Recent Developments in Mathematical Programming

470 Pages·1991·23.139 MB·English

by  Santosh Kumar

Recent Developments
I•n

Mathematical Programming

Developments
•
In
Mathematical Programming
Edited by
Santosh Kumar
Department ofM athematics
Royal Melbourne Institute ofTechnology
Melbourne, Australia
on behalf of the
Australian Society for Operations Research
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First issued in hardback 2019
© 1991 by Tay10r & Francis Group, LLC
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ISBN-13: 978-2-88124-800-9 (pbk)
ISBN-13: 978-1-138-41318-4 (hbk)
OOI: 10.1201/9780429333439
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Library of Coogress Catalogiog-io-Publicatioo Data
Recent developments in mathematical programming I edited by Santosh
Kumar on behalf of tbe Australian Society for Operations Research.
p. cm.
Includes bibliographical refereJlces and indexes.
ISBN 2·88124·800-4 (softcover) 2·88124·820·9 (hardcover)
1. Programming (Mathematics) L Kumar. Santosh. 1936
D. Australian Society for Operations Research.
QA402.5.R43 1991
519.7-dc20 91·14324
CIP
Visit the Taylor & Francis Web site at
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CONTENTS
Preface ix
List of Contributors xi
PART 1: REVIEW ARTICLES IN MATHEMATICAL
PROGRAMMING
1 Recent Advances in Global Optimization: A Tutorial Survey
Reiner Horst 1
2 Two-level Resource Control Preemptive Hierarchical Linear
Programming Problem: A Review
Subhash C. Naruia and Adiele D. Nwosu 29
3 Some Recent Developments in Infinite Programming
A. B. Philpott 45
4 Recent Developments in Mathematical Programming Software
for the Microcomputer
R. Sharda andD. M. Steiger 61
5 C-Programming: lts Theory and Applications
Moshe Sniedovich 79
PART 2: MULTICRITERIA OPTIMIZATION
6 Aspects of Multicriteria Optimization
B.D. Craven 93
7 A Duality Theorem for a Fractional Multiobjective Problem with
Square Root Terms
R. R. Egudo 101
8 Efficiency and Duality Theory for a Class of Differentiabie
Multiobjective Programming Problems with Invexity
Zulfiqar Ali Khan 115
v
vi CONTENTS
9 Efficiency and Duality Theory for a Class of Nondifferentiable
Multiobjective Programs
Zulfiqar Ali Khan 125
10 Symmetrie Duality for Nonlinear Multiobjective Programming
B. Mond and T. Weir 137
PART 3: SYSTEM OPTIMIZATION AND HEURISTICS
11 Data Envelopment Analysis: A Comparative TooI
M. J. F oster 155
12 A Study of Protean Systems ­ Some Heuristic Strategies for
Redundancy Optimization
Radha Kalyan and Santosh Kumar 181
PART 4: INTERIOR-POINT APPROACH AND QUADRATIC
PROGRAMMING
13 Nearest Points in Nonsimplicial Cones and LCP's with PSD
Symmetrie Matrices
K. S. Al-Sultan and K. G. Murty 199
14 A Study on Monotropie Piecewise Quadratic Programming
Jie Sun 213
15 Interior-Point Algorithms for Quadratie Programming
Yinyu Ye 237
PART 5: COMPUTATIONAL EFFICIENCY, METHODS
AND SOFfWARE
16 Problems in Protean Systems ­ Computer Programs for Some
Solution Methods
Radha Kalyan and Santosh Kumar 263
17 Altemative Methods for Representing the Inverse of Linear
Programming Basis Matrices
Gautam Mitra and Mehrdad Tamiz 273
18 Toward Parallel Computing on Personal Computers in
Mathematical Programming
Moshe Sniedovich 303
CONTENTS vii
PART 6: MATHEMATICAL PROGRAMMING
APPLICA TIONS
19 A Mixed Integer Model of Petroleum Fields with Moving
Plaûorms
Dag Haugland. Kurt Jornsten and Ebrahim Shayan 323
20 Optimal Stochastic Hydrothermal Scheduling Using Nonlinear
Programming Technique
D. P. Kothari 335
21 Nonlinear Programming Applied to the Dynamic Rescheduling of
Trains
R. G. J. Mills and S. E. Perkins 345
22 Network Routing Applications in National and Regional Planning
J. P. Saksen a 359
23 An Application of the Lagrangean Relaxation Based Approach to
the Bulk Commodity Production Distribution Problem
R. R. K. Sharma 369
PART 7: ALGORITHMS, GAMES AND PARADOX
24 Flow Truncation in a Four Axial Sums' Transportation Problem
L. Bandopadhyaya and M. C. Puri 383
25 Continuous Linear Programs and Continuous Matrix Game
Equivalence
S. Chandra. B. Mond and M. V. Durga Prasad 397
26 A Short Note on a Path-following Interpretation of the Primal-
dual Algorithm
Patriek Tobin and Santosh Kumar 407
27 On a Paradox in Linear Fractional Transportation Problems
Vanita Verma and M. C. Puri 413
28 Nash Equilibrium Points of Stochastic N-uels
P. Zeephongsekul 425
APPENDICES
Subject Index 453
Author Index 456
List of Referees 457

PREFACE
Although the genesis of mathematica! programming cao be traced back to the
work ofL.V. Kantorovich a major advance in the field occurred in 1949
(1.2),
when George Dantzig(3) developed the simplex method for solving the linear
program ming problem. Since that time the subject has grown in various ways:
theory, computing efficiency and applications (4.5.6>. Mathematica! program­
ming bas provided a charge which seems to have an endless energy in it.
Harvesting this energy will depend on the work of the mathematica! program­
ming community. The ever increasing theoretica! and computationa! develop­
ments in mathematica! programming already have applications in science,
engineering, and business activities in the private and public sectors.
The initial idea for this publication was supported by the Australian Society
for Operations Research. The origina! aim was to publish papers in the ASOR
Bulletin. However, significant contributions from international researchers
justifieda separate publication. Further, the involvementofGordon and Breach
Science Publishers has made it available in the international market place,
which would not have been possible under the origina! plan.
The book is divided ioto the foUowiog sectioos:
• Review Articles in Mathematica! Programming
• Multicriteria Optimization
• System Optimization and Heuristics
• Interior-Point Approach and Quadratic Programming
• Computational Efficiency, Methods and Software
• Mathematica! Programming Applications
• Algorithms, Games and Paradox
It is hoped that this book will be of interest to researchers and practitioners,
and that it will provide useful information on recent developments in this
rapidly growing field.
In editing this volume I am indebted to a large number of referees whose
critical comments resulted in a better presentation of the papers. A list of the
names and affiliations of the referees is included in the appendices. My thanks
ix