
R{iclihard Cottle. Stanford University, Stan-
ford, CA. U.S.',.

S-IN , N.-i ., CG

September 8 10, 1981, at Austin, Texas

An 1C (, 1 '; Committee of .,,
nieinbjers from 14. countries is soliciting
abstracts for miinute presentations.
Abstracts ( 'II: to 300 words) should
be sent to the .11. ( I .....1 S.Zlobec,
Mathattlics Department, ec( i1' UIniversity,
Monltreal 1 10, (Quebec H13A i .I, Canada,
hy january .'.. 1981.
For further information contact K.O.
Kortanek generalal ( 1.......: ), IE/OR De-
partilent, Virginia Polyt'chnlic Institute,
Si i.... VA. or jamexs Vick (Arrange-
Imens ( .1 ..), Mathematics Departnient,
1,liversitv of Texas, Austin, Texas '.

a~l_ ~~


' "' (

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