PTI
MA
MATHEMATICAL PROGRAMMING SOCIETY NEWSLETTER
N 27
AUGUST 1989
t HE MAJOR CHANGES IN THE JOURNAL IN THE LAST THREE
years have been the establishment of Mathematical
Programming Series B and the reduction from three
volumes (nine issues) to two for MPA. As a result of
the considerable efforts of Michel Balinski, Jan Karel
Lenstra, Bill Pulleyblank and Laurence Wolsey and
their negotiations with NorthHolland, I believe we
have a much more rational structure for the Society's
publications, with more control over quality and
scheduling for MPB than with the Studies and a more
realistic frequency of publication for MPA, with no loss
to the members.
The editorial board consists of distinguished and
dedicated members of the mathematical programming
community and reflects the international nature of the
Society. We have two CoEditors from Europe and two
from the U.S. Of the 26 associate editors, 12 reside in
the U.S., eight in Europe, three in Canada, and one
each in Japan, South America and the Soviet Union.
MPB has eight associate editors, including three who
also serve on the editorial board of MPA, as does its
EditorinChief, Bill Pulleyblank. It is clear that there
should be a close relationship between the Editorsin
Chief of the two publications to allow the flexibility of
transfers when appropriate and agreed to by the
authors.
Two special issues have appeared in MPA, 35(2) on
probabilistic analysis of the simplex algorithm and
41(2) on nonconvex optimization. Both were published
in order to alleviate scheduling difficulties (lack of
material for MPA and backlogs for the Studies) and
CONTINUES, PAGE TWO
Report on
Mathematical
Programming,
Series A
OPTIMA
NUMBER 27
JOURNALS
CONFERENCE NOTES
TECHNICAL REPORTS &
WORKING PAPERS
BOOK REVIEWS
GALLIMAUFRY
711
12
Illrrca~
lW9110 RY MP011
with the new structure I do not antici
pate the need for future special issues in
MPA.
The quality of the journal remains high,
and the mix of papers appears to be
roughly constant. For example, in the
nine issues in 1987, a crude characteri
zation reveals 14 papers each in nonlin
ear programming algorithms and com
binatorial optimization, 13 in nonlinear
programming theory, 10 in complemen
tarity and homotopy theory and
methods, and seven on linear program
ming. The comparative figures for 1986
were 17, 15, 10 and 19 (including the
special issue on probabilistic analysis of
the simplex method). We are attracting
a reasonable number of good papers in
combinatorial and integer optimization
(with strong competition from Combi
natorica, Discrete Mathematics,
Journal of Combinatorial Theory and
the computer science journals) and
computationally oriented nonlinear
programming (competing with SIAM's
journals on Numerical Analysis
(SINUM), and on Control and Optimi
zation (SICOPT), and with the Journal
of Optimization and Applications
(JOTA)). As always we have stiff
competition from Mathematics of
Operations Research on more theoreti
cal papers and Operations Research
and Management Science on more
applied papers. (While the division
above is on methodological lines, we
publish a small but reasonable number
of good applications.) Finally, we have
been able to attract some good papers
related to parallel computation, and we
are in excellent shape with regard to
articles on new linear programming
methods, with three of the five papers
on standardform variants of the
projective method, five of the six on
pathfollowing methods, etc.
It was pointed out at the Council
meetings in Tokyo that the SIAM
journals SINUM and SICOPT have
become if anything less serious com
petitors to MPA; SINUM has moved
more towards differential equations,
SICOPT to control theory. Perhaps
closer are SISSC, the SIAM Journal on
Scientific and Statistical Computing,
and certainly the new Journals on
Discrete Mathematics and on Matrix
Analysis and Applications. Further
more, SIAM is splitting SICOPT and
developing a new journal devoted to
optimization.
I have heard from a number of mem
bers that they are concerned that the
Society and its publications are chang
ing their emphasis more and more
away from continuous and towards
discrete optimization. I do not believe
this is the case and so informed the
members; however, there is certainly a
perception among some that the
balance has changed considerably. I
believe it is important that this balance
be maintained and seen to be main
tained.
We receive about 200 papers each year.
Of the 212 received in 1986, 68 (31%)
were accepted, 114 (54%) rejected or
withdrawn, and 32 (15%) are still active.
For 1987, the figures are 37 (19%)
accepted, 71 (35%) rejected/withdrawn,
and 94 (46%) in process, out of a total of
204. In 1988, we received 201 papers
and so far in 1989 we have 89 papers.
The current backlog is about nine
months.
Overall, I judge that the quality of MPA
remains very high and that the new
structure has alleviated the pressing
problems of the past. I would like to
wish Bob Bixby all the best as the new
EditorinChief.
M. J. TODD
Vol.44, No.2
F. Barahona, M. Junger and G. Reinelt,
"Experiments in Quadratic 01
Programming."
Y. Crama, "Recognition Problems for
Special Classes of Polynomials in 01
Variables."
Y. Ye and E. Tse, "An Extension of
Karmarkar's Projective Algorithm for
Convex Quadratic Programming."
A. Sassano, "On the Facial Structure of
the Set Covering Polytope."
M.E. Dyer and A.M. Frieze, "A
Randomized Algorithm for Fixed
Dimensional Linear Programming."
W. Kern, "A Probabilistic Analysis of the
Switching Algorithm for the Euclidean
TSP."
S. Wright, "An Inexact Algorithm for
Composite Nondifferentiable
Optimization."
D. deWerra, "Generalized Edge Packings."
Computational
Reporting Guidelines
Distributed
The draft report of an ad hoc committee on
the guidelines for reporting computational
experiments has been published in the
COAL newsletter dated March, 1989, and
sent to all Society members. The report
reviews existing guidelines and discusses
the issues of performance claims, measure
ments of performance and computational
testing on the new computer architectures.
Researchers in computational mathemati
cal programming are urged to study the
report and communicate their comments to
the committee: Richard H. F. Jackson
(NIST), Chair; Paul T. Boggs (NITS),
Stephen G. Nash (George Mason) and
Susan Powell (London School of Econom
ics). Full addresses are given in the report.
 ~
PAGE 2
number twentyseven
AUGUST 1989
EdilorinChiet: Peter L. Hammer, RuIcor. Hill Center for the Mathcmatical Sciernes.
Rl[ger.s L;nii csi Bu,.,:h Canpus. Newv BrLi1.'.icL.. NI ).9013.
Ne\ in 1988:
M I.TI\T FRIBL IlE 1E( IOIN Ni %kl\G 11 \
O.R. BASIll) LX\PFRT I .\T" M
Editor,: R.I. h,nc%., R.H. %fohrirn. H11. '., ..
1 ... Hlladrmather and \1.t1. R\h.,r
IP'1 ,.e. :e dl _N in : t I .r .,_. I[ i '. I' 1 t ,l ,... I *,. ..,,.ir',...
. r . i( l ,
%nnul a.t Oprraltii'n' Reearch. idl. It,
!. (, \11RI4 1111 \ 1 IrROM %R1 I1 1 \l. 1 .I.1 I 1
A .'f .1,',. 'r ,' f'l nin irri . Ir i. 1, 2 ,J \r i.t .. I i n. .,: .
L .. D' .i 1 I, i.
C B ,. '/ .. ;, ,' ,. l ,' ... r i" r ..
Kn .. .'L:J c Kc ri.'jnt ,:t .i,. l. r *' :.:." . i ..' ...,'
h I.B I'foir D',i'n iliJ Di,,'i ri 1 .u..I .ji r
('5 JLu._ S'r, S if'. 1 "''..ai \p:' .' I Int..rr:i.i .n P .. .: .i,
l' ..tl a.v t.r. \ ''...' t l t'" f.. :J Pr' . r ;' i t ". r.. L
/L P ;, l, .A r. i n elli'. :. ; ': .:. .' .,d ,.r . I r: .. 
i/. I o '/rer. On tlhe N aur.l L anrgu..i rO r, nt d 1 E '.
II. MIODLI.%(, A. ) PRI[I RENCI_ \'I MI\T
(. Harn.v'r.': l i Ri/,:r. .D i. : ilth, i ,r
Enr.;:aged is.._mi Ta\ R t.rri t,,r FR(.. .J L5
i lurc'rr a.tl'. 11. Thiura lTh 1. tb'rinllh ..: [ ..F ri. 'lind.
.o'nm e RK.a orijrng .tjtate:, . r.'l'th.r P tr l' ll
R? Rcsin..t. I J. TI,i .r C .:" ' I I. i
DL)ci:,io Mai irN L
8/. u il Sfc.''.'t '/, [J..' nirc' it .. '. luii rr rLi'ui.. L p..r..J
'.t lir:. Fur:r..'r
ji s...' if !',F i lt'; i. L .rni d.: inri.r. t ,, '! D .' ., i :. ''Fr r
S. iorims for ku,. \lanag'mentri
III. L.At111TATI 1 MONIDEi I.1 T lTRLCTL RI(,I
AND I%FORMA.'lO% PROCELSING
.l Barim aci : S.h dutLihn Proc.; \ [ 'i tll P u,_ijr..
C'o stri.i ajid Time \' ind.: ,
.1 .1 %1 b 'i,"ti 1 ranr formi. ng % _, hra!.: .)jr.3 Y1rut:w.  i .
R.:lIaunal Data siructur,: in DS5
.1 B::.': L it." ri a SL. heduhnm y I. ri rTime Ix," r.n Fin h.'pr:
d:J.r Rei our., C:r.,ira'rin.
A LDownsr, Duat Structure' and .D'. nicT' Picerrnr'riL
Background for EdIinrnc Highi., rulIIurLd I"',.,
it. lHa.ri Perp :'.'i '': .t DL tarl,.. ALl.h,:c.rur,.,
i. .. 
U.r... .r : L "l F.i ; F. '. .
/.. '.. \ .. : lr a r, .r : .... r.. .J .r .
SL ii 1d '
.. r H r a PI.
Ir 'is., r.] ah N. "' I \l.S.r.ii i: \,, '. U L ,.i r ".i I i.i'i,
.. v. F.air
P. E,., ,r : \r ,. I \ i a b'.3 1* \ .! l' .. ,. d ln .t 
lirriria ' ;r k r. '.:I l Fir' r i'.t
', t..ritn u l I .: itr. a l.:i .l Tr., :. _.
S l'.L ,.". '" C .,' t' t H r D L L ', crthi. 5 .[. r
Mlsthine S., d..m.r=:
H O_ t, P ih ;:':'!,', D u:.__'m n. P.,.L 11.,h ,n',err "..irr.,'
H. rn,
/' i1,'. ':, : N\r . r.J E ilu Ii.n I.. u A.. S Trr . .
[iJe e:' .ttn t P la ii nn t...jr \l...J .IJ, 1,' jl.i,. T .;..hr,..i,:,g ,,:,
FORTR.A CODE FOR ET\ 0Rk OPTIMIZATION
I dilur!: B. Sinieune. P. I olhi (I. allowo F. aflfl'inli and
1,. Palliattino.
I .4 Z. 44. r ,:... i. a '. ..2; 4 ": ,'
innal. of Operation. Rrtcarch, ,il. 13
i. r u. '.., ... Pa ti:. r ; r' F \ r. ".; 
I i ,' .I '. ', ,, ; \ 'r'l ii Arl .' I jl r .1 ll' ..
o, lt .. Dril ,. .J, LI r i rn l r 's 'r . ..m II.:.
LD.P I :re ; ; .P 7 ., Th R, . .J , l irncr
\ nmrurrnm Co,.r ',,.,.or, l.' Prub,, ml
_ ('. .rpar, r;. .; V \ in .., ,h r .ir. J .r n i . .\: :.4 !i,, .
Pr .bi, m
L .'.' .' ",,i' in \ ..>n a]J .raT' l ',lar:hl n P r,:,l:.l I r ,
S 1 .*I ;.L Path F..hriiLii...
P'. \1 Cu,' it. .' Lil 1 A ..rihm I,.r F.riJid n C)i'lll ,iT TrI..n
D i.:* i r , i ,, .and E .al. ,it .h
S I rdeli '.' .S I,./ t '.'. r. A H r. r J \l I .ri r.r ..r F i .. '
A h i5rallr:it or a Elr:ni nr.. l ini T.nm
A uihiT Inde., Lt ',I Al,_ )rirhnr l 1; 1 t :. I L:uin, ": [ .:.I
Sid]dirc.:T..:,r i
'ailable 1984 19R7:
Vol 1011. Ibarali, T.. Enun ierat,. Apr .' l. r.
Combinlniorial O'p[umi:.ajin 2 'olumnie 1 tic i. p
\ ol S9: Albin. S L and C \1 Harmr, '[rilrria[l 3rd
C onmput.i:'.nrrii [,uC. n Prou ahliht. M. l L r.. r 2 .i.'lurnei
1lYS. 644 pa%..
\ 01. . Blaze. F ':, al.. 5...r'ditinh ; under Fl.c our . C 'r r ir'n'
 DL[e[niiniL 11 oJIl I 3 c) p'ge.
\ oi 6: Ol.(' eb, J.P. and S 1. Ratu.. l.ol'.ilia.0 l DIc:Ll 'i n.
MNtrhljdo[logC and A\rpiiLaclicn. 19.Ah. '32 FPas
.i 4. \Il,? nrr:a. .. C L \!u.:.r[lin': and nli.ar. .r
(pFtmrinii'a .i .n. 2 i 'ui.'m 19r,. ,, 32 r1u.9.
,:.. 3 Sl L K E. :ind KR 'ur' iI.'. l i: a ul,im..i rn
.,:r r:' RL Mar.:h Lod. .' J .AFpl, .,[ .in 19. V r 1. ; :
,1. 2 Thomirp.on. R G .artd R '1 Thrill, \Nirmat'..: ; \rn '
i,?r P,11.:, De.',i.,>nt. Pubhi.; and Pr it.: l 91. _9t .' 1 rjs'a '
\, 1. 1 r.H Tit F .and IF \la! t'f ., ..haist,. and
I 1 ml[' i ,i :a tlri ti. l19 4 3 r,. pF'a g" ,
Price per %olumi incl. poaIe: 5 153.61. or S 114.411 fiir menhbers, (IRS%. Plra.e reque't e\teni'le prriipeclu for while
series: mil. 121. 19841989
Hluo to order:
'PI':a. e cnJd ':.C:* r ordi: r either rt '..Ll,r i.liu l jLa en or Jd.rLL i r'. .'.IJr BHact HiL'.. (Ult.... a3 ni clrl in d lI' '.'. I the I ri
St.'rlts pic'ae addr. ,4 % 'ur c rd r r Iv .1 B'. [ibl/er A.G.
S.i.nufl: Pulhlhin Z Comn.anr,. P B.., .". RJ Ban. J iI".','
10 H408Bses1teln
PAGE 4
number twentyseven
Conference Notes
Mathematical Sciences Institute
Workshop Announcement
Cornell University
Ithaca, New York
October 1920, 1989
The Mathematical Sciences Institute (MSI) at
Cornell University is sponsoring a work
shop on LargeScale Numerical Optimiza
tion. This workshop will discuss recent
algorithmic and software developments in
numerical optimization with a special focus
on largescale problems. Particular empha
sis will be on practical methods, specific
applications, and parallel computation. In
addition, recent advances in parallel
methods for sparse linear systems will be
considered and discussed with respect to
their relevance for largescale optimization.
Approximately 18 halfhour, invited talks
will be delivered by leading researchers in
the field. There will be no contributed talks.
The workshop will conclude with a discus
sion session on the topic, "What should
optimizers do with parallelism?"
Published proceedings will be .w\.ill., bl.
soon after the conclusion of the workshop
which will be held at Cornell immediately
following the ORSATIMS meeting in New
York City.
For more information on the scientific
content contact:
Tom Coleman
Department of Computer Science
311a Upson Hall
Cornell University
Ithaca, NY 14853
(607) 2559203
coleman@gvax.cs.cornell.edu
or
Yuying Li
Department of Computer Science
311b Upson Hall
Cornell University
Ithaca, NY 14853
(607) 2559203
yuying@gvax.cs.cornell.edu
To attend the workshop, contact MSI at 201
Caldwell Hall, Cornell University, Ithaca,
NY 148532602, (607)2557740, 8005, or
7763.
Computational Aspects of Combinatorial Optimization
Oberwolfach
January 913, 1989
The conference was organized by R. E.
Burkard (Technical University of Graz)
and M. Gr6tschel (University of
Augsburg). The participants came from
13 countries and presented (in 52 talks)
new results on the following topics:
* Generalized traveling salesman and
routing problems;
" Design of survivable networks;
* New algorithms for network flows;
* Combinatorial problems in VLSI
design;
* Solving NPhard problems on
supercomputers or on distributed
machines;
* Scheduling problems;
* Probabilistic analysis of simple
algorithms.
Several participants provided a
demonstration of their software
packages, featuring:
a Linear programming codes;
* Algorithms on graphs;
* Codes for scheduling problems;
* A CAMsystem for manufacturing.
The unique setting of the research
institute in Oberwolfach was, as usual,
very inspiring for all the participants
and contributed considerably to the
success of the conference.
M M
Th Edtra Bor fth rba
eniern apliaios Th 3. 3
Thotehnialedtr are Dr. Ka .,
*3. 3 '',D . .ai Osa3tiu
KFPM D. Shor .1iSeSytm
Engnerin DpatmetKF3.3 an
Dr bu auAS dtrfrSse
Engi.een.3g.
The copie .f coplt manscrpts
incldin ilutain and reerncs
sh ul be s b ite b y 3a u r ,1 9
,to .: 33 3
Maagn Editor
THE ARBA JORA FO
Dhhrn31261 Sad Ar.bi
Paer acepe b..t no inlue inth
thm isu wil. becnieedfrpbi
tatig the Maagn Edito at thaov
AUGUST 1989
~I0
s~ ~~
PAGE,5 number twentseve AUGUST,1989
Technical Reports &
Working Papers
Y
Northwestern University
Department of Industrial
Engineering and Management
Sciences
Evanston, IL 60208
S. Mehrotra and J. Sun, "A Method of
Analytic Centers for Quadratically
Constrained Convex Quadratic Programs,"
TR 8801.
S. Mehrotra, "A Method for Solving Piece
Wise Linear Programs by Shrinking
Polytopes," TR 8804.
J.T. Simon and W.J. Hopp, "Availability
and Average Inventory of Balanced
AssemblyLine Flow Systems," TR 8805.
E.S. Theise and P.C. Jones, "Alternative
Implementations of a Diagonalization
Algorithm for Multiple Commodity Spatial
Price Equilibria," TR 8806.
N. Pati and W.J. Hopp, "Optimal
Inventory Control in a Production Flow
System with Failures," TR 8807.
S. Mehrotra and J. Sun, "An Interior
Point Algorithm for Solving Smooth
Convex Programs Based on Newton's
Method," TR 8808.
WL. Hsu and WK. Shih, "An
Approximation Algorithm for Coloring
CircularArc Graphs," TR 8809.
WL. Hsu and WK. Shih, "An
0(minlm*n, n2loglog n]) Maximum Weight
Clique Algorithm for CicularArc Graphs,"
TR 8810.
S. Mehrotra and J. Sun, "On Computing
the Center of a Quadratically Constrained
Set," TR 8811.
WL. Hsu and WK. Shih, "An 0(N15)
Algorithm to Color Proper CircularArc
Graphs," TR 8812.
E.S. Theise and P.C. Jones, Thi ty
Linear, Single Commodity Spatial Price
Equilibrium Problems and Their
Solutions," TR 8813.
E.S. Theise and P.C. Jones, "A
Computational Comparison Between an
Import Equilibration Algorithm and the
Expanding Equilibrium Algorithm for the
Linear, Single Commodity Spatial Price
Equilibrium Problem," TR 8814.
E.S. Theise and P.C. Jones, "Nonlinear,
Single Commodity Spatial Price Equilibria
and the Expanding Equilibrium Algorithm:
Two Strategies for Implementation,"
TR 8816.
R.R. Inman and P.C. Jones, "Economic
Lot Scheduling of Bottlenecks with External
Setups," TR 8817.
M.L. Spearman, "An Analytic Congestion
Model for Closed Production Systems,"
TR 8823.
RUTCOR
Rutgers Center for Operations
Research
Hill Center
New Brunswick, New Jersey 08903
L.J.Billera and L.L.Rose, "Gribner Basis
Methods for Multivariate Splines,"
RRR 189.
M.H. Rothkopf, T.J. Teisberg and E.P.
Kahn, "Why are Vickrey Auctions Rare?"
RRR 289.
A.S. Manne and M.H. Rothkopf,
"Analyzing U.S. Policies for Alternative
Automotive Fuels," RRR 389.
P. Hansen, B. Jaumard, SH. Lu, "An
Analytical Approach to Global
Optimization," RRR 489.
J. Kahn and R. Meshulam, "On mod p
Transversals," RRR 589.
F. Harary, S. Kim and F.S. Roberts,
"Extremal Competition Numbers as a
Generalization of Turan's Theorem,"
RRR 689.
S.D. FlAm, "On Finite Convergence and
Constraint Identification of Subgradient
Projection Methods," RRR 789.
M. Zheng and X. Lu, "On the Maximum
Induced Forest of a Connected Cubic Graph
without Triangles," RRR 889.
B. AviItzhak and S. Halfin, "Response
Times in Gated M/G/1 Queues: The
ProcessorShaRing Case," RRR 989.
P. Hansen, B. Jaumard and 0. Frank,
"An 0(N2) Algorithm for Maximum Sum
ofSplits Clustering," RRR 1089.
R.P. McLean, "Random Order Coalition
Structure Values," RRR 1189.
P.L. Hammer, U.N. Peled and X. Sun,
"Difference Graphs," RRR 1289.
P.L. Hammer, N.V.R. Mahadev and
U.N. Peled, "Bipartite Bithreshold
Graphs," RRR 1389.
E. Boros, Y. Crama and P.L. Hammer,
"Upper Bounds for Quadratic 0 1
Maximization," RRR 1489.
E. Boros and P.L. Hammer, "A Max
Flow Approach to Improved Roof Duality
in Quadratic 0 1 Minimization,"
RRR 1589.
P.L. Hammer, F. Maffray and M.
Preissmann, "A Characterization of
Chordal Bipartite Graphs," RRR 1689.
P. Hansen, B. Jaumard and G. Savard,
"A Variable Elimination Algorithm for
Bilevel Linear Programming," RRR 1789.
University of Southern California
Department of Industrial and
Systems Engineering
Los Angeles, CA 900890193
B.C. Tansel and E. Erkut, "On
Parametric Medians of Trees," 8801.
B.C. Tansel and G.F. Scheuenstuhl,
"Facility Location on Tree Networks with
Imprecise Data," 8803.
AUGUST 1989
PAGE 5
number twentyseven
PAGE 6 number twentyseven AUGUST 198
A.S. Kiran and P. Kouvelis, "The Plant
Layout Problem in Automated
Manufacturing Systems," 8804.
A.S. Kiran, "A Tardiness Heuristic for
Scheduling Flexible Manufacturing
Systems," 8806.
G. Nadler, J.M. Smith and C.E. Frey,
"Problem Formulation Methods in
Engineering Design," 8808.
A.S. Kiran, "A Combined Heuristic
Approach to Dynamic Lot Sizing
Problems," 8809.
M.H. Chignell and R.G. Narayan, "An
Empirical Evaluation of Efficient Ranking
Methods," 8810.
G.F. Scheuenstuhl and B. Tansel, "Tree
Network Facility Location with Normal
Random Demands," 8820.
E. Balas and S.M. Ng, "On the Set
Covering Polytope: II. Lifting the Facets
with Coefficients in (0,1,2,3)," 8821.
A.S. Kiran and S. Karabati, "The Station
Location Problem on Unicyclic Material
Handling Networks," 8825.
Operations Research Group
The Johns Hopkins University
Baltimore, MD
M.H. Schneider, "Matrix Scaling,
Entropy Minimization, and Conjugate
Duality (I): Existence Conditions," 8902.
M.H. Schneider, "Matrix Scaling,
Entropy Minimization, and Conjugate
Duality (II): The Dual Problem," 8903.
H. Schneider and M.H. Schneider,
"MaxBalancing Weighted Directed
Graphs," 8904.
R.D. Parker, "Calculating the Weights of a
Mask for Character Recognition," 8905.
H. Schneider and M.H. Schneider,
"Towers and Cycle Covers for Max
Balanced Graphs," 8906.
J.R. Current, C.S. ReVelle and J.L.
Cohon, "An Interactive Approach to
Identify the Best Compromise Solution for
Two Objective Shortest Path Problems,"
8907.
W. Cook, M. Hartmann, R. Kannan and
C. McDiarmid, "On Integer Points in
Polyhedra," 8908.
V.A. Hutson and C.S. ReVelle,
"Maximal Direct Covering Tree Problems,"
8909.
JS. Shih and C.S. ReVelle, "Hedging
Rules for the Single Water Supply
Reservoir," 8910.
University di Pisa
Dipartimento di Matematica
Sezione di Matematica Applicata
Gruppo di Ottimizzazione e
Ricerca Operativa
Pisa, Italy
J. Naumann, "Existence of Lagrange
Multipliers in Classical Calculus of
Variations," 150.
L. Pellegrini, "An Extension of Hestenes
Necessary Condition for Nondifferentiable
Constrained Extremum Problems," 151.
L. Favati, "Generalizzazione del Modello di
MossinKuppermanLisei per il Controllo
Ottimale," 152.
M. Pappalardo, "A Priori Bounds for
Strongly Convex Nondifferentiable
Extremum Problems," 153.
L. Martein, "An Approach to Lagrangian
Duality in Vector Optimization," 154.
K.H. Elster, "Generalized Notions of
Directional Derivatives," 155.
D.T. Luc, "A Theorem of the Alternative
and Axiomatic Duality in Mathematical
Programming," 156.
O. Ferrero, "On a Property of the
Generalized Subdifferential," 157.
P. Favati, F. Tardella, "A Notion of
Convexity for Functions Defined Over the
Integers," 158.
G. Finke, E. MedovaDempster,
"Combinatorial Optimization Problems in
Trace Form," 159.
E. MedovaDempster, "The Circulant
Traveling Salesman Problem," 160.
L.F. Escudero, "On Solving a
Nondifferentiable Transshipment Problem,"
161.
Ib"~~llll~
AUGUST 1989
I
1
PAGE 6
number twoentyseven
PAE7nme wnyee UUT18
Combinatorics of Experimental Design
A. P. Street and D. J. Street
Oxford University Press, Oxford, 1987
ISBN 0198532555
The book under review is intended as an introductory text (aimed at
3rd and 4th year undergraduates in both mathematics and statistics) on
the combinatorial and statistical aspects of Design Theory. To quote
from the introduction: 'There is an obvious dichotomy in the literature
of designs; they are considered as incidence structures by combinatori
alists and as experimental plans or layoutsbystatisticians, and members
of each of these groups are sometimes unaware of related developments
and problems arising in the other area. We aim to bridge this gap by
providing the background necessary to make the combinatorial aspects
of statistical literature more easily accessible to combinatorialists, and
vice versa." Consequently, the book contains parts where the emphasis
is on combinatorics as well as parts where the statistical aspect domi
nates. Unfortunately, there is quite often the feeling of a rather abrupt
transition between both points of view; thus Iam not quite sure whether
the authors have fully achieved their (difficult) goal. However, the book
certainly is quite interesting and worth studying.
Let me list the main topics covered as indicated by the titles of chap
ters: 1. Introduction; 2. Balanced incompleteblock designs; 3. Difference
set constructions; 4. Isomorphism and irreducibility; 5. Latin squares
and triple systems; 6. Mutually orthogonal Latin squares; 7. Further
results on Latin Squares; 8. Resolvable designs and finite geometries; 9.
Symmetrical factorial designs; 10. Single replicate factorial designs; 11.
Designs with partialbalance; 12. Existence results: Symmetric balanced
designs; 13. Existence results: designs with index 1 and given block size;
14. Designs balanced for neighboring varieties; 15. Competition de
signs. As this list indicates, the main concern is on the existence and con
struction of various types of (pairwise) balanced designs; thus some
rather important basic topics like tdesigns, automorphism groups,
characterizations, connections to coding theory have been (almost)
totally excluded. In viewof thevast amount of literature on designs, this
is justified for an introductory text, though a few more references to the
missing topics would have been welcome. Also, I would have liked to
have some other applications of Design Theory (except for statistical
ones) at least mentioned, in particular, those to computer science and
algorithms.
Still, the reader gets a
good introduction
at least to
thecon
struc
tive
aspects regarding block designs and Latin squares. The presentation is
generally clear and wellwritten. As always, one finds minor faults; e.g.,
the terminological confusion between difference families and sets is
annoying. The proof of the first multiplier theorem given in Ch. 4 is the
original involved one, even though a much more transparent approach
(due to Lander) is known now. In Ch. 7, the three mutually orthogonal
Latin squares of order 14 should not have been displayed explicitly, as
they are in fact constructed by a difference method which would have
simplified the presentation considerably. These imperfections are
balanced by some highlights not yet found in any other text book: e.g., a
proof of the sufficiency of the necessary conditions for triple systems
based on Latin squares or Stinson's proof forTarry's theorem (i.e., for the
nonexistence of a pair of orthogonal Latin squares of order 6).
There are two other recent books on Design Theory: Another
introductory text by D. R. Hughes and F. C. Piper ("Design Theory,"
Cambridge UniversityPress, 1985) and one coauthored by the reviewer
(T. Beth, D. Jungnickel and H. Lenz: "Design Theory," Bibliographis
ches Institut Mannheim, 1985, and Cambridge University Press, 1986)
which aims at graduates and experts in the area. All three books stress
quite different aspects: While Hughes and Piper also is of an introduc
tory nature, this text emphasizes the algebraic aspects of designs (treat
ing e.g. Witt designs and Mathieu groups) and quite neglects the
existence question. Thus this book and the one under review rather
nicely complement each other and together provide an introduction to
all the most important parts of Design Theory. As already mentioned,
myown (and my coauthors') efforts were more concerned with provid
ing a somewhat deeper treatment and a reference for the expert working
in the area. Thus all three books serve their different purposes: If one
wants to specialize in Design Theory, all three books are needed; if one
only wants to get acquainted with designs, either the present text or that
by Hughes and Piper or both (depending on your personal preference
for a more constructive or more algebraic treatment) are well worth
buying.
D.JUNGNICKEL
Surveys in Game Theory and Related Topics
Edited by H. J. M. Peters and 0. J. Vrieze
CWI Amsterdam, 1987
ISBN 9061963222
This book is a collection of 13 survey papers on game
theory and related topics and was dedicated to Profes
sor Stef Tijs of the Catholic University of
Nijmegen in The Netherlands on the occa
sion of his 50th birthday. The forward tells
us the wonderful history of how he has
developed the Dutch school of game
theory, now one of the leading
CONTINUES
dp~~
II1IIICil~lllllll~
ACIarall llrlIllrB
~11111
AUGUST 1989
PAGE 7
number twentyseven
P. PAGE 8 number twentyseven AUGUST 198~
research groups in this field, since he finished his Ph.D. thesis, "Semi
infinite and infinite matrix games and bimatrix games," in 1975. All the
authors of the papers were introduced to game theoryby Professor Tijs,
and 10 of them have finished or are preparing their Ph.D. theses under
his supervision.
The papers cover a wide range of game theory and related topics:
equilibrium points in noncooperative games (by Eric van Damme and
by MathijsJansen), games with incomplete information (by Peter Borm),
stochastic games (by Koos Vrieze and by Frank Thuijsman), a relation
ship between game theory and decision theory (by Peter Wakker),
cooperative games in characteristic function form (by Theo Driessen
and by Jean Derks), cooperative games arising from combinatorial and/
or linear optimization problems (by Imma Curiel and byJos Potters), the
bargaining theory (by Hans Peters) and the theory of social choice (by
Ton Storcken). All papers are clearly written and provide concise
surveys of recent developments in their respective topics. They also
include both new results by the authors themselves and useful refer
ences. The readers can obtain a review of the state of the art in the areas
of game theory mentioned above and also can learn that many tools in
mathematical programming play an important role in those areas. Since
most papers emphasize mathematical aspects of the results such as the
proof methods for the existence of various solution concepts and their
computation, I think that the book should be accessible to many re
searchers in the field of mathematical programming who have little
knowledge of game theory.
This book is recommended to researchers and graduate students
who are interested in recent developments in various fields of mathe
matical game theory.
A. OKADA
Recent Advances and Historical Development of
Vector Optimization
by J. Jahn and W. Krabs
Springer, Berlin, 1987
ISBN 3540182152
In August 1986, J. Jahn and W. Krabs organized an international
conference on vector optimization in Darmstadt, West Germany. Be
sides four stateoftheart tutorials, numerous talks cover various as
pects and purposes of vector optimization, such as: abstract theory,
duality, sensitivity, numerical methods, parametric optimization, multi
criteriadecisionmaking, application of MCDM, etc. Several talks are
collected in this proceedings. In the following, the stateoftheart
tutorials of the Professors W. Stadler, J. M. Borwein, P. L. Yu, and H.
Eschenauer will be discussed in detail.
In his article "Initiators of Multicriteria Optimization," Stadler de
scribes the historical development of vector optimization. A vector
optimization problem is a problem with several objective functions. In
,,
~
P. PAGE 8
0
C
w
general, there is conflict between them. Usually, one solves such
problems by introducing a socalled utility function such that a solution
of the problems with this utility function is a solution of the initial
problem. Such questions were first handled in economic theory. The
economists A. Smith (The Wealth of Nations, 1776), F. Edgeworth (The
Edgeworth Box in Mathematical Physics, 1881), and V. Pareto (Pareto
optimality, 1906) can be said to be the founders of multicriteria optimi
zation as an inherent part of economic equilibrium.
Stadler presents the fundamental statements in the work of Edge
worth and Pareto for welfare theory. In their original papers, one can
already see the wellknown scalarization of the weighted objective
functions. Instead of n objectives and m variables, they speak about n
consumers and m goods. The notion of "efficiency" occurs for the first
time in Koopmans' work on production theory in 1951.
Mathematically, as Stadler writes, the first formulation of a vector
optimization problem is due to Kuhn and Tucker. In their famous paper
from 1951, they give a necessary condition for "proper" solutions. The
first basic treatment of vector optimization can be found in Hurwicz's
paper in 1958 where he considered optimization problems in linear
spaces.
In a conclusion section, some areas of future research are pointed
out: (1) vector optimization theory with respect to partial orders and
preorders; (2) development of computational algorithms to generate the
efficient point set; (3) multicritera aspects of natural phenomena; (4)
further applications.
This paperisvery interesting to read becauseof itsdetailed historical
information and the biographies and pictures of the founders of mul
ticriteria optimization which are added to the article. In my opinion, the
only missing thing is a discussion about the general development and
movement in vector optimization after Hurwicz's paper to the present.
In the article "Convex cones, minimality notions, and consequences,"
Borwein presents vector optimization problems in arbitrary vector
spaces. In every section and subsection, he uses the following scheme:
(a) definitions, (b) properties and relations between the introduced
concepts, (c) theorems, and (d) examples and applications in some
special spaces as L and Qp. Most proofs are omitted (but references are
cited); some proofs are sketched.
The section on cone structures deals, among other things, with order
intervals, monotone sequences and nets, normalityof acone, the Daniell
property of a cone, the base of a cone, and Banach lattices. In every
subsection, Borwein shows the relationships between the introduced
concepts in complete detail. Thus, this section is a referencebook on
where to find conditions on whether a cone with property (A) has
property (B), or property (C) is equivalent to property (D).
Minimality notions are introduced in the next section: Pareto
optimal (or efficient, nondominated, minimal) points, least elements
(or strong minimum point, dominating point), weakefficient point,
proper efficient point are optimal points of a set with respect to a given
cone. Figures illustrate the differences between these concepts. Some
existence theorems of efficient points and a characterization of proper
number twentysevent
AUGUST 198!
PAGE MINuM
efficiency are given.
Finally, Borwein outlines the theory of lattice complementary prob
lems, i.e. to solve minK (x,F(x)) = 0 for F:XX, X a Banach lattice, K a cone.
For instance, a standard linear programming pair can be rewritten as
such a problem.
The paper of Borwein treats the introduced concepts very compre
hensively, but in my opinion it is a little bit too compact. More
discussion would be better for a reader who is not familiar with vector
optimization problems in abstract spaces. Nevertheless, the complete
discussion of the broached questions is impressive as was Borwein's
excellent talk at the conference.
In their article, "Foundations of Effective Goal Setting", Yu and
Chien give a readable, detailed introduction to the field of effective goal
setting. Their purpose is to formulate a complex multicriteria optimal
control system in which problems of effective goal setting can be
transformed.
Usually in multicriteria decision making there is a fixed set of
objectives and alternatives, and the aim is to find "optimal" solutions.
But many decision problems have alternative sets and criteria functions
which are not fixed, but change, for instance, with time. For example, in
reaching a great goal one gives oneself a series of "increasing" goals for
motivation.
For their purpose, the authors use the concepts of human behavior
mechanism and habitual domain: each individual is endowed with an
internal information processing and problem solving capacity and has a
set of goals to reach and maintain. In comparison between real and ideal
values, one tries to find goals and alternatives which produce great
charges and reduce the level of charges by selecting other alternatives or
by active problem solving or avoidance justification. This dynamic
behavior mechanism, although changing with time, can stabilize and
can have stable habitual patterns for processing information. This lead s
to habitual domains, divided into potential domains, actual domains,
and reachable domains. An essential role is played by the cores of the
habitual domains, i.e. the set of central ideas or concepts.
Utilizing these concepts, the authors can formulate problems of
effective goal setting into a complex multiple criteria optimal control
system by (a) selecting measurable goal functions, (b) setting goal
achievement levels, and (c) determining effective supportive systems as
control variables. The stated variables are working conditions, charge
structures and confidence; the objectives are to maximize the attention
allocation of time to jobrelated works, to maximize the efficiency and
effectiveness of work performance, and to maximize the favorability of
the working environment. Finally, some empirically known results are
discussed.
In his paper, "Multicriteria Optimization Procedures in Application
on Structural Mechanics Systems," Eschenauer presents a computer
program package called SAPOP (Structural Analysis Program and
Optimization Procedure) to support a decision maker by solving vector
optimization problems for structural analysis. What objectives are to be
considered for these problems? Of course, a decision maker wants to
I
minimize the costs of developing and manufacturing machines. But
other criteria may shape accuracy and reliability of the systems, among
others.
The program SAPOP coordinates the three main parts of the optimi
zation process and the data exchange between them: (1) optimization
algorithms, (2) optimal modelling, and (3) structural analysis.
In part (1), SAPOP makes available a lot of optimization algorithms
because there is no procedure which is at the same time efficient and
applicable for all problems.
Part (3) is the starting point of every structural optimization prob
lem. As Eschenauer indicates, this first step must be done very carefully
because the computation depends essentially on the quality of the
mathematicalmechanical model. Among these models one distin
guishes between (a) ordinary differential equation models, (b) differ
ence equation models, (c) partial differential equation models, and (d)
algebraic (nondifference) equation models.
Part (2) is the link between the other two parts. Here, strategies to
find efficient solutions were created. Some scalarizations (weighted
objective functions, distance functions, tradeoffmethod, minmax
formulation) are discussed.
Finally, some applications and numerical results are quoted. Esch
enauer describes how to find an optimal layout of a shell structure.
These problems arise, for instance, in the field of antenna and telescope
construction.
This paper gives a good discussion of problems of structural analysis
with several objectives and a brief introduction to the program SAPOP.
For deeper insight, references are cited.
S. HELBIG
Algorithmic Information Theory
by G. J. Chaitin
Cambridge Tracts in Theoretical Computer Science 1
Cambridge University Press, Cambridge, 1987
ISBN 0521343062
One way of stating certain famous theorems of G6del, Church, and
Turing is that there is a function f such that no computer program can
decide, for all natural numbers a, whether there is a natural number x
with
f(x) = a.
The f in these results typically examined an x intended to encode a
proof (or a computation) with f(x) being an encoding of the final result.
The functions f constructed in these results involved many definitions
by cases using one formula if x was even, another if
x = 4k + 1, and so forth. The search for results involving f with
"neater" definitions culminated in Matijasevic's 1970 solution of Hil
bert's tenth problem: a polynomial in several variables f (x,a,) was
CONTINUES

AUGUST 1989
PAGE 9
number twenttysevuen
PAGE 0 numer tentyevenAUGUS 198
constructed such that no program can tell, for all natural number vectors
a, whether there is a natural number vector x with f (x,a) = 0. The
construction is quite complex, in spite of simplifications by Davis,
Robinson, and others. In 1984, Jones and Matijasevic gave a much
simpler construction for f which included expressions involving expo
nents.
The author presents this most recent construction and explores its
implications. No advanced results from number theory or theory of
equations are required. In order to establish results about computer
programs, one must have a precise definition. The author has chosen for
this purpose a version of LISP which he develops from scratch in twelve
pages. Perhaps fortunately, the reader unfamiliar with LISP can accept
on faith the construction of f and proceed to the half of the book dealing
with implications.
The proof of noncomputability is different from the usual one. The
author obtains contradictionsby focussing on the smallest program that
will print a specified string. The author has done much work in which
finite strings which require long programs are considered to be pseudo
random, and this aspect receives considerable attention here.
In both halves of the book, the author has taken the trouble to supply
motivational remarks and exhortations ("Initially, the material will
seem completely incomprehensible, but all of a sudden the pieces will
snap together into a coherent whole"). It would help the reader if he has
seen previous work by the author on these issues (for example, "Ran
domness and Mathematical Proof," Scientific American, 1975).
Matijasevic's work was used in a paper by Jeroslow, "There Cannot
be any Algorithm for Integer Programs with Quadratic Constraints"
(Operations Research, 1973). I suspect that most Mathematical Pro
gramming Society members are more interested in establishment of
lower bounds on the difficulty of problems for which computer pro
grams exist. This book does not directly address such issues, but my
impression is that the type of reasoning developed here might help on
some problems of this kind.
C. E. BLAIR
Mathematical Programming: An Introduction to
Optimization
Pure and Applied Mathematics Series
by Melvyn W. Jeter
Marcel Dekker, Basel, 1986
ISBN 0824774787
Whenever a new textbook with a title like "Mathematical Program
ming" or "Introduction to Optimization" is published, my first reaction
is usually a rather cynical comment on this (n+1)si[n *] book of its
type.
With Jeter's book my reaction was different. Students will enjoy
using this bookbecause of two main reasons: (1) Most o fthe mathemati
r
I
PAGE 10
number twentyseven
AUGUST 1989
cal facts which are stated are proved in a clear and understandable way.
There are hardly any of these "obviously" or "as can easily be seen"
sequences which scare so many of our students away; (2) Every detail of
the presented material is accompanied by worked examples and further
supported by exercises. But Jeter avoids the flaw of many mathematical
programming textbooks of replacing theory completely by examples.
Because of the thoroughness of the presentation of the chosen
material, the author evidently had to make some sacrifices in the
material selection. In Chapter 1 different types of mathematical pro
grams are introduced. Chapter 2 reviews elementary linear algebra and
affine and convex sets. Furthermore, LPs and their basic properties are
introduced. Chapters 3, 4 and 5 cover various versions of the simplex
method including a chapter on duality and linear complementarity. The
cycling phenomenon is discussed, but I was surprised not to see Bland's
simple cycle avoiding rule.
The sixth chapter on network programming is somewhat disap
pointing. The classic Ford/Fulkerson algorithm for finding maximal
flows is discussed without any reference to more efficient procedures.
Sections on network programming problems different from flow prob
lems are missing.
Chapter 7 provides the mathematical tools needed in dealing with
convex functions of one or more variables. The last three chapters give
an overview of nonlinear, continuous programs. In Chapter 8 optimal
ity conditions are discussed. Chapter 9 deals with search techniques for
unconstrained problems, and Chapter 10 introduces penalty methods.
As the preceding summary shows, most instructors will add supple
mental material to various parts ofJeter's book. Since thebook is written
so nicely, one may in an advanced course actually concentrate on
supplemental material and assign large parts of Jeter's text as reading
assignments.
H. HAMACHER
Fractional Programming
by B. D. Craven
Heldermann Verlag, Berlin, 1988
ISBN 3885384043
The book deals with nonlinear programming problems where the
objective function is a ratio of two functions or involves even several
ratios. These socalled fractional programs often have properties which
they do not share with general nonlinear programs. A linear fractional
program is one where both numerator and denominator are affine
linear and the constraints are linear. The book covers applications,
theory and algorithms for linear and nonlinear fractional programs.
In Chapter 1 several (potential) applications of fractional program
ming are surveyed. These include planning problems in production,
scheduling, finance as well as stochastic programming and stochastic
processes. Chapter 2 is devoted to linear fractional programs where
number twentyseven
PAGE 11
equivalent programs and duality are discussed. Chapter 3 focuses on
the more general problem of maximizing the ratio of a concave and a
convex function. Equivalent problems and the relationship to general
ized convexity are dealt with. Duality and sensitivity of nonlinear
fractional programs are presented in Chapter 4. In Chapter 5 the author
discusses algorithms in linear and nonlinear fractional programming.
The final chapter addresses three problems in multiratio fractional
programming: maximizing the sum of ratios, maximizing the smallest
of several ratios and multiobjective fractional programming.
Each chapter ends with exercises and a selective bibliography. The
book can serve as a textbook for students who are famr ni.,' with the
basics of linear and nonlinear programming and who are acquainted
with the fundamentals of linear algebra and calculus. The book is an
introduction to fractional programming rather than a detailed survey of
the extensive literature. But it reaches a depth that makes it attractive
also to the researcher in the field. It is the first book on fractional pro
gramming that appeared after the initial monograph of the reviewer in
1978. I warmly recommend it to anyone interested in fractional pro
gramming or general nonlinear programming.
S. SCHAIBLE
Application for Membership
Mail to:
THE MATHEMATICAL PROGRAMMING SOCIETY, INC.
do International Statistical Institute
428 Prinses Beatrixlaan
2270 AZ Voorburg
The Netherlands
Cheques or money orders should be made payable to
THE MATHEMATICAL PROGRAMMING SOCIETY, INC.
in one of the currencies listed below.
Dues for 1989, covering subscription to volumes 4345 of
Mathematical Programming, are Dfl.115.00 (or $55.00 or
DM100.00 or 32.50 or FF345.00 or Sw.Fr.86.00).
Student applications: Dues are onehalf the above rates.
Have a faculty member verify your student status and send
application with dues to above address.
I wish to enroll as a member of the Society. My subscrip
tion is for my personal use and not for the benefit of any
library or institution. I enclose payment as follows:
Dues for 1989
Name (please print)
Mailing Address (please print)
Signature
Faculty verifying status
Institution
Ir~B~saRp~rrpsl]ll~.r~tdrrBL33
AUGUST 1989
m
 
PAGE 2 numbr~ twnysvn UUT18
Gallimaufry
Kurt Anstreicher (Yale) will spend the 198990
academic year at CORE...Carl Harris (George
Mason University) has issued a call for
nominations for the 1988 Lanchester
SPrize...The IFORS '90 conference will be
held June 2529, 1990 in Athens, Greece.
Jens Clausen has taken over production
and distribution of the COAL newsletter
and Faiz A. AlKhayyal (Georgia Tech) is
the U. S. coeditor.
I OPTIMA Wine is available from Op
tima Vineyards, Sonoma County, CA.
II Deadlinefor the next OPTIMA is Octo
ber 1, 1989.
P T I M A
MATHEMATICAL PROGRAMMING SOCIETY
303 Weil Hall
College of Engineering
University of Florida
Gainesville, Florida 32611 USA
FIRST CLASS MAIL
PAGE 12
number t~wentyseven
AUGUST 1989
Books for review should be
sent to the Book Review Editor,
Prof. Dr. Achim Bachem,
Mathematiches Institute der
Universitfit zu Kiln,
Weyertal 8690, D5000 Kiln,
West Germany.
Journal contents are subject
to change by the publisher.
Donald W. Hearn, EDITOR
Achim Bachem, ASSOCIATE EDITOR
PUBLISHED BY THE MATHEMATICAL
PROGRAMMING SOCIETY AND
PUBLICATION SERVICES OF THE
COLLEGE OF ENGINEERING,
UNIVERSITY OF FLORIDA.
