Title: Optima
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00090046/00021
 Material Information
Title: Optima
Series Title: Optima
Physical Description: Serial
Language: English
Creator: Mathematical Programming Society, University of Florida
Publisher: Mathematical Programming Society, University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: June 1987
 Record Information
Bibliographic ID: UF00090046
Volume ID: VID00021
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.


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PT MA No21


JUNE 1987

Martin Beale

Memorial Symposium

The Programme of this symposium (which
will be held at the Royal Society, London, from
July 6-8, 1987) will include a reception, a dinner
(speaker: S. Vajda), contributed talks (the dead-
line for submissions was March 1), and the
following invited papers:
P. Hughes (Logica), "Martin Beale: A Per-
sonal Memory"
G. B. Dantzig (Stanford), "Solving Large
Scale Mathematical Systems Is Becoming a
Practical Reality"
K.C. Bowen (Royal Holloway and Bedford
New College), "A Mathematician's Journey
Through Operational Research"
P.J. Green (University of Durham), "Regres-
sion, Curvature and Weighted Least Squares"
R.D. Ripley (University of Strathclyde),
"Uses and Abuses of Statistical Simulation"
J.A. Tomlin (Ketron), "Special Ordered Sets
and an Application to Gas Supply Operations
A. Orden (University of Chicago), "The As-
sessment of OR Models"
B.R.R. Butler (British Petroleum), "Applica-
tions of OR in the Oil Industry."
Further information is available from Mrs.
B.A. Peberdy, Scicon Limited, Wavendon
Tower, Wavendon, Milton Keynes MK17 8LX,
England. &.

number twenty-one

List of contents


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a p_ g I

Symposium on Parallel Optimization

August 10 12, 1987
Computer Sciences Department
University of Wisconsin
Madison, Wisconsin

Partial List of Invited Speakers:
D.P. Bertsekas, Y. Censor,
M.D. Chang, G.B. Dantzig,
R. DeLeone, R.S. Dembo, J.G. Ecker,
L. Grandinetti, S.-P. Han, J.K. Ho,
O.L. Mangasarian*, R.R. Meyer*,
J.M. Mulvey, J.-S. Pang,
A.H.G. Rinnooy Kan, K. Ritter,
J.B. Rosen, R.B. Schnabel,
D. Sorensen, S.A. Zenios

This symposium will address computational aspects of parallel algorithms
for optimization. Emphasis will be on algorithms implementable on parallel
and vector architectures. Further information may be obtained by writing to the
SPO Secretary or to either of the symposium co-chairmen at the above address.
The symposium will be supported by grants from the Air Force Office of
Scientific Research and from the Office of Naval Research. The proceedings will
be published as a Mathematical Programming Study.
*Symposium Co-chairmen ^

Editor-in Chief: Peter L. Hammer, RUTCOR, Rutgers Univ., New Brunswick NJ 08903
The Annals of Operations Research will publish a series of volumes dedicated to the presentation of the current level of the main trends
of the development of specific areas of the field. Each volume will consist of original manuscripts, survey articles, selected and tested
computer programs, etc. The Annals of Operations Research hope to play an active role in the publication of well refereed conference
proceedings or selected papers thereof and in publishing volumes of contributed papers in well defined areas of OR from highly
theoretical to the algorithmic and also to the very applied. Every volume will have one or more Guest Editors who will be personally
responsible for the collection of papers to appear in that volume, for the refereeing process and for the time schedule.
All papers will be subject to peer refereeing and there will be no page charge.
Interested contributors to volumes currently in preparation as well as potential Guest Editors of new refereed volumes (proceedings of
conferences, monographs or focused collections of papers) in major OR areas are cordially invited to write to the Editor-in-Chief.

Vol. 7: Blazewicz et al.,
Scheduling under Resource Constraints: Deterministic Models. 1986.
Vol. 6: Osleeb & Ratick, Ed.,
Locational Decisions, Methodology and Applications. 1986.
Vol. 4-5: Monma, Ed.,
Algorithms and Software for Optimization. 1985.
Vol. 3: Stecke & Suri, Ed.,
Flexible Manufacturing Systems. Operations Research Models
and Appl. 1985.
Vol. 2: Thompson & Thrall, Ed.,
Normative Analysis in Policy Decisions, Public and
Private. 1985.
Vol. 1: Archetti & Maffioli, Ed.,
Stochastics & Optimization. 1984.

In Preparation:
Albin & Harris, Ed.,
Statistical and Computational Problems in Probability Modeling

Keeney et al., Ed.,
Multi-Attribute Decision Making via OR-based Expert Systems.
Stecke & Suri, Ed.,
Flexible Manufacturing Systems. A new volume, based on the
1986 FMS meeting, Ann Arbor.
Kusiak, Ed.,
Analysis, Modeling and Design of Modern Production Systems.
Gallo et al., Ed.,
Fortran Codes for Network Optimization.
Yue Minyi, Ed.,
Operations Research in China.
Louveaux, Ed.,
Locational Decisions. A new volume, based on the 1987
ISOLDE, Louvain meeting.
Meyer & Zenior, Ed.,
Parallel Optimization on Novel Computer Architectures.
Fishburn & LaValle, Ed.,
Choice under Uncertainty.
Jeroslow, Ed.,
Approaches to Intelligent Decision Support.

Volumes 1-7, 1984-1986 are available at $ 94,60 per vol. incl. postage, or at $ 45,90 each for OR/TIMS members.

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0 P TI M A number twenty-one

JUNE 1987

fit (he LISA please send yonr order to:
J.C. Baltzer AG, Scien(ific Publ. Co.,
PO. Box 8577, Red Bank, NJ 07701-8577.

From all other countries to:
J.C. Baltzer AG, Scientific Publ. Co.,
Wettst.einplatz 10, CH-4058 Basel, Switzerland.

STechnical Reports & Working Papers

University of Missouri-Columbia
College of Engineering
Design Productivity Center
1080 Engineering Building
Columbia, Missouri

B.M.E. de Silva, "Substructuringfor Multilevel Structural
Optimization," 86DPC005 ($2.42).
V. Bhatt and B.M.E. de Silva, "Sensitivity of Optimum
Designs to Problem Parameters," 86DPC015 ($2.70).
J.K. Blundell and B. Greenway, "LBO Line Balancing
Optimization," 86DPC017 ($1.38).
K.M. Ragsdell, "State-of-the-Art In Parallel Nonlinear
Optimization," 86DCP027 ($2.41).

Cornell University
School of Operations Research
and Industrial Engineering
Upson Hall
Ithaca, NY

. R. Roundy, "Efficient, Effective Lot-Sizing for Multi-Product
Multi-Stage Production/Distribution Systems with Correlated
Demands, "TR 671.
L.J. Billera and K. Magum, "Balanced Subdivision and
Enumeration in Balanced Spheres," TR 672.
M.Todd, "Reformulations of Economic Equilibrium Problems
for Solution by Quasi-Newton and Simplicial Algorithms,"
TR 673.
R.Roudy, "94%-Effective Lot-Sizing in Multi-Stage Assembly
Systems," TR 674.
J. Sand and P. Jackson, "Operating Policies for Water-Supply
Reservoirs in Parallel, I: The Single Demand System,"
TR 675.
M. Phelan, "Estimating the Compensator from Poisson -Type
Counting Processes," TR 676.
C. Jennison, "On the Stochastic Minimization of Sample Size
by the Bechhofer-Kulkarni Bernoulli Sequential Selection
Procedure," TR 677.
R. Bechhofer and C. Dunnett, "Two-Stage Selection of the
Best Factor-Level Combination in Multi-Factor Experiments:
Common Unknown Variance," TR 678.
R. Dalang, L.E. Trotter, Jr., and D. de Werra, "On Random-
ized Stopping Points and Perfect Graphs," TR 679.
S. Tipnis, "Integer Rounding and Combinatorial Max-Min
Theorems," TR 680.
M.J. Todd and C. Ip, "Conditioning in Rank I Quasi-Newton
Jpdates," TR 681.
M.J. Todd, "On Bounds in Anstreicher's Monotonic Projective
Algorithm," TR 682.

R. Bechhofer and D. Goldsman, "Truncation of the
Bechhofer-Kiefer-Sobel Sequential Procedure for Selecting the
Multinomial Event which has the Largest Probability (II): Ex-
tended Tables and an Improved Procedure," TR 683.
J.A. Muckstadt, P.L. Jackson, W.T. Martin, S.Bellantoni
and R. Ferstenberg, "Cornell Simulator of Manufacturing
Operations," TR 684.
M. Phelan, "Nonparametric Inference from Poisson-Type
Counting Processes," TR 685.
P. Domich, "Residual Methods for Computing Hermite and
Smith Normal Forms," TR 686.
M. Todd, "The Symmetric Rank-One Quasi-Newton Method
is a Space Dilation Subgradient Algorithm," TR 687.
I. Barany and Z. Furedi, "Computing the Volume Is
Difficult," TR 688.
I. Barany and Z. Furedi, "Empty Simplices in Euclidean
Space," TR 689.
W. Cook, "Cutting-Plane Proofs in Polynomial Space,"
TR 690.
I. Barany and Z. Furedi, "On the Convex Hull of Random
Points," TR 691.
P. Jackson, W.L. Maxwell, J. Muckstadt and R. Roundy,
"The Interaction Between Design and Scheduling in Repetitive
Manufacturing Environments," TR 692.
W.L. Maxwell, "Scheduling the Factory of the Future-
Results of a Research Planning Session," TR 693.
I. Barany, "Rearrangement of Series in Infinite-Dimensional
Spaces," TR 694.
H. Taylor, "A Model for the Failure Process of Semi-Crystal-
line Polymer Materials Under Static Fatigue," TR 695.
R. Bland and D. Cho, "Arranging Points in Rd: A Question of
Balances," TR 696.
R. Sheldon, "The Lot Scheduling Problem in the Hierarchy of
Decision Models," TR 697.
T. Santner and S. Yamagami, "A New System of Small
Sample Confidence Intervals for the Difference of Two Success
Probabilities," TR 698.
P. Jackson, "The Simplex Method in Cyclic Scheduling,"
TR 699.
D. Joneja and W. Maxwell, "Buffer Replacement in Sequen-
tial Production Lines: Considerations of Processing Time Variabil-
ity," TR 700.
R. Dalang, "On Infinite Perfect Graphs and Randomized
Stopping Points on the Plane," TR 701.
Y. Herer, "Buffer Placement in Sequential Production Lines:
Further Studies," TR 702.
D. Duffy and T. Santner, "Estimating Logistic Regression
Probabilities," TR 703.
D. Goldsman and R. Bechhofer, "Sequential Selection
Procedures for Multi-Factor Experiments Involving Koopman-
Darmois Populations with Additivity," TR 704.
R. Bechhofer and C. Dunnett, "Percentage Points of Multi-
variate Student t Distributions," TR 705.

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0 P T I M A number twenty-one

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PAE~ 4 I M A1 numbe twnyoe UE18

M. Phelan, "Nonparametric Estimation from a Censored
Markov Renewal Process Observed over a Long Period of Time,"
TR 706.
M.J. Todd, "Polynomial Algorithms for Linear Programming,"
TR 707.
M. Phelan, "Life-Testing and Estimation with Arbitrary
Distribution Function," TR 708.
M. Phelan, "Nonparametric Estimation from Discrete-Time
Nonhomogeneous Finite Markov Chains with Applications to
Inference from Multiwave Panel Data," TR 709.
M. Hartfnan, "An Improvement of Various Elimination
Procedures," TR 710.
J. Ryan, "Integral Monoid Duality Models," TR 711.
M. Kulldorff, "Tandem Queueing Systems with Blocking,"
TR 712.
R. Bland and B. Dietrich, "Abstract Duality," TR 713.
L. Schruben and S. Jacobson, "A Frequency Selection
Algorithm for Frequency Domain Experiments in Simulation,"
L. Schruben and S. Jacobson, "Techniques for Simulation
Optimization," TR 715.
R. Roundy, "Rounding Off to Powers of Two in Continuous
Relaxations of Capacitated Lot Sizing Problems," TR 716.
W. Morris, "Oriented Matroids and the Linear Complementar-
ity Problem," TR 717.

Charles University
Department of Applied Mathematics
KAM Series
Malostransk6 nam. 25
11800 Praha 1

J. Nesetril, and V. Rodl, "Complexity of Diagrams."
P. Sgall, "From Expression through Meaning to Intention."
I. Kriz, "A Hypergraph-less Construction of Highly Chromatic
Graphs without Short Cycles."
M. Loebl and S. Poljak, "On Matroids Induced by Packing
K. Zimmermann, "One Optimization Problem with Max-Min
R. Svarc, "Some Combinatorial Results about the Operators
with Jumping Nonlinearities."
J. Matousek, "A Few Colored Cuts or Cycles in Edge Colored
E. HajicovA, "Machine Translation Research in Czechoslova-
J. Nesetril and P. PudlAk, "A Note on Boolean Dimension of
L. Kucera, "Greedy Coloring Is a Bad Probabilistic Algo-

S. Poljak and M. Chrobak, "On Common Edges in Optimal
Solutions to Travelling Salesman and other Optimization Prob-
R. Svarc, "The Operators with Jumping Nonlinearities and
R. Thomas, "A Counterexample to Wagner's Conjecture for
Infinite Graphs."
P. Sgall and J. PanevovA, "Dependency Syntax, Its Problems
and Advantages."
J. Kratochvfl and D. Zeps, "On the Minimum Number of
Hamiltonian Cycles in Triangulations."
J. Nesetril, "For Graphs There Are Only Four Types of
Hereditary Ramsey Classes."
S Poljak and Z. Tuza, "Maximum Bipartite Subgraphs of
Kneser Graphs."
J. Nesetril and R. Thomas, "Well Quasi Orderings, Long
Games and a Combinatorial Study of Undecidability."
M. Loebl and J. Matousek (x), "On Undecidability of the
Weakened Kruskal Theorem."
M. Loebl and S. Poljak, "Remark on Restricted and Strongly
Unimodular Matrices and a Class between Them."
E. Hajicovd, "Focusing A Meeting Point of Linguistics and
Artificial Intelligence."

Mathematisches Institut
Universitit zu Kiln
Preprints in Optimization
Weyertal 86 -90
D-5000 K6ln 41, West Germany

A. Wanka, "Matroiderweiterungen zur Existenz endlicher
LP-Algorithmen, von Hahn-Banach-Sitzen und Polaritdt in
Orientierten Matroiden," WP 86.24.
A. Bachem and A Wanka, "Euclidean Intersection
Properties," WP 86.25.
W. Kern, "On the Rate of Convergence of Some Stochastic
Processes," WP 86.26.
A. Bachem and A. Wanka, "Matroids without Adjoint,"
WP 86.27.
W. Kern, "A Probabilistic Analysis of the Switching Algo-
rithm for the Euclidean TSP," WP 86.28.
J. Rieder, On k-Tuple-Colorings of Graphs," WP 86.29.
W. Kern and A. Wanka, "On a Problem About Covering
Lines by Squares," WP 86.31.
M. Leclerc, "Slices of the Matching Polytope,"
WP 86.32.
W. Kern, "On the Depth of Combinatorial Optimization
Problems," WP 86.33.
M. Leclerc, "Optimization Over a Slice of the Bipartite
Matching Polytope," WP 86.34.


0 PT IM Anumber twenty-one

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PAG 5~ 0 MAnmbrtetyoeJUE18

W. Kern, "Optimization and Optimality Test for Weighted
Max Cut," WP 86.35.
M. Leclerc, "The 2-Matching Lattice of a Graph," WP 86.36.
W. Nettekoven, "The Hyperbolic n-Space as a Graph in
Euclidean (6n-6)-Space," WP 86.37.
C. Bold, "Order-Degree Sequences," WP 86.38.

Technical University Graz
University Graz
Reports of the Mathematical Institutes
Kopernikusgasse 24
A-8010 Graz, Austria

R.E. Burkard and R.A. Cunninghame-Green, "Saddle
Points in Groups and Semigroup Minimization," No. 68.
G. Rote, "On the Connection between Hexagonal and Undirec-
tional Rectangular Systolic Arrays," No. 72.
G. Rote, "A Proposal of a Heuristic for Decomposing Traffic
Matrices in TDMA Satellite Communication," No. 73.
H. Edelsbrunner, G. Rote, and E. Welzl, "Testing the
Necklage Condition for the Shortest Tours and Optimal Factors in
the Plane," No. 83.

M. Perusch, "Simulated Annealing Applied to a Single
Machine Scheduling Problem with Sequence Dependent Setup
Times and Due Dates," No. 84.

Northwestern University
Department of Industrial Engineering
and Management Sciences
Evanston, Illinois 60201

G.B. Hazen, "Differential Characterizations of Nonconical
Dominance in Multiple Objective Decision Making," Report No.
P.C. Jones, and R.R. Inman, "Analytic Results for the Two-
Product Fully-Loaded Economic Lot Scheduling Problem," Report
No. 86.06.
P.C. Jones and R.R. Inman, "When is the Economic Lot
Scheduling Problem Easy?," Report No. 86-13.
J. Sun, "Basic Theories and Selected Applications of Mon-
otropic Piecewise Quadratic Programming," Report No. 86.09.
J. Sun, "A Simplex-Active-Set Algorithm for Piecewise
Quadratic Programming," Report No. 86-10. w

SJournals & Studies

Vol. 37, No. 1

L. Mathiesen, "An Algorithm Based on a Sequence of Linear
Complementarity Problems Applied to a Walrasian Equilibrium
Model: an Example."
A. R. Conn and N. I. M. Gould, An Exact Penalty Func-
tion for Semi-Infinite Programming."
D. de Werra, "Partitions into Odd Chains."
M.A. Hanson and B. Mond, "Necessary and Sufficient
Conditions in Constrained Optimization."
C.G.E. Boender and A.H.G. Rinnooy Kan, "Bayesian
Stopping Rules for Multistart Global Optimization Methods."
D.M. Gay, "A Variant of Karmarkar's Linear Programming
Algorithm for Problems in Standard Form."
S.M. Grzegorski, "Multilevel Least-Change Newton-like
Methods for Equality Constrained Optimization Problems."
M.Fischetti and S. Martello, "Worst-Case Analysis of the
SL ifferencing Method for the Partition Problem."

Vol. 37, No. 2

M.-C. Noel and Y. Smeers, "Nested Decomposition of
Multistage Nonlinear Programs with Recourse."
P. Kleinschmidt, C.W. Lee and H. Schannath, "Transporta-
tion Problems Which Can Be Solved by the Use of Hirsch-Paths for
the Dual Problems."
S. Sen and H. D. Sherali, "Nondifferential Reverse Convex
Programs and Facetial Convexity Cuts via a Disjunctive Charac-
H.C.P. Berbee, C.G.E. Boender, A.H.G. Rinnooy Kan,
C.L. Scheffer, R.L. Smith and J. Telgen, "Hit-and-Run Algo-
rithms for the Identification of Nonredundant Linear Inequalities."
S.M. Robinson, "Local Epi-Continuity and Local Optimiza-
M. Aganagic and R. W. Cottle, "A Constructive Characteri-
zation of Qo-Matrices with Nonnegative Principal Minors."
S.J. Wright, "Local Properties of Inexact Methods for Minimiz-
ing Nonsmooth Composite Functions."

~ s~ ~lb_ ~ ~_~~~


0 P I MA number twenty-one

JUNE 1987

PAG 6. 0 Anme tet-n

Vol. 38, No. 3

S. Hashizume, M. Fukushima, N. Katoh and T. Ibaraki,
"Approximation Algorithms for Combinatorial Fractional Pro-
gramming Problems."
E. R. Panier, "An Active Set Method for Solving Linearly
Constrained Nonsmooth Optimization Problems."
M.J.M. Jansen and S.H. Tijs, "Robustness and
Nondegenerateness for Linear Complementarity Problems."
E. Allen, R. Helgason and J. Kennington, "A Generalization
of Polyak's Convergence Result for Subgradient Optimization."
D. Talman and T. Doup, "A New Simplicial Variable
Dimension Algorithm to Find Equilibria on the Product Space of
Unit Simplices."
S.H. Lu and A.C. Williams, "Roof Duality for Polynomial 0-1

Vol. 38, No. 1

G. van der Laan and A.J.J. Talman, "Simplicial Approxima-
tion of Solutions to the Nonlinear Complementarity Problem with
Lower and Upper Bounds."
M. Conforti and M.R. Rao, "Structural Properties and
Recognition of Restricted and Strongly Unimodular Matrices."
M.J.D. Powell, "Update Conjugate Directions by the BFGS
R.M. Freund, "Dual Gauge Programs, with Applications to
Quadratic Programming and the Minimum-Norm Problem."
M.H. Gerards and A. Sebo, "Total Dual Integrality Implies
Local Strong Unimodularity."
P.H. Calamai and A.R. Conn, "A Projected Newton Method
for I Norm Location Problems."

Vol. 38, No 2

E.M.L. Beale, FRS: "Friend and Colleague," edited by G.B.
Dantzig and J.A. Tomlin.
S.W. Wallace, "A Piecewise Linear Upper Bound on the
Network Recourse Function."
A. Bouchet, "Greedy Algorithm and Symmetric Matroids."
M.N. Broadie and B. C. Eaves, "A Variable Rate Refining
J. Kyparisis, "Sensitivity Analysis Framework for Variational
S. -K. Sim, "Clarification of Certain (a, P ) -Polarity Results of
Bachem and Grotschel."
Z. Drezner, "On the Complexity of the Exchange Algorithm
for Minimax Optimization Problems."

S. Chopra and E.L. Johnson, "Dual Row Modules and
Polyhedra of Blocking Group Problems."
B. Betro and F. Schoen, "Sequential Stopping Rules for the
Multistart Algorithm in Global Optimisation."
J.V. Burke, "Second Order Necessary and Sufficient Condi-
tions for Convex Composite NDO."
P. Tseng and D.P. Bertsekas, "Ralaxation Methods for
Problems with Strictly Convex Separable Costs and Linear
P. Zencke and R. Hettich, "Directional Derivatives for the
Value-Function in Semi-Infinite Programming."

Mathematical Programming Study 31

F.A. Al-Khayyal, "An Implicit Enumeration Procedure for
the General Linear Complementarity Problem."
M.C. Bartholomew-Biggs, "Recursive Quadratic Program-
ming Methods Based on the Augmented Lagrangian."
R.S. Dembo, "A Primal Truncated Newton Algorithm with
Application to Large-Scale Nonlinear Network Optimization."
S.D. Flam, "Approximating some Convex Programs in T i in
of Borel Fields."
H.J. Greenberg, "Computer-Assisted Analysis for Diagnosing
Infeasible or Unbounded Linear Programs."
D.W. Heam, S. Lawphongpanich and J.A. Ventura,
"Restricted Simplicial Decomposition: Computation and
J.K. Ho, "Recent Advances in the Decomposition Approach to
Linear Programming."
M. Kupferschmid and J.G. Ecker, "A Note on Solution of
Nonlinear Programming Problems with Imprecise Function and
Gradient Values."
Z.A. Maany, "A New Algorithm for Highly Curved Con-
strained Optimisation."
R. Mifflin, "An Implementation of an Algorithm for Univari-
ate Minimization and an Application to Nested Optimization."
W. Ogryczak, "On Practical Stopping Rules for the Simplex
J.A. Tomlin, "An Experimental Approach to Karmarkar's
Projective Method for Linear Programming."

Vol. 37, No. 3

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ji_-i ~j I~

Finite Algorithms in Optimization and Data
By M.R. Osborne
Wiley, Chichester, 1985
ISBN 0-471-90539-9

While most optimization problems are computed by some version
of the simplex method for linear programming, many nonlinear
problems require different treatment. Some linear problems may be
better approached by other methods which take into account the
structure of the problems. This book analyses various finite algo-
rithms, methods involving a strictly limited number of steps, both for
linear and some nonlinear problems. The results presented will
interest those who want better algorithms and who are interested in
both mathematical and computational aspects. The emphasis is on
problems of moderate size and some interesting structure, so sparse-
ness is not a factor here. Questions of scaling, degeneracy, and
stability are discussed at some length, not only for the simplex method
but also for some rival methods arising in some applications. These
include various data analysis problems and some statistical ques-
SAfter an initial chapter on convex analysis, linear programming is
extensively discussed, not only by the simplex method but also by
descent methods (both reduced and projected gradient) and an exact
penalty algorithm. Attention is paid to degeneracy and comparing the
amount of computation required. The next chapter applies linear
programming to questions of discrete approximation, which is re-
lated to linear programming using a polyhedral norm. Both primal
and dual algorithms are discussed. Next, polyhedral convex func-
tions are analysed; these are nondifferentiable functions obtained as
the maximum of a finite number of affine functions. What is interest-
ing here, as well as in other contexts of nondifferentiable convex
programming, is finding tractable compact representations for the
subdifferentials which arise. This theory is then applied to least
squares and related methods. There is a considerable discussion of
robustness and "resistance", the latter meaning insensitivity to a few
large residuals. Several nonconvex problems are also analysed. The
final chapter, on complexity and performance, discusses the number
of iterations and amount of computing for various algorithms, includ-
ing the ellipsoid method. There is a useful discussion, with some
numerical data, on the various possibilities for randomly generated
test problems. A great deal of interesting research on algorithms from
very scattered sources in the literature, as well as the author's own
considerable contributions, are summed up in these chapters.
-B.D. Craven

Mathematical Programming Essays in Honor of
George B. Dantzig
Parts I and II
Edited by R.W. Cottle
North-Holland, Amsterdam, 1985

Two volumes of the series, Mathematical Programming Studies,
comprise 28 papers dedicated to Professor George B. Dantzig on the
occasion of his 70th birthday. Their topics cover a broad range of
mathematical programming. A common feature of the majority of
papers is presentation of a new algorithm or a new variant of a known
method for solving either some classical optimization problem or its
restriction to more specified data.
To this group belong papers which deal with linear programming
problems having staircase or network structure. Other contributions
treat nonlinear or stochastic programming. Furthermore, two papers
present algorithms immediately motivated by practical applications:
Circuit routing for design of VLSI chips and optimal balancing be-
tween expansion cost and security index in the location of reactive
sources in electrical power planning. Most of the above papers report
also on computational experience with the implementation of the
suggested methods and present a comparison with another standard
method in favour of the new one. On the other hand, the conclusion
of one is that the use of "deep cuts" in ellipsoid algorithms does not
provide any substantial decrease in the number of iterations. Many of
the above papers use the decomposition technique. A general ap-
proach to decomposition algorithms for ordered structures is also
The first two papers study sensitivity of linear programming. A
further one shows that each pair of feasible primal and dual solutions
gives a computable bound on some components of the optimal
solution. Other papers survey results on faces of a convex polyhedron
and on complementarity problems. Moreover, a principle of mono-
tone likelihood is introduced that is related to an exponential family
of distributions. Besides that, a new condition for a minimum of a
concave function and a class of matrices allowing certain type of
scaling is given.
A small portion of papers is of rather combinatorial character,
namely, showing that any basis of a 2-connected greedoid can be
obtained from any other by a finite sequence of pivots and a polyhe-
dral approach to scheduling problems.
The editorial intention was to stress the connection of the included
papers with the scope of G.B. Dantzig's own work. The contributions
are organized into six groups: linear programming, large-scale linear
programming, network optimization and integer linear program-
ming, complementarity, nonlinear programming, and stochastic
programming. Each of these groups is separately surveyed with
references to the list of 15 selected publications by G.B. Dantzig.
-S. Poljak


JUNE 1987

0 PT IM A number twenty-one



Combinatorial Optimization, Annotated
Edited by M. O'Eigeartaigh, J. K. Lenstra and
A.H.G. Rinnooy Kan
Wiley, Chichester, 1985
ISBN 0-471-90490-2

The purpose of the book is to present annotated bibliographies for
most of the rapidly developing subareas of combinatorial optimiza-
tion. To this end, twelve well-known specialists have been asked to
select main references and important new preprints and to provide
brief annotations.
The presentation is such that the book is somewhere in the middle
between a pure bibliography and a collection of surveys. This makes
it extremely useful for readers who are only slightly familiar with
some subarea and want a brief and to-the-point introduction to the
main results and the main research development.
Naturally, due to the fast expansion of the field, it is almost
impossible for such a book to cover all subareas. So the book concen-
trates on the following topics: polyhedral combinatorics, duality for
integer optimization, packing and covering, submodular functions
and polymatroids, computational complexity, probabilistic analysis,
randomized algorithms, parallel algorithms, location and network
design, vehicle routing, scheduling, and software. Personally, I would
have liked to see also chapters on perfect graphs or algorithmic graph
theory and to cover in greater detail topics such as oriented matroids,
project scheduling and stochastic scheduling.
Altogether, the book represents a very valuable source of informa-
tion and can be highly recommended as an up-to-date reference book
for research and teaching in combinatorial optimization.
-Rolf H. M6hring

Analysis and Design of Algorithms for Combina-
torial Problems
Edited by G. Ausiello and M. Lucertini
North Holland, Amsterdam, 1985
ISBN 0-444-87699-5

The continuously growing interest for fast and efficient algorithms
for combinatorial problems has led to a large number of schools,
specialized conferences and workshops on this subject in the last
decade. This volume contains a selection of the contributions pre-
sented at one of these meetings, an international workshop held in
September 1982, at CISM in Udine, Italy.
Quite often proceeding volumes of this kind suffer from an intrin-
sic uneveness. This is particularly true when the subject lies in the
interface between different disciplinary areas as in the case of combi-
natorial algorithms. Although it contains many valuable papers, the
volume we are considering is no exception. The reader finds contribu-
tions belonging to quite different sectors; while some are of rather

_______________________________________ .1- -- -

general interest, others are very technical. J
The 15 papers in this volume cover several subjects which can be
grouped as follows.
Several contributions deal with graph theoretic concepts. Among
them we would like to mention a quite interesting study of algorithms
to detect the equivalence among directed hypergraphs (a problem
arising in relational database theory) and an elegant characterization
of the relations between the K6nig-Egervary properties for graphs
and the consistency of Boolean quadratic equations.
One paper deals with abstract computational complexity of enu-
meration problems. The comparison among complexity classes with
respect to Counting Turing Machines and Random Access Machines
is investigated.
Another group of papers contains quite interesting results on the
analysis of approximation algorithms for hard problems. Most of
them are based on a probabilistic approach. Among the problems
investigated in these papers are the weighted vertex cover, the domi-
nating set, the maximum clique, the maximum set packing and the
multiple edge cover. As an example, it is shown that for a certain class
of random graphs, a randomly selected feasible solution is asymptoti-
cally optimal, almost surely for the dominating set problem. A nice
generalization and unification of known results concerning the
probabilistic analysis of the greedy algorithm for the maximum clique
and the maximum set packing problems is provided in one of these
papers. Several approximation techniques for the weighted vertex
cover problem are presented in a paper based on a new "Local-Ratio"
Another paper deals with a particular type of binary tree structure
called "trie". A systematic way to obtain estimates of trie parameters,
such as size, pathlength, height, etc., as a function of the number of
elements on which the trie is built, is presented.
A couple of papers are in the area of parallel algorithms. In
particular, a collection of algorithms is presented to store and process
relational databases on VLSI mesh-of-trees structures. Unfortunately
this interesting contribution is quite hard to follow since the figures,
which the authors refer to in the text, for some mysterious reason,
have not been printed.
Finally, two application oriented papers are concerned with par-
ticular network design problems. One problem is to set the arc
capacities in a network where the flow demand is not known in
advance. An approximation algorithm is proposed for the case in
which the demand vector must belong to a polyhedron, and the
objective is to maximize the subset of satisfied demand vectors under
a budget constraint. The other problem, which arises in the design of
electrical circuits, is to connect sets of terminals lying on the border of
a grid by means of "wire-trees" in order to minimize the number of
used rows ("tracks") of the grid. An optimal algorithm to solve this
problem, known as the "multiterminal channel routing" problem, is
In summary, this volume contains enough valuable contributions
to be recommended to all scientists working in the Combinatorial
Optimization area.
-Alan A. Bertoss;
-Giorgio Gallo

JUNE 1987


0 PT IM Anumber twenty-one

PAGE 90 PTI~ M I A number twenty-one JUNE 198

4 General Theory of Optimal Algorithms
3y J.F. Traub and H. Wozniakowski
Academic Press, New York
ISBN 0-12-697650-3

The authors develop a framework for discussing optimality of
algorithms, the emphasis lying on approximation questions. Major
topics treated are interpolation, integration, approximation and par-
tial differential equations. The book is essentially based on the funda-
mental work of Kiefer, Sard, Nikolski, Golumb, Weinberger, Michelli,
Rivlin and many other mathematicians in the field of approximation
theory. Given this background, the monograph stresses as a newly
introduced basic instrument a notion of general information. As it
turns out, this notion is intimately connected with classical concepts
in approximation theory (like Gelfand-and Kolmogorov-n-width).
The translation and interpretation of classical results into the present
framework is a major aspect of the book. Consequently, a reader
should not expect a treatment of the computational aspects of, e.g.,
combinatorial optimization (centering around NP-completeness and,
in fact, not even the (explicit) treatment of Kashian's or Karmarkar's
polynomial time algorithms for linear (and certain nonlinear) optimi-
zation problems.
Instead, in its main part (Part A up to chapter 6) the book is
concerned with studying the worst case behaviour of non-iterative
approximation algorithms for so-called linear problems, such as
numerical integration. The (usually) available linear information for
Such problems consists, e.g., of function values at certain points. This
means, in the author's terminology, that the information operator is
linear. As a measure of the "size" of information the rank of the
information operator (called the cardinality of information) is intro-
The best information operator with a certain cardinality is asked
for, and complete characterizations are given, e.g., for the Hilbert case.
General perhaps surprising results obtained in this framework are
the following:
There are linear problems, for which there is no c-approximation
possible using any finite number of linear functionals as information
operator (no matter how large e is chosen).
In the linear context, adaptive information is not superior to
Interesting features from the complexity point of view are the
observations that every linear algorithm with error less than e is a
nearly optimal complexity algorithm for this error rate. On the other
side, the complexity of linear problems can be arbitrarily high with no
complexity gap existing (essentially any decreasing real function on
the positive reals is a complexity function for some suitable linear
problem). As already mentioned, these principal insights are enriched
with a wide variety of details from classical problem solutions, refor-
mulated in the present framework. Aspects of symbolic integration
are briefly addressed. Also, improved results on the treatment of
differential equations are among the subjects covered, as is the critical
role of the chosen norms.
/ Part A, chapters 8 to 10, deals with the case of nonlinear problems.
As a particular central result it is established that nonlinear informa-
tion operators with cardinality one are sufficient in this case. A good

I J._

example for the ideas followed in this section is the treatment of the
maximization of unimodular functions, where a result of Keifer is
discussed and improved in a certain sense. As is to be expected, the use
of non-adaptive techniques proves very favourable in the non-linear
context. Quite a number of complexity results are included. In certain
cases, the algorithmic complexity for e-approximation is proportional
to l/e, i.e., not polynomial any more in the usual sense.
As was mentioned above, the results so far are subject to a worst-
case analysis. Average case models, relative models, perturbed
models and asymptotic models are then briefly discussed. Two inter-
esting observations are the following:
Contrary to many combinatorial optimization problems, the
worst case and the average case complexity for linear problems with
linear and non-adaptive information seem to be nearly the same.
In a certain sense, studying perturbations (sensitivity analysis)
seems not necessarily to lead to a really higher degree of correspon-
dence between mathematical models and real life applications in the
given framework. For instance, in a certain sense, the occurring
models can have the nasty property of model-inherent instabilities.
The authors themselves point out this deficiency of their treatment of
stability aspects and ask for further research on this important ques-
Part B of the book, strongly separated from Part A, is a compara-
tively small (50 pages) review of the situation for iterative approaches
with a restriction to linear information. To mention one of the main
results, the authors discuss the conjecture that essentially only
(non)linear equations can be solved by iteration.
To summarize, given a basic knowledge in approximation theory,
the book is useful as a unifying approach to a scattered variety of
algorithmic and computational problems in this area. An outstanding
feature of the monograph is its excellent bibliography with many
-K. Donner
-F.J. Radermacher

Graphs (Vol. 6, Part 1)
By Claude Berge
North Holland, Amsterdam, 1985

This is in fact the third edition of Part One of the English translation
of Graphes et Hypergraphes (1970) and may thus be regarded as a
legitimate descendant of the author's classic Thdorie des Graphes et ses
Applications (1958), even though focuses and setup of the presentation
have changed and, naturally, the volume of material has grown
The present edition is divided into chapters as follows: Basic
Concepts; Cyclomatic Number; Trees and Arborescences; Paths,
Centers and Diameters; Flow Problems; Degrees and Demi-degrees;
Matchings; c-Matchings; Connectivity; Hamiltonian Cycles; Cover-
ing Edges with Chains; Chromatic Index; Stability Number; Kernels
and Grundy Functions; Chromatic Number; and Perfect Graphs. As
compared to Part One of the second English edition (1976) which
shows the same titles of chapters, the following changes are worth
mentioning: Updating and/or revision of the sections on edge con-

JUNE 1987


0 PT IM A number twenty-one

PAE100P Anmbrtwnyon L''I.18

nectivity, Hamiltonian circuits and cycles, bounds for the chromatic
index, the stability number, vertex colourings, triangulated graphs,
addition of new sections on the correlation of maximal path length
and vertex colouring (Gallai-Roy theorem) and LovAsz's perfect
graph theorem.
Occasional confusion in theorem numbering and referencing
caused by these changes should not blur their positive impact. They
do confirm the role of the book as one of the leading accounts of
modern graph theory.
The discussion of planarity has been reduced, the author renewing
his promise to write a monograph on topological aspects of graph
theory. Part Two of the previous editions (hypergraph theory) will
also be re-published separately.
An unusual defect hinders the use of this prominent text as a
reference book: There is no subject index. The useful English-French-
I I I a n i j L : of: definitions of the previous editions has disappeared.
-M. Armbrust

Multiple-Criteria Decision Making
By Po Lung Yu
Plenum; London, 1985
ISBN 0-306-41965-3

Po Lung Yu is a very intelligent, inscrutable, and funny man. His
book entitled Multiple-Criteria Decision Making (Concepts, Tech-
niques, and Extensions) is a reflection of Professor Yu. He is also a
friend and colleague. According to the dust cover, Professor Yu
"...offers the reader an integral and systematic introduction to a
number of concepts and techniques of MCDM (Multiple-Criteria
Decision Making) and an exploration of some extensions and applica-
tions at the frontiers of the field." It does this, according to the preface,
"...at an 'introductory' level... (for a student having)... the mathemati-
cal maturity equivalent to a course in operations research or optimi-
zation theory....The book is an outgrowth of formal graduate courses
in ... (MCDM) that the author has taught...."
In spite of the author's professing the book to be an introductory
text, I regard the book as a monograph of the author's own work with
a smattering of other material added. The book is very much a no-
nonsense presentation of Professor Yu's work in a Theorem-Proof
style with remarks and examples that illustrate the mathematical
concepts thrown in to help the student. It appears to be well done,
though I do not think it as introductory as the author makes it out to
be. In the preface, the author counsels those interested in applications
to concentrate on Chapters 3 through 6. A reader might expect those
chapters to discuss applications and to offer advice to those wishing
to apply MCDM techniques. Not so, as a brief review of those chapters
reveals! The titles of Chapters 3 through 6 are: Pareto Optimal or
Efficient Solutions; Goal Setting and Compromise Solutions; Value
Function; and Some Basic Techniques for Constructing Value Func-
tions. These chapters contain lemmas, proofs, and remarks and would
not be regarded as application material by most readers. Professor Yu
apparently regards Chapter 7 as a heavy chapter, because he invites
readers having sophisticated mathematical training to study it care-
fully and "... (hopefully) make a breakthrough in the area of local

analysis of preference and domination structures." That chapter
draws heavily on Yu's work on domination structures.
Chapter 8 presents methods for finding all nondominated solu-
tions to multiobjective linear programming problems and an ap-
proach for solving a multiobjective, multiple right-hand-side linear
programming problem.
The book is not large, weighing in at less that 400 pages. ( I, i h r
8 ends on page 270, and the bibliography begins on page 361.
What I found particularly interesting was Chapter 9, "Behavioral
Bases and Habitual Domains of Decision Making," also based very
much on Professor Yu's own research. This is presented as "(filling
in).... the gap between the technical concepts and the application arts
by presenting the basic mechanism of human behavior and decision
making in a larger scope than just mathematical optimization."
Though my knowledge of behavioral science is less than vast, it is not
zero. My impression is that Yu covers the material from his own point
of view from what a behavioral scientist would call a nonstandard but
valid perspective. He introduces and discusses extensively the con-
cept of habitual domain, "the collection of ideas and actions that can
be activated at (a) time." Then with a little bit of mathematical
development (section 9.3), the author turns to "some observations in
social psychology" (section 9.4) where he draws on his theory and
deduces numerous behavioral effects, such as the "halo" effect and
proximity theory. Then in the next section (section 9.5) the author
presents some applications. These applications are essentially what
the author calls common wisdom, and he discusses such topics as self-
awareness, happiness, success, decision making, persuasion, negotia-
tion, gaming, and career management. I particularly liked his section
on career management (9.5.4) in which he reproduced someone else's
"ground rules for business success." They are common sense and
useful. Some of these applications are tied into the behavioral hierar-
chy set up by the author. Though I found this chapter rather interest-
ing, I decided to ask some of my behavioral science colleagues for their
interpretation of what was covered in Chapter 9. Though their review
was not thorough, they provided support to my assessment above.
Chapter 10, "Further Topics," is a brief synopsis of the rest of the
field. From my perspective it is too brief. It constitutes roughly ten
percent of the entire volume. What it does cover, it covers correctly but
tersely. Many readers may find it too terse. Further, I would have liked
to see other approaches included.
As stated above, I regard the book as a monograph of Yu's work.
A colleague and I regularly teach a seminar on multiple criteria
decision making (mathematically oriented) at the State University of
New York at Buffalo. Every time we conduct the seminar, we use a
different format. We have used several different books, generally
supplemented by current articles, as well as a rather overweight
working paper that I have written for such courses, also supple-
mented by current articles. In spite of our optimistic feelings at the
beginning of the seminar, we always have felt disappointed as we
wend our way through the chosen book. Yu's volume appears to be
a first-class piece of work: We are seriously considering using it in our
next MCDM seminar. However, to provide the breadth that we
believe is necessary, we will have to supplement the book substan-
tially with papers. -Stanley Zionts


~ I

I~ _I~I~ ~ II_ I ___ ~I~

JUN 1 1987


0 P T I M. A number twenty-one

PAG 11 0 MAnmbrtetyoeJUE18

~I odel Building in Mathematical Programming
2nd Edition
By H.P. Williams
John Wiley, Chichester, 1985

This book addresses the needs of students who desire practical
experience with mixed-integer programming (MIP) problem formu-
lations at a greater depth than is possible even with the best texts at the
introductory level.
A large number of challenging formulations are given which are
between "mini-cases" and cases in difficulty. These are first stated in
words; then formulated in a following chapter; then solution output
is given in a third chapter. In this manner, the text allows the students
to obtain a good deal of realistic experience on small to medium-sized
H.P. Williams has been among the earlier researchers to recognize
the importance of MIP formulation techniques and to systematically
study these techniques. Formulation has been, until recent years, a
much neglected mathematical subject. It has unfortunately been
associated with ad hoc "practitioners' tricks," a fact which has de-
layed a more rigorous development.
For nontechnical students, in the introductory course of mathe-
matical programming I use the text by G. Eppen and F.J. Could,
Quantitative Concepts for Management Decision Making Without Algo-
rithms. This text contains far more formulation exercises than is typical
of most other introductory texts.
) The easier program formulations in H.P. Williams' text are at the
harder end of the formulations of Eppen and Gould. The discussions
of MIP formulations are the core of his book, and consequently this
matter is studied at far greater length than in introductory texts, which
have a broader scope.

This book is a good choice as a text for a second and more advanced
course. I used it partially in this manner in a graduate seminar which
also touched on some research issues in MIP.
The author emphasized the importance of obtaining a good (i.e.
small or "tight") linear relaxation (LR) in an MIP formulation. This has
been recognized to be a crucial factor in computational success since
at least the 1970s, dating from the discovery of the importance of
disaggregatedd constraints" in a flow setting by A. Geoffion and G.
Graves and in a logical implication setting by Williams. The impor-
tance of an appropriate partitioning strategy is also emphasized both
in the discussion of the SOS sets of Beale and Tomlin and in terms of
adding new integer variables which represent better branching alter-
natives in highly symmetric MIPs. Total unimodularity and network
structures are briefly treated. The "standard list" of specially-struc-
tured MIPs (e.g., knapsack, travelling salesman, quadratic assign-
ment, covering, packing, and partitioning problems) is briefly devel-
oped, with the apt remark (p. 184) that "most practical IP models do
not fall into any of these categories...."
The text does not systematically use the best MIP formulation, in
the sense of the LR, to derive the MIP formulations given (as either
best or a specific consequence of a best formulation). However, such
derivations are recent developments, and in general many develop-
ments in IP and MIP formulation of the last five or so years are not
Inclusion of Lagrangian relaxation, the ability to use special
combinatorial structures when they occur as subprograms, and a
more systematic use of best LRs, represent potential additional mate-
rial for future texts, for a somewhat more advanced audience than the
present text addresses. The present text provides a good means for
familiarizing students with the use of MIP, and in this way, of having
MIP more widely used. -Robert G. Jeroslow Wa

Application for Membership

Mail to:
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or FF300.00 or Sw.Fr.75.00).

Subscription to volumes 30-31 of Mathematical Programming Studies,
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-----~ III~-E--FI~ ~


OP TIM A number twenty-one

] UNE 1987

O P T I M A number twenty-one


The 13th International Symposium on Mathematical Programming will
be held at Chuo University, Tokyo, Japan, August 29 September 2, 1987.
See OPTIMA Number 20 for details... In preparation for the Symposium,
MPS Council Chairman Michel L. Balinski will visit organizers Iri, Kone
and Tone in November... David Shanno, formerly of University of
California, Davis has joined MPS Treasurer A.C. Williams at Rutgers
University... Michael Held is retiring from IBM to accept a position in the
School of Business Administration at Columbia University... There were
over 300 attendees at the May 17-20 SIAM Conference on Optimization in
Houston. Featured were many sessions on the Karmarkar LP Algorithm...
Richard Karp is giving ten lectures on Probabilistic Analysis of Algorithms
at Johns Hopkins, June 15-19, 1987... Ashok Idnani offers OPTPAK
optimization software through 3i Corporation, 49 Oak Avernue, Box 144,
Park Ridge, NJ 07656.

Deadline for the next OPTIMA is September 15, 1987.

Books for review should be sent to the
Book Review Editor,
Prof. Dr. Achim Bachem,
Mathematiches Institute der
Universitit zu K61n, Weyertal 86-90,
D-5000 Kl1n, West Germany.

Journal contents are subject
to change by the publisher.

Donald W. Heam, Editor
Achim Bachem, Associate Editor
Published by the Mathematical
Programming Society and
Publication Services of the
College of Engineering,
University of Florida.
Composition by Lessie McKoy,
Graphics by Lise Drake.


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


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JUNE 1987


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