MATHEMATICAL PROGRAMMING SOCIETY NEWSLETTER JUNE 1988
Journal Series B Replaces Studies
SN 1988, all members of the Mathematical Programming
I Society will begin to receive Mathematical Program-
ming, Series B (MPB), in addition to the journal Mathe-
matical Programming, which will now be referred to as
Series A. MPB replaces the Mathematical Programming
ii Studies, which ceases publication.
In many respects, MPB will serve a function similar to
that performed by the Studies. Generally, each issue will deal
with a unified subject of interest to Society members. Each year
we will publish three issues dealing with theoretical, computa-
tional and applied aspects of mathematical programming. An
issue may be a collection of articles or a single research mono-
graph. For example, three of our first issues will be proceedings
of recent conferences: The Martin Beale Memorial Symposium
(edited by M.D. Powell), the Symposium on Parallel Comput-
ing in Mathematical Programming (edited by O. Mangasarian
and R. Meyer) and the Capri Workshop on Applications of
Combinatorial Optimization (edited by M. Padberg, G. Rinaldi
and A. Sassano).
Because of the diversity of interests of the Society mem-
bership, it is neither likely nor intended that all issues will have
the same interest for all members. It is our goal to maintain a
broad balance of topics and our hope that all members will find
something of interest in each three issue volume.
A major difference between MPB and the Studies is that
MPB has an editorial board separate from Series A. The respon-
sibilities of its members are to ensure that a high editorial
standard is maintained, to assist in the generation of new issues
and to provide advice concerning the acceptance of proposals
for issues received. Most issues will be edited by a guest editor
who will be responsible for carrying out the editorial process in
accordance with our standards.
A main objective is to continue to publish high quality
collections of papers dealing with the various aspects of linear,
nonlinear and integer programming and continuous and dis-
crete optimization. In addition, MPB provides us with an op-
portunity to be proactive rather than reactive. We hope to be
able to produce timely issues on topics of current interest. One
such topic is the application of mathematical programming to
real world problems as well as other branches of science. Several
issues will focus on this over the next few years. Another area of
continues, page eleven
Workshop on Mathematical
Catholic University of Rio De
October 10-14, 1988
Combinatorial Optimization, Nondif-
ferentiable Optimization, Projective
Celso Ribeiro, Chairman, Michel Balinski,
Martin, Nelson Maculan, Philippe Mahey,
J. Araoz, M. Balinski, F. Barahona, R. A. Cu-
ninghame-Green, J. Ferland, C. Gonzaga, M.
Grotschel, P. Hammer, P. Hansen, J. B.
Hiriart-Urruty, K. C. Kiwiel, B. Korte, F.
Louveaux, F. Maffioli, N. Maculan, P.
Mahey, M. Minoux, V. H. Nguyen, M.
Padberg, W. Pulleyblank, C. Ribeiro, R. T.
Rockafellar, J. Spingarn, M. Todd, P. Toth,
Information and Mail:
Professor Celso C. Ribeiro
Catholic University of Rio De Janeiro
Department of Electrical Engineering
Gavea Caixa Postal 38063
Rio De Janeiro 22452
Phone: (55) (21) 529-9334/529-9336/529-
PAGE 2 0 P T M A n t J
~Ii*~ Ii' -
A SPECIAL ISSUE OF
GRAMMING Series B
devoted to large scale problems
is being prepared under the joint
editorship of A.R. Conn, N.I.M.
Gould and Ph.L. Toint. The em-
phasis is intended to be large
scale nonlinear programming
rather than linear programming.
However, articles that empha-
size applications, algorithms
and/or theory that is not pri-
marily linear programming
oriented could be suitable and
Mathematical Programming Series B is now
on a similar schedule to Series A with similar
standards for publication and the same
circulation. The advantage of a special issue,
besides collecting articles on a coherent
theme, is that the refereeing process can often
If you have a suitable paper for such an issue
you are invited to submit it to one of the
A. R. Conn
Department of Combinatorics and Optimiza-
Faculty of Mathematics
University of Waterloo
Waterloo, Ontario, CANADA N2L 3G1
Tel: (519) 888-4458
N. I. M. Gould
Computer Science and Systems Division
Oxforshire OX11 ORA, UNITED KINGDOM
Tel: 235-24141 extn 3357
Ph. L. Toint
Department of Mathematics
Facultes Universitaires Notre Dame de la
Rue de Bruxelles, 61
B-5000, Namur, BELGIUM
Tel: 32-81-229061 extn 2592
The deadline for submission is August 1,
1988 for the issue that is to be published in
1989. Late submissions, an excess of submis-
sions, etc., would automatically be consid-
ered for Mathematical Programming Series
A, unless the author wishes otherwise.
- A. Conn
NUMERICAL OPTIMISATION CENTRE
announces the availability of software licences for
The OPTIMA Library of FORTRAN Optimisation
Codes on the IBM-PC and look-a-likes as well as
VAX, IBM, DEC and other main frames.
2 A library of Ada optimisation codes for the VAX
Ada V 1.0 complier on VAX/VMS and VERDIX
compiler for the SUN. The library is based on Ex-
tended Operator Implementation of Automatic Dif-
Enquiries for annual or permanent
licences should be addressed to:
Professor LAURENCE DIXON
Numerical Optimisation Centre
College Lane, Hatfield, Herts,
Tel. (07072) 79761
-- ~---_I~ --~I~I_
0 P T I M A number twenty-four
Editor-in-Chief: Peter L. Hammer,
Rutcor, Hill Center for the Mathematical Sciences, Rutgers University, Busch Campus,
New Brunswick, NJ 08903.
New, so far in 1988:
Vol. 14: Meyer, R.R. and S.A. Zenios, Parallel
Optimization on Novel Computer Architectures.
1988, about 400 pages, to appear in July 1988.
Vol. 13: Simeone, B., P. Toth, G. Gallo,
F. Maffioli and S. Pallottino, Fortran Codes
for Network Optimization.
1988, about 400 pages, to appear in May 1988.
Vol. 12: Jeroslow, R.G., Approaches to
Intelligent Decision Support.
1988, 359 pages, published in March 1988.
Available 1984 1987:
Vol. 10-11: Ibaraki, T., Enumerative
Approaches to Combinatorial Optimization.
2 volumes. 1987. 602 pages.
Vol. 8-9: Albin, S.L. and C.M. Harris,
Statistical and Computational Issues in
2 volumes. 1987. 644 pages.
Vol. 7: Blaiewicz, J., W. Cellary,
R. Slowifiski and J. Weglarz, Scheduling under
Resource Constraints Deterministic Models.
1986. 359 pages.
Vol. 6: Osleeb, J.P. and S.J. Ratick,
Locational Decisions: Methodology and
1986. 328 pages.
Vol. 4-5: Monma, C.L., Algorithms and Software
2 volumes. 1986. 632 pages.
Vol. 3: Stecke, K.E. and R. Suri, Flexible Manu-
facturing Systems: Research Models and Applications
1985. 488 pages.
Vol. 2: Thompson, R.G. and R.M. Thrall, Normative
Analysis for Policy Decisions, Public and Private.
1985. 360 pages.
Vol. 1: Archetti, F. and F. Maffioli, Stochastics and
1984. 366 pages.
Stecke, K.E. and R. Suri, Flexible Manufacturing
A new volume based on FMS'86, Ann Arbor
Radermacher, F.-J., R.L. Keeney, R.H. M6hring and
M.M. Richter, Multi-Attribute Decision Making via
O.R.-based Expert Systems. 1988.
A new vol. based on the 1986 Passau meeting.
Fishburn, P.C. and I. LaValle, Choice under
Kusiak, A. and W.E. Wilhelm, Analysis, Modeling
and Design of Modern Production Systems.
Louveaux, F., Locational Decisions.
A new volume based on ISOLDE'87, Louvain
vol. 12-16, 1988: Sfr. 1687.50/$ 1088.70 including postage & handling.
Back volume price:
Vol. 1-11, 1984-1987: Sfr. 175.00/$ 113.00 per volume including postage & handling.
ORSA/TIMS members price:
Vol. 1-11, 1984-1987: Sfr. 110.00/$ 71.00 per volume including postage & handling.
How to order:
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mentioned below. In the United States please address your order to: J.C. Baltzer AG, Scientific
Publishing Company, P.O. Box 8577, Red Bank, NJ 07701-8577.
8 Wetstin~atz 0, H408, asel Swtzelan
0 P T I M A number twenty-four
O P T I M A number twenty-four
C4- Technical Reports & Working Papers
University Di Pisa
Dipartimento Di Matematica
Sezione Di Matematica Applicata
Gruppo Di Ottimizzazione E Ricerca Operativa
G. Pesamosca, "On Numerical Resolution of a Steiner-Weber Type
Problem via Subgradient Method," 142.
P. Pieroni, G. Saviozzi, "Condizioni di Ottimaltia per una Classe di
Problem di Ottimizzazione in uno Spazio Discreto," 143.
G. Lisei, "On the Functional Equation (x,y,z)=L((x,y,t),t,z)," 144.
M. Pappalardo, "A Necessary Optimality Condition for Nondifferenti-
able Constrained Extremum Problems," 145.
S. Nanda, "On a Complementarity Problem in Mathematical Program-
ming in Banach Space," 146.
M. Pappalardo, "Error Bounds in Locally Lipschitz Programming," 147.
S. Nanda, "Variational Inequalities and Complementarity Problems in
Banach Spaces," 148.
K.-H. Elster, A. Wolf, "On a General Concept of Conjugate Functions,"
L. Martein, "An Approach to Lagrangian Duality in Vector Optimiza-
Department of Operations Research
Erasmus University Rotterdam
P. 0. Box 1738
3000 DR Rotterdam
J. Csirik, J.B.G. Frenk, G. Galambos and A.H.G. Rinnooy Kan,
"Probabilistic Analysis of Algorithms for Dual Bin Packing Problems,"
M. Meanti, A.H.G. Rinnooy Kan, L. Stougie and C. Vercellis, "A
Probabilistic Analysis of the Multiknapsack Value Function,", 8709/A.
G.A.P. Kindervater, J.K. Lenstra and A.H.G. Rinnooy Kan, "Per-
spectives on Parallel Computation," 8719/A.
A. de Bruin, A.H.G. Rinnooy Kan and H.W.J.M. Trienekens, "A
Simulation Tool for the Performance Evaluation of Parallel Branch-and-
Bound Algorithms," 8720/A.
M. Haimovich, A.H.G. Rinnooy Kan and L. Stougie, "Analysis of
Heuristics for Vehicle Routing Problems," 8727/A.
A.H.G. Rinnooy Kan, "Mathematical Programming as an Intellectual
O.E. Flippo, A.H.G. Rinnooy Kan and G. van der Hoek, "Duality
and Decomposition in General Mathematical Programming," 8747/B.
J. Birge, J.B.G. Frenk, J. Mittenthal and A.H.G. Rinnooy Kan, "Single
Machine Scheduling Subject to Stochastic Breakdowns," 8748/B.
Operations Research Group
The Johns Hopkins University
M. Daskin, K. Hogan and C. ReVelle, "Integration of Multiple, Excess,
Backup and Expected Covering Models," 87-01.
C.S. ReVelle and K. Hogan, "A Reliability Constrained Siting Model
with Local Estimates of Busy Fractions," 87-02.
J.H. Ellis, "Multiobjective Mathematical Programming Models for Acid
J.H. Ellis and C.S. ReVelle, "A Separable Linear Algorithm for Hydro-
power Optimization," 87-04.
H. Schneider and M.H. Schneider, "An Io Balancing of a Weighted
Directed Graph," 88-01.
ONR Computational Combinatorics URI
Institute for Interdisciplinary Engineering
304A Potter Engineering Center
West Lafayette, Indiana 47907
S.S. Abhyankar and C. Bajaj, "Automatic Rational Parameterization of
Curves and Surfaces II: Cubics and Cubicoids," CC-87-1.
S.S. Abhyankar and C. Bajaj, "Automatic Parameterization of Rational
Curves and Surfaces III: Algebraic Plane Curves," CC-87-2.
R.K. Kincaid, T.J. Lowe and T.L. Morin, "The Location of Central
Structures in Trees," CC-87-3.
M.G. Pilcher and R. Rardin, "A Random Cut Generator for Symmetric
Traveling Salesman Problems with Known Optimal Solutions," CC-87-4.
G.N. Frederickson and R. Janardan, "Efficient Message Routing in
Planar Networks," CC-87-5.
G. Frederickson and S. Rodger, "A New Approach to The Dynamic
Maintenance of Maximal Points in a Plane," CC-87-6.
G.N. Frederickson and S.E. Hambrusch, "Planar Linear Arrange-
ments of Outerplanar Graphs," CC-87-7.
M. Atallah and C. Bajaj, "Efficient Algorithms for Common Transver-
M. Atallah, Cole and Goodrich, "Cascading Divide-and-Conquer: A
Technique for Designing Parallel Aglorithms," CC-87-9.
M. Atallah and Kosaraju, "Minimizing Robot Arm Travel," CC-87-10.
Goodrich, "Triangulating A Polygon in Parallel," CC-87-11.
Y. Chang, S. Hambrusch and J. Simon, "On the Computational
Complexity of Continuous Routing," CC-87-12.
C. Guerra and S. Hambrusch, "Parallel Algorithms for Line Detection
on a Mesh," CC-87-13.
V.J. Chandru and R. Venkatesan, "Automatic Prehension with Three
V.M. Chandru and M.A. Trick, "On the Complexity of Lagrange
Multiplier Search," CC-87-15.
M.G. Pilcher and R. Rardin, "Invariant Problem Statistics and
Generated Data Validation: Symmetric Traveling Salesman Problems,"
PAGE~ 5_ 0 P MAnmbrtenyforJNE18
R. Rardin and B.A. Campbell, "Steiner Tree Problems on Steiner-
Parallel Block Graphs. 1: Polynomial Recognition and Solution,"CC-87-17.
A. Balakrishnan, J.E. Ward and R.T. Wong, "Integrated Facility
Location and Vehicle Routing Models: Recent Work and Future Pros-
S.S. Abhyankar and D.M. Kulkarni, "On Hilbertian Ideals," CC-87-19.
D.B. Hartzigsen and D.K. Wagner, "Recognizing Linear Programming
Problems with the Max-Flow-Min-Cut Property," CC-87-20.
C.R. Coullard, J.G. delGreco, and D.K. Wagner, "Representations of
Bicircular Matroids," CC-87-21.
A. Balakrishnan, T. Magnanti and R. Wong, "A Dual Ascent Procedure
for Large Scale Uncapacitated Network Design," CC-87-22.
A.K. Gupta and S.E. Hambrusch, "Simulating Tree Algorithms with
Limited Parallelism," CC-87-23.
R.K. Martin, R.L. Rardin and B.A. Campbell, "Polyhedral Characteriza-
tion of Discrete Dynamic Programming," CC-87-24.
R.L. Rardin, B.A. Campbell and R.K. Martin, "Steiner Problems on
Series-Parallel Block Graphs II: Polyhedral Characterization," CC-87-25.
G.N. Frederickson and M.A. Srinivas, "Algorithms and Data Struc-
tures for an Expanded Family of Matroid Intersection Problems," CC-87-
T.W. Chien, A. Balakrishnan and R.T. Wong, "An Integrated Inventory
Allocation and Vehicle Routing Problem," CC-87-27.
N. Balakrishnan and R.T. Wong, "A Network Model for the Rotating
Work Force Scheduling Problem," CC-87-28.
J.E. Ward, R.T. Wong, P. Lemke and A. Oudjit, "Properties of the Tree
K-Median Linear Programming Relaxation," CC-87-29.
V. Chandru and D. Dutta, "Composition of Planar Offsets," CC-87-30.
A. Aman, A. Balakrishnan and V. Chandru, "Maintenance of Optimal
M.J. Atallah, G.N. Frederickson and S.R. Kosaraju, "Sorting with
Efficient Use of Special-Purpose Sorters," CC-87-32.
C. Coullard and W.R. Pulleyblank, "On Cycle Cones and Polyhedra,"
A. Gupta and S. Hambrusch, "On Tree Embeddings with Even Leaf
R.L. Carraway, R.J. Chambers, T.L. Morin and H. Moskowitz,
"Scheduling with Multiple Performance Measures: Generalized Dynamic
Programming for Nonlinear Multicriteria Cost Functions," CC-87-35.
V. Chandru and R. Samuel, "How to Draw a Circumscribing Gleich-
V. Chandru and R. Swaminathan, "Recognizing Monotone Line
Obstacles in Subquadratic Time," CC-87-37.
S. Hambrusch and L. TeWinkel, "A Study of Connected Component
Labeling Algorithms on the MPP," CC-88-1.
R. Rardin, C.A. Tovey and M.G. Pilcher, "Polynomial Constructability
and Traveling Salesman Problems of Intermediate Complexity," CC-88-2.
Department of Industrial Engineering and
Evanston, IL 60201
S. Mehrotra, "On the Relationship of the Method of Centers with Some
Interior Point Methods," 87-01.
P.C. Jones and E.S. Theise, "On the Equivalence of Competitive Trans-
portation Markets and Congestion in Spatial Price Equilibrium Models",
R. Fourer, D.M. Gay, and B.W. Kernighan, "AMPL: A Mathematical
Programming Language", 87-03.
E.S. Theise, "A Turbo Pascal Implementation of the Expandable
Equilibrium Algorithm", 87-04.
P.C. Jones and E.S. Theise, "A Microcomputer-Based Implementation of
the Expanding Equilibrium Algorithm for Linear, Single Commodity
Spatial Price Equilibrium Problems", 87-05.
J. Sun, "Reformulating Convex Piecewise Linear Programs as Monotropic
Piecewise Linear Programs," 87-09.
J. Sun, "A Parallel Algorithm for Network Linear Programming Based on
Chip Decomposition," 87-10.
P.C. Jones, J.C. Swarts and G. Morison, "Nonlinear Spatial Equilib-
rium Algorithms: A Computational Comparison," 87-11.
P.C. Jones and R.R. Inman, "Decomposition of a Group Technology
Economic Lot Scheduling Problem," 87-13.
J. Sun, "On the Equivalence Between Piecewise Quadratic Programs and
Quadratic Programs," 87-14.
J. Sun, "Tracing the Characteristic Curve of a Quadratic Black Box," 87-
S. Mehrotra and J. Sun, "An Algorithm for Convex Quadratic Program-
ming that Requires O(n35L) Arithmetic Operations," 87-23.
Department of Electrical and Computer
The Johns Hopkins University
Barton Hall Room 105
Baltimore, MD 21218
G.G.L. Meyer and L.J. Podrazik, "Parallel Implementations of Gradient
Based Iterative Algorithms for a Class of Discrete Optimal Control
G.G.L. Meyer, "Convergence of Relaxation Algorithms by Averaging,"
G.G.L. Meyer and L.J. Podrazik, "Parallel Iterative Algorithms to Solve
the Discrete LQR Optimal Control Problem with Hard Control Bounds,"
Stichting Mathematisch Centrum
Centrum voor Wiskunde en Informatica
Centre for Mathematics and Computer Science
P. O. Box 4079
1009 AB Amsterdam
A. Schrijver, "Polyhedral Combinatorics," 0S-R8701.
J.L. van den Berg and O.J. Boxma, "Throughput Analysis of a Flow-
Controlled Communication Network with Buffer Space Limitations," OS-
M. Desrochers, "A Note on the Partitioning Shortest Path Algorithm,"
J.W. Polderman, "A State Space Approach to the Problem of Adaptive
Pole Assignment," OS-R8704.
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0 P T IM A number twenty-four
PAGE~ 6 0 ubrtwnyfu UE18
0* Technical Reports & Working Papers
J.W. Polderman, "Adaptive Exponential Stabilization of a First Order
Continuous-Time System," OS-R8705.
S.A. Smulders, "Modelling and Filtering of Freeway Traffic Flow," OS-
O.J. Boxma and W.P. Groenendijk, "Waiting Times in Discrete-Time
Cyclic-Service Systems," OS-R8707.
J.L. van den Berg, O.J. Boxma and W.P. Groenendijk, "Sojourn Times
in the M/G/1 Queue with Deterministic Feedback," OS-R8708.
G.A.P. Kindervater, J.K. Lenstra and A.H.G. Rinnooy Kan, "Perspec-
tives on Parallel Computing," OS-R8709.
J.L. van den Berg and O.J. Boxma, "Sojourn Times in Feedback
M.W.P. Savelsbergh, "Local Search for Constrained Routing Problems,"
O.J. Boxma and W.P. Groenedijk, "Two Queues with Alternating
Service and Switching Times," OS-R8712.
P.R. de Waal, "Performance Analysis and Optimal Control of an M/M/
1/k Queueing System with Impatient Customers," OS-R8713.
J.K. Lenstra, D.B. Shmoys and E. Tardos, "Approximation Algorithms
for Scheduling Unrelated Parallel Machines," OS-R8714.
M. Desrochers, J.K. Lenstra, M.W.P. Savelsbergh [et al.], "Vehicle
Routing with Time Windows: Optimization and Approximation," OS-
J.M. Anthonisse, J.K. Lenstra and M.W.P. Savelsbergh, "Functional
Description of CAR, an Interactive System for Computer Aided Routing,"
O.J. Boxma and G.A.P. Kindervater, "A Queueing Network Model for
Analyzing a Class of Branch and Bound Algorithms on a Master-Slave
A. Schrijver, "Edge-Disjoint Homotopic Paths in Straight-Line Planar
A. Schrijver, "Decomposition of Graphs on Surfaces and a Homotopic
Circulation Theorem," OS-R8719.
G.A.P. Kindervater and J.K. Lenstra, "Parallel Computing in Combi-
natorial Optimization," OS-R8720.
M. Desrochers, J.K. Lenstra and M.W.P. Savelsbergh, "A Classifica-
tion Scheme for Vehicle Routing and Scheduling Problems," OS-R8721.
School of Operations Research and
Ithaca, NY 14853
D. Ruppert, "Fitting Mathematical Models to Biological Data: A Review
of Recent Developments," TR 760.
M.J. Todd and Y. Ye, "A Centered Projective Algorithm for Linear
Programming," TR 763.
J.S.B. Mitchell, "Shortest Paths Among Obstacles, Zero-Cost Regions,
and Roads," TR 764.
D. Joneja, "The Joint Replenishment Problem: New Heurisitics and
Worst Case Performance Bounds," TR 765.
R. Roundy, "Optimal Cyclic Schedules for Job Shops with Identical
Jobs," TR 766.
P.L. Jackson and R.O. Roundy, "Minimizing Separable Convex Objec-
tives on Arbitrarily Directed Trees of Variable Upper Bound Con-
straints," TR 767.
R.O. Roundy and E. Arkin, "Weighted-Tardiness Scheduling with
Weights Proportional to Processing Times," TR 768.
G. Gallego and R.O. Roundy, "The Extended Economic Lot Scheduling
Problem," TR 769.
G. Gallego, "Linear Control Policies for Scheduling a Single Facility
After an Initial Disruption," TR 770.
G. Gallego, "Produce-Up-To Policies for Scheduling a Single Facility
After an Initial Disruption," TR 771.
L.W. Schruben and E. Yucesan, "On the Generality of Simulation
Graphs," TR 773.
M.J. Todd, "On Anstreicher's Combined Phase I Phase II Projective
Algorithm for Linear Programming," TR 776.
D. Goldfarb and M.J. Todd, "Linear Programming," TR 777.
J.S.B. Mitchell, "An Algorithmic Approach to Some Problems in Terrain
Navigation," TR 779.
M.J. Todd, "On the Convergence of Algorithms for Unconstrained
Minimization," TR 780.
M.J. Todd, "Karmarkar as Dantzig-Wolfe," TR 782.
M. Rudemo, D. Ruppert, and J.C. Streibig, "Random Effect Models in
Nonlinear Regression with Applications to Bioassay," TR 786.
E. Willekens and S.I. Resnick, "Quantifying Closeness of Distributions
of Sums and Maxima When Tails are Fat," TR 787.
G JOURNALS & STUDIES
Vol. 41, No. 1
T.F. Coleman, "A Chordal Preconditioner for Large-Scale Optimiza-
P.T. Harker, "Accelerating the Convergence of the Diagonalization and
Projection Algorithms for Finite-Dimensional Variational Inequalities."
D.F. Shanno, "Computing Karmarkar Projections Quickly."
H. Kawasaki, "An Envelop-Like Effect of Infinitely Many Inequality
Constraints on Second-Order Necessary Conditions for Minimization
M.J. Todd, "Exploiting Special Structure in Karmarkar's Linear
Vol. 41, No. 2
D. Aze, "An Example of Stability for the Minima of a Sequence of D. C.
Functions: Homogenization for a Class of Nonlinear Sturm-Liouville
M. Bougeard, "Morse Theory for Some Lower-C2 Functions in Finite
H. Tuy and R. Horst, "Convergence and Restart in Branch-and-Bound
Algorithms for Global Optimization. Application to Concave Minimiza-
tion and D. C. Optimization Problems."
H. Konno, "Minimum Concave Cost Production System: A Further
Generalization of Multi-Echelon Model."
J.-P. Penot, "Approximation and Decomposition Properties of some
Classes of Locally D. C. Functions."
P.T. Thach, "The Design Centering Problem as a D. C. Programming
T.V. Thieu, "A Note on the Solution of Bilinear Programming Problems
by Reduction to Concave Minimization."
M. Voile, "Concave Duality: Application to Problems Dealing with Dif-
ference of Functions."
0 PT IM A number twenty-four
PAGE 0 PT I A nmber went-fou JUN 198
SB 0 0 I
Optimal Block Search
By L. Weixian
Heldermann, Berlin, 1984
Let f be a unimodal function in [a,b]. Kiefer, in 1953, showed that
the golden section method has certain optimal properties with respect
to a sequential search for a maximum. Since then there have been
many articles dealing with extensions of this result, e.g., Avriel,
Beamer and Wilde in 1966, 1969 and 1970.
In the beginning of the seventies when the so-called "cultural revo-
lution" came towards an end, there were many Chinese mathemati-
cians who were enthusiastic about such extensions. The book re-
viewed is designed to summarize the results obtained in that period.
It consists of seven chapters: (1.) Introduction, (2.) Strategies of finite
order, (3 and 4.) The optimal block search problem, (5.) Strategies of
infinite order, (6 and 7.) Sequential search with time delay. The author
made an attempt to give a unifying approach to these results, but I
have to say his efforts cannot be counted as successful. When the
author introduced the terms "approximation" and "remaining inter-
val," he referred to a fixed function (p.4). From this he introduced a
concept "state" (p.5,1.-7). But this does not agree with formal defini-
tion of "state" (Def. 1.4). Meanwhile, the formal definitions of ap-
proximation and remaining interval are given only in terms of state.
On p.4, it says "since we have seen that theoptimal point of a unimodal
function is within the remaining interval," the author referred again
to a function. It seems that the author intended to avoid use of a
specific function in defining his "K-strategy" but could not avoid it. In
fact, the first chapter is full of conceptual confusions. Nevertheless,
the remaining part is readable. Yue Minyi
Encyclopedia of Mathematics, Volume I
By W. T. Tutte
W.T. Tutte is without doubt one of the pioneers of graph theory in
the sense that he has been personally responsible for inventing many
of the subdisciplines of that area which occupy graph theorists today.
But it would be grossly unfair to interpret the term "pioneer" only in
the sense of pollination! From early on, he has striven to put graph
theory on a firm footing with respect to rigor. The present book is a
beautiful culmination of these efforts to "do things right" in graph
But Tutte is an indivdualist too, to say the least, in his approach to
graph theory and this side of the man is strongly reflected in this book,
both with respect to the selection of topics and his treatment of them.
A number of other important topics in graph theory are not covered
in this book. This is not really a complaint but perhaps just an
indication that any attempt to write an "Encyclopedia" on any mathe-
matical discipline is brought with danger!
In Chapter I, the author gets us off the ground by defining graphs
and subgraphs and providing a bevy of beginning definitions for the
reader. We would be remiss, however, if we did not point out at once
that Tutte's definitions and notation do not always agree with those of
a large part of the rest of the graph theory community. (For example,
his "binding number" is quite a different thing from the parameter of
the same name first introduced and studied by Woodall.) But the tone
is set for rigor here at the onset, as Tutte presents a particularly careful
treatment of vertices of attachment and the bridges of a graph.
In Chapter II, the author introduces the idea of edge contraction,
wisely indicating to the reader early in the game that proofs by
induction on the number of edges of a graph (edge deletion) and on the
number of points of a graph (edge contraction) abound in graph
theory. Here we also are first introduced to the concept of a graph
minor. The idea of a minor is of central importance to Tutte, not only
in the context of graphs, but in the field of matroid theory, yet another
fruitful branch of combinatorics which must list Tutte as one of the
The vertex connectivity version of Menger's famous minimax theo-
rem is then introduced and proved. Tutte notes that Menger's result
has an important analogue in transportation theory. However, this
analogue, the max-flow min-cut theorem, is not seen until Chapter VI
where it is stated and proved and the directed vertex version of
Menger's theorem is derived as a corollary. Unfortunately, the other
two main versions of Menger's theorem, namely, the directed and
undirected edge variants, are not mentioned at all.
But let us backtrack slightly. The reader encounters on page 36 the
first mention of the concept of duality in graph theory. This portent of
things to come is to be applauded as duality ultimately becomes a
centerpiece of the book as a whole. (But more about this below.)
Next the author uses Menger's theorem to prove the classical result
of P. Hall on bipartite matching. It might have been nice here to
mention the minimax result of D. K6nig which is equivalent to Hall's
result and which actually was proved by K6nig after finding an error
of omission in the first proof offered by Menger of his own result.
In the notes at the end of this chapter, Tutte mentions a conjecture
attributed to Kruskal on minors in cubic graphs. This result has
recently been proved by Robertson (once a student of Tutte) and
Seymour as a consequence of their work on graph minors and their
proof of the celebrated conjecture of Wagner.
In Chapter III we are presented with Tutte's rigorous development
of the theory of 2-connection in graphs. Among other things, he shows
that all 2-connected graphs can be obtained from smaller ones by
adding paths joining distinct vertices. The blockgraph (perhaps more
widely known as the block-cutpoint tree) is then developed. Finally, the
- I ~----`- --
0 PT IM A number twenty-four
PAGE ~ ~ 8- 0 IMAnubrtwnyforJNE18
author reminds us again of the duality yet to come by proving in the
last theorem of the chapter that for every edge in a 2-connected graph,
either the graph with the edge deleted or the graph with the edge
contracted retains the property of being 2-connected.
Chapter IV deals with 3-connection and culminates in Tutte's
beautiful Wheel Theorem for producing all 3-connected graphs. He
begins with his own definition of 3-connection which, he is quick to
point out, is slightly different from the more common definition of this
property. Indeed, for graphs without loops or multiple edges, the two
definitions coincide. Tutte's theory of 3-connection presented in this
chapter formed the core of one of his earlier books devoted entirely to
the study of connectivity in graphs.
This brings the reader to Chapter V which deals with the topic of
graph reconstruction. The brevity of this chapter-the shortest in the
book-belies the impact of Tutte's own work on this topic. Here he is
content with a short survey of results mostly of a counting nature.
Digraphs are introduced and studied in Chapter VI. The B(de
Bruijn)E(van Aardenne-Ehrenfest)S(Smith)T(Tutte) Theorem relat-
ing the number of closed Eulerian trails and the number of spanning
arborescences is proved as is the classical result of Euler relating the
existence of a closed Eulerian trail and equality of in- and outdegrees
of a connected digraph. Then stressing analogies with electrical
network theory, the author defines the so-called Kirchhoff matrix and
relates determinants of certain submatrices of this matrix to the
number of spanning arborescences emanating from a root point in the
well-known Matrix-Tree Theorem. Kirchhoff's Laws for digraphs are
treated next and the chapter closes with a treatment of the max-flow
Chapter VII begins with a development of a very general theory of
alternating paths which is then brought to bear in proving Tutte's own
f-factor theorem. Let fbe a function which assigns to each point of a
graph a non-negative integral value bounded above by the degree of
the point. An factor is a spanning subgraph which has as its degree
the value offat each point. Thef-factor theorem states that given such
a function Jon the vertices of a graph, then either the graph has anf-
factor or a certain type of "blocking configuration" called anf-barrier.
Almost hidden from view here is one of Tutte's most famous theo-
rems, the 1-factor theorem, which gives necessary and sufficient condi-
tions for an arbitrary (i.e., not necessarily bipartite) graph to have a
perfect matching. This result is arguably the single most important
result in all of matching theory.
The chapter ends with a nice application off-factor theory to obtain
a classical result due to Erd6s and Gallai which characterizes which
sequences of non-negative integers are the degree sequences of
Chapter VIII is, in the opinion of this reviewer, the high point of the
entire book. The author undertakes the construction of an algebraic
theory of duality for graphs. He begins by developing the theory of
chain-groups in the abstract. He then applies chain groups to graphs
incorporating the "duality" of circuits and bonds in the more general
setting of dual chain groups. To the reviewer's knowledge, this
approach cannot be found anywhere other than in the work of Tutte.
In the final section of the chapter, Tutte gleans from the properties of
chain groups two which together form one (of a number) of the axiom
systems for a matroid. He then observes that the concept of matroid is
broad enough to encompass both chain groups and graphs.
Graph polynomials form the subject matter of Chapter IX. Starting
with the very general idea of a V-function, Tutte specializes first to the
concept of a dichromatic polynomial and finally to the chromatic polyno-
mial P(G;,). If the indeterminant X is set equal to a positive integer n,
then P(G;n) is the number of vertex colorations of graph G in n colors.
The Four Color Theorem can be expressed as the assertion that P(G;4) >
1 for all planar graphs G.
The author also includes in this chapter a proof of Brooks' Theo-
rem which states that if a graph G has maximum degree A>3 and is
not complete, then G has a vertex coloration in no more than Acolors.
Also the author presents a theorem dual to that of Grinberg which
deals with the existence of Hamilton circuits for planar graphs, but
Tutte's version holds even when the planarity demand is dropped.
Next, Tutte turns to the concept of aflow polynomial which, at least
for connected graphs, is dual (in the setting of chain-groups) to that of
chromatic polynomial. He uses the language of flow polynomials to
state the still unsolved Five Flow Conjecture. He then turns to a brief
outline of the theory of Tait colorings and introduces us to that sinister
animal, the "snark"!
Once again, duality is the motivating influence as Tutte next intro-
duces a polynomial in two variables called the dichromate. It is sym-
metrically related, in a sense, to the two dual functions, the chromatic
polynomial and the flow polynomial. In addition, the dichromate is
quite intimately related to the set of spanning trees in the case when
the graph under consideration is connected. Call a graph property
reconstructible if it can be inferred to hold for a graph G if it holds for
all the vertex-deleted subgraphs of G. (This term is actually intro-
duced earlier in Chapter V on reconstruction.) Tutte proves his
dichromate is reconstructible and from this fact it follows that a
number of other graph properties are reconstructible as well. Among
these are the dichromatic polynomial, the chromatic polynomial, the
flow polynomial, the chromatic number, whether or not the graph as
a 5-flow, the number of Hamilton circuits and, at least for graphs
without loops or multiple lines, the characteristic polynomial.
Chapter X on combinatorial maps is a gem. Here Tutte carefully
introduces and develops a purely combinatorial theory of maps, sur-
faces, orientability and non-orientability, Euler Characteristic, pla-
narity and genus. Heretofore, purely topological concepts all! The
author even obtains a combinatorial version of the classification
theorem for both orientable and non-orientable surfaces.
In Chapter XI, he concentrates on planar graphs. There is even a
combinatorial analogue to the Jordan Curve Theorem, another fa-
mous result which, at least up to now, has been firmly planted in the
topologists' garden! Tutte precedes to get an algorithm for planarity
- ------- -- I --~-------------------
0 P T IM A number twenty-four
PAGE- 9 MAnme tet-or UE18
testing as well as proofs of the classical characterizations of planar
graphs due to MacLane and to Kuratowski. Sadly, the chapter and
book are then brought to a close without a mention of another of
Tutte's most celebrated theorems, namely, that a 4-connected planar
graph must always have a Hamilton circuit. (However Nash-Wil-
liams does mention the result in his forward to the book.)
This book is unique both in its approach to graph theory and in the
rigor the author brings to the discipline. There seems to be no doubt
that duality is always in the back of the author's mind throughout, as
the book pivots on this notion.
By the very uniqueness of this approach, however, the book would
profit well by the inclusion of more examples. But to the reviewer, the
only truly annoying facet of this book is the failure to include an index
of terms and symbols. The text is remarkably free of misprints. The
reviewer found only a few, the most amusing being the running head
on page 241 which tells the reader that he is studying Trait colorings!
In closing, the reviewer feels bound to emphatically disagree with
the remarks on the dust cover which begin with the phrase "Designed
for the non-specialist,....."! This book is for the experienced graph
theorist, if ever a book were. Having said that, however, I firmly
believe that this truly important book should be in the library of every
practicing graph theorist. M. D. Plummer
Map Coloring, Polyhedra, and the Four
By D. Barnette
John Wiley, Chichester, 1984
Rarely before has a famous and long-standing problem aroused
such strong emotions as the four-color problem. On the negative side
it was claimed that the problem was of no mathematical significance
and the eventual solution preposterous. On the other hand, the
opinion was also heard that this problem had almost single-handedly
given birth to a whole new and ever more important branch of
mathematics graph theory, and that even the solution with its
manyfold implications on the future of mathematical research may
prove to be of lasting significance. The author of the book under
review squarely throws his weight on the positive side, and he does
so in a light-handed and thoroughly enjoyable way. Professor Bar-
nette is a geometer and he more or less confines his subject to the
connections between maps, graphs and polyhedra. The result is a
delight for both the insider and the casual reader who just wants to
learn what this coloring business is all about. Along the way he gets
acquainted with Euler's equation, Hamiltonian circuits, isomorphism
and duality of maps, Steinitz' and Eberhard's theorems to name just
a few of the topics. Numerous exercises, illustrations and historical
remarks keep up an easy flow of reading. Barnette shows how all
these concepts emerged in the search for a proof of the four-color
conjecture, how they were refined, altered, strengthened, and failed.
"What good is it?" is the title of the last section. After reading
Barnette's magnificent little book one should not want for an answer.
- M. Aigner
Discrete and Combinatorial Mathematics
By R. P. Grimaldi
Addison Wesley, Amsterdam, 1985
With his book R. P. Grimaldi gives "an applied introduction" (sub-
title) to the basic areas of discrete and combinatorial mathematics.
According to the objective to address to the beginning student with
only a background in high school algebra, the first half of the book is
concerned with introductory chapters such as the fundamental prin-
ciples of counting, enumeration in set theory, functions and relations,
the set theory of strings, the system of integers, the principle of
inclusion and exclusion, rings and modular algebra, and boolean
algebra. The next part of the book deals with combinatorial topics as
generating functions, recurrence relations, groups, coding theory and
Polya's method of enumeration, andfinite fields and combinatorial
design. In the last sections of the book, Grimaldi presents a short
introduction to graph theory with special attention to trees (for their
application to data structures) and first steps in combinatorial optimi-
zation, as weighted trees, the max-flow-min-cut theorem and bipar-
All topics presented in this book are illustrated by some simple
examples (applications), and each subsection is followed by a series of
exercises most of them with solutions. Thus the student may get
familiar with combinatorial subjects. The section "summary and
historical review" following each chapter contains references for
Grimaldi gave his book the structure of a lecture (with many ex-
amples), so it might serve well as a companion through a course on
discrete and combinatorial mathematics for undergraduate students.
- J6rg Rieder
Multiple Criteria Optimization: Theory,
Computation, and Application
By Ralph E. Steuer
John Wiley and Sons, Chichester, 1986
This textbook presented by Steuer will hold very soon the cardinal
place of a highly esteemed standard work on the area of decision
making with multiple objectives, especially in the field of linear and
nonlinear programming with multiple criteria. It contains a great
0 PT IM A number twenty-four
I~G 10 0 ubrtwnyfu UE18
number of numerical examples and figures which serve to convey
easily the complicated matter of multiple criteria decision making and
algorithms. Also many references are given, ordered by chapters and
recommended as reading for further detailed studies. The book is
written at a high level but makes nevertheless the theoretical exposi-
tions easy to understand. The impressive combination of the didac-
tically skillful processing of the presented matter with the broad
bibliographical foundation of the analytical deliberations will cer-
tainly guarantee the success of this textbook at universities. Steuer has
succeeded in a convincing manner with this book for beginners as well
as for experts in the area of decision making with multiple criteria.
The book contains 17 chapters. Chapter 1 is a short introduction.
The mathematical background needed for the following expositions
is prepared in Chapter 2. The basic findings and theorems of set
thoery, linear algebra and properties of extreme points polyhedra and
matrices are given. Chapter 3 presents the theory of linear program-
ming with one objective. The determination of all alternative optima
in Chapter 4 is directly linked to this.
Then in chapers 5-9 the theory of linear programming with mul-
tiple criteria is developed. In this context Steuer deals with the
importance of the notions of efficiency, dominance and Pareto-opti-
mality for these cases. Relations to parametric programming are
pointed out. Within these presentations the stress is on estimating
optimal weighting vectors for given goal vectors in order to determine
an optimal compromise solution for multiple criteria decision prob-
lems. Subsequently, the author demonstrates the possibilities of
applying algorithms available today for solving vector maximum
Chapter 10 is devoted to the concept of goal programming. In
chapter 11 the interesting question is to what extent a representative
subset will be sufficient to solve a problem formulated on a larger set
of decision alternatives. Chapter 12 deals briefly with problems of
multiple objective linear fractional programming.
Additional focal points of thebook are chapters 13-15, where inter-
active solution approaches for multiple objective decision problems
are discussed. Chapter 16 gives applications, which show in an
attractive way how the methods presented can be implemented in
order to solve practical decision problems with multiple objectives.
The concluding chapter 17 addresses future developments.
Summing up one can say that the textbook of Steuer recommends
itself for an intensive reading. The reviewer has read it with joy and
profit. Giinter Fandel
Applied Mathematical Programming for
Engineering and Production Management
By Turgut Ozan
Prentice Hall, 1986
From the Preface: "This book has been written as a first course in
mathematical programming for engineering and production man-
agement students and for practicing engineers and managers.... The
basic features emphasized in writing the book were simplicity of
explanations, avoidance of rigorous theory (without being superfi-
cial), and concentration on model building with single and multiple
Chapter 1 presents the fundamental concepts, while the simplex
method is given in Chapter 2. Dual simplex method and sensitivity
analysis follow in Chapter 3 and applications (model building, case
studies) in Chapter 4. The transportation problem and its extensions
are presented in Chapters 5 and 6 and integer programming in
Chapters 7 and 8. The last four chapters deal with multiple objective
programming, project management techniques and dynamic pro-
Let us compare in more detail the present book with the text
Applied Mathematical Programming by S. P. Bradley, A. C. Hax & T. L.
Magnanti (Addison-Wesley, Reading, MA, 1977) which is used at
many universities for the first course in mathematical programming.
Bradley, Hax and Magnanti cover slightly more material (revised
simplex method, large scale systems, nonlinear programming)
though PERT-type activities are covered in less detail. The reviewer
feels, moreover, another advantage of Bradley, Hax and Magnanti is
that the length of the initial chapters is more balanced: Chapter 1 (in-
troduction of basic concept and graphical solution of 2-dimensional
LP problems) is shorter, duality and sensitivity analysis are treated in
separate chapters, as are general remarks on MP applications and case
On the other hand, this book also has many advantages. Some
examples (from mechanical and electric engineering) were quite new
and unusual (at least for the reviewer) and it bibliography contains
many references from the last decade as well. It gives references to
commercially available computer programs too and quotes excerpts
from various surveys (like the ones on the organizational location of
the OR/MS groups within a firm, or on the distribution of the major
field of study of the directors and staff of the OR/MS departments in
large U.S. industrial corporations).
Summarizing, the book can be recommended as a text for a first
course in mathematical programming. AndrAs Recski
_ ~ _~
OPT I M A number twenty-four
PAE 10 I M nmertwny-ou UN 18
special interest is high quality computational
work. I hope to be able to produce issues
which deal with the problems encountered
when implementing mathematical program-
ming algorithms as well as their solutions.
Also, I hope to be able to produce issues
focusing on the strong emerging links with
I strongly encourage members of the
Society who have an idea for a suitable issue
to discuss it with me or another member of
the board. If it appears promising, a proposal
will be requested which will be circulated to
appropriate members of the board, after
which a decision will be made.
I am personally very pleased by the
opportunity MPB provides and am looking
forward to its development as a high quality
publication of the Society.
Mathematical Programing Series B
W.R. Pulleyblank (Editor-in-Chief)
University of Waterloo
tel. (519) 888-4461
University of Waterloo
Augsburg, FR Germany
George Mason University
Fairfax, VA, USA
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cole Polytechnique Federale de Lau-
Massachusetts Institute of Technology
Cambridge, MA, USA
Saarbruecken, FR Germany
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New York, NY, USA
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Boulder, CO, USA
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0 PT IM A number twenty-four
PAGE- 12 0- P-- T MAnubr wnt-fu JN 18
An International Workshop on Generalized Concavity,
Fractional Programming and Economic Applications was
held in Pisa, Italy, May 30-June 1. For information contact
Prof. Alberto Cambini, Dipartimento di Statictica e
Matematica Applicata all'Ecomomia, Via Ridolfi 10, 56100
Pisa... OPTIMA 22 incorrectly reported that the Gold
Medal of EURO had been awarded to Peter Hammer rather
than Pierre Hansen, the actual recipient. Peter Hammer
received the Docteur es Sciences Honoris Causa from the
Swiss Federal Institute of Technology... A Workshop on
Supercomputers and Large-Scale Optimization was held
May 16-18 at the University of Minnesota. For further
information contact J.B. Rosen, Computer Science Depart-
ment, 136 Lind Hall, Minneapolis, MN 55455... COAL
member Stein W. Wallace, formerly of Chr. Michelsen
Institute, Bergen, Norway has joined Haugesund Maritime
College, Skaregaten 103, N-5500 Haugesund, Norway...
F.H. Clarke, V.F. Dem'yanov and F. Giannessi are directing
a workshop on Nonsmooth Optimization in Sicily, Italy,
June 19-July 1, 1988.
Deadline for the next OPTIMA is October 1, 1988.
Books for review should be
sent to the Book Review Editor,
Prof. Dr. Achim Bachem,
Mathematiches Institute der
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Weyertal 86-90, D-5000 Kiln,
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to change by the publisher.
Donald W. Hearn, Editor
Achim Bachem, Associate Editor
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