Extremal Methods and Systems Analysis: An International Symposium on the Occasion of Professor Abraham Charnes’ Sixtieth Birthday Austin, Texas, September 13 – 15, 1977 PDF
Preview Extremal Methods and Systems Analysis: An International Symposium on the Occasion of Professor Abraham Charnes’ Sixtieth Birthday Austin, Texas, September 13 – 15, 1977
Lecture Notes in Economics and Mathematical Systems (Vol, 1-15: Lecture Notes in Operations Research and Mathematical Economics, Vol, 16-59: Lecture Notes in Operations Research and Mathematical Systems) For information about Vols, 1-29, please contact your bookseller or Springer-Verlag Vol. 30: H. Noltemeier, Sensitivitatsanalyse bei diskreten linearen Vol. 58: P. B. Hagelschuer, Theorie der linearen Dekomposition. Optimierungsproblemen. VI, 102 Seiten. 1970. VII, 191 Seiten. 1971. Vol. 31: M. Kuhlmeyer, Die nichtzentrale t-Verteilung. II, 106 Sei Vol. 59: J. A. Hanson, Growth in Open Economies. V, 128 pages. ten. 1970. 1971. Vol. 32: F. Bartholomes und G. Hotz, Homomorphismen und Re duktionen Ii nearer Sprachen. XII, 143 Seiten. 1970. OM 18,- Vol. 60: H. Hauptmann, Schatz- und Kontrolltheorie in stetigen dynamischen Wirtschaftsmodellen. V, 104 Seiten. 1971. Vol. 33: K. Hinderer, Foundations of Non-stationary Dynamic Pro gramming with Discrete Time Parameter. VI, 160 pages. 1970. 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X, ten. 1971. 267 pages. 1973. continuatl.on .on paga 547 Lectu re Notes in Economics and Mathematical Systems Managing Editors: M. Beckmann and H. P. Kunzi 174 Extremal Methods and Systems Analysis An International Symposium on the Occasion of Professor Abraham Charnes' Sixtieth Birthday Austin, Texas, September 13 - 15, 1977 Edited by A. V. Fiacco and K. O. Kortanek Springer-Verlag Berlin Heidelberg New York 1980 Editorial Board H. Albach A V. Balakrishnan M. Beckmann (Managing Editor) P. Dhrymes J. Green W. Hildenbrand W. Krelle H. P. KOnzi (Managing Editor) K. Ritter R. Sato H. Schelbert P. Schonfeld Managing Editors Prof. Dr. Martin J. Beckmann Prof. Dr. H. P. KOnzi Brown University Universitat ZOrich Department of Economics 8090 ZOrich/Schweiz Providence, RI 02912/USA Editors Anthony V. Fiacco Department of Operations Research Institute for Management Science and Engineering The Washington University Washington, DC 20052/USA Kenneth O. Kortanek Department of Mathematics Carnegie-Mellon University Pittsburgh, PA 15213/USA AMS Subject Classifications (1980): 60J50, 60J99, 90A05, 90A15, 90BlO, 90B15, 90C05, 90C15, 90C25, 90C35, 90C99, 90010, 90012,90040 ISBN-13: 978-3-540-09730-3 e-ISBN-13: 978-3-642-46414-0 001: 10.1007/978-3-642-46414-0 Library of Congress Cataloging in Publication Data International Symposium on Extremal Methods and Systems Analysis, University of Texas at Austin, 1977. Extremal methods and systems analysis. (Lecture notes in economics and mathematical systems; 174) Bibliography: p. Includes index. 1. System analysis··Congresses. 2. Programming (Mathematics)--Congresses. 3. Game theory--Congresses. 4. Economics, Mathematical--Congresses. 5. Charnes, Abraham, 1917-1. Charnes, Abraham, 1917-11. Fiacco, Anthony V.III. Kortanek, K. 0., 1936- IV. Title. V. Series. 0A402.1571977 00379-27040 ISBN-13: 978-3-540-09730-3 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or_similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin Heidelberg 1980 214113140-543210 ABRAHAM CHARNES In recognition of your many outstanding contributions as a scholar, mathematician, management scientist, engineer, teacher, and friend, we have convened the INTERNATIONAL SYMPOSIUM ON EXTREMAL METHODS AND SYSTEMS ANALYSIS in your honor. We extend our sincere greetings and good wishes on the occasion of your sixtieth birthday. It has been our good fortune to ha ve had our professional and personal lives greatly enriched by our associations with you. Austin, Texas September 13-15, 1977 PREFACE The papers appearing in this Volume were selected from a collec tion of papers presented at the Internationa~ Symposium on Extrema~ Methods and Systems Ana~ysis on the Occasion of Professor A. Charnes' 60th Birthday, at the University of Texas in Austin, 13-15 September 1977. As coeditors, we have followed the normal editorial procedures of scholarly journals. We have obtained invaluable assistance from a number of colleagues who essentially performed the duties of associate editors, coordinating most of the reviews. All papers except those appearing in the Historica~ Perspectives section were refereed by at least two individuals with competency in the respective area. Because of the wide range and diversity of the topics, it would have been im possible for us to make a consistently rational selection of papers without the help of the associate editors and referees. We are indeed grateful to them. The breadth of extremal methods and systems analysis, suggested by the range of topics covered in these papers, is characteristic of the field and also of the scholarly work of Professor Charnes. Extre mal methods and systems analysis has been a pioneering and systematic approach to the development and application of new scientific theories and methods for problems of management and operations in both the pri vate and public sectors, spanning all major disciplines from economics to engineering. Representative of the topical areas discussed at the Symposium, we have categorized 29 papers under ten basic themes: His torica~ Perspectives, Economic Mode~ing and Equi~ibrium, P~anning and Decision Mode~s, Genera~ized Inverses and Matrices, Transportation and VI Networks, Game Theory, Mathematical Programming Theory, Mathematical Programming Computations, Complementarity and Fixed Point Theory, and Stochastic, Dynamic, and Ma2·kov Models. We hope that you will experience some of the high quality and ex- citement of the Symposium itself as you discover the competent and avant-garde sampling of the themes that we have been able to represent in this Volume. The list of titles and authors may, it is hoped, be enticement enough to read on. This illustrious collection of papers does indeed honor the past achievements of the science and of the man to whom this Volume will be an enduring tribute, by no means an easy task. The conference was widely publicized and open to the scientific community, the result being a reliable assessment of past achieve- ments and a vi?ionary identification of many directions of signifi- cance and promise for the field, by highly reputable methodologists and theoreticians and from diverse viewpoints. We would like to take this opportunity to express our gratitude to those professional societies who gave the Symposium their official endorsement: The Association of European Operational Research Soci eties within the International Federation of Opera tional Research Societies The Center for Operations Research and Econometrics (CORE), Belgium F6ndation Nationale pour l'Enseignement de la Gestion des Entreprises, France Deutsche Gesellschaft fur Operations Research (DGOR) The Mexican National Academy of Engineering The Operations Research Society of Japan The Society for Industrial and Applied Mathematics The State Committee for Science and Technology, USSR The Institute of Management Sciences The Operations Research Society of America We are especially pleased to acknowledge major financial support of the Symposium from the Mathematical Sciences Section of the Nation- al Science Foundation, as well as contributions from Analysis, Re- search and Computation, Inc.; the Mathematics, Computers and Systems Department at the EXXON Corporation; and Gulf Science and Technology Company. We must also acknowledge the valuable support of the Univer- sity of Texas, whose facilities were placed at our disposal, particu- larly through that university's president, Lorene L. Rogers, and Dean George Kozmetsky and Professor Darwin Klingman. The Symposium Committee, the list of the Symposium participants, and Symposium Volume authors, together with their affiliations, and the list of acting associate editors appear at the end of the Volume. Their support of the Symposium and this Volume was indispensable. Our appreciation must also be directed to our publisher, Springer-Verlag, who has been extremely encouraging and helpful in every phase of manu script preparation and whose methodical and timely attention to detail has considerably simplified our work. A final word of gratitude is reserved for our many illustrious colleagues who took the time and ef fort to prepare and present Symposium papers, and to those authors herein represented who have patiently borne with us through the long review process to the final preparation of this manuscript. A. V. Fiacco K. O. Kortanek The George Washington University Carnegie-Mellon University Washington, D.C. 20052 Pittsburgh, Pennsylvania 15213 TABLE OF CONTENTS PART I HISTORICAL PERSPECTIVES A Biography of Professor A. Charnes and His Scientific Work . . . . . . 2 K. O. Kortanek Abraham Charnes--A Strategy for Research and a Record of Results ....... ........... 10 W. W. Cooper Publications of A. Charnes 2S PART II ECONOMIC MODELING AND EQUILIBRIUM Multi-page Format Economic Systems ......... S2 Sten Thore The Need for Dynamic Extensions of General- Equilibrium Methods ........... . 68 William P. Drews A Few Words on Application of Optimization Methods to Economic Problems . . . . . . . . . . . .. 8S L. V. Kantorovich and J. V. Romanovsky PART III. PLANNING AND DECISION MODELS Designing Investment Strategies for Fixed-Income Portfolios . . . . . . .. ....... 98 Morton Lane and Jerome Kreuser Multiple Criteria Decision Making for Discrete Alternatives with Ordinal Criteria ..... 13S Stanley Zionts PART IV. GENERALIZED INVERSES AND MATRICES Generalized Inverses of Matrices and Their Applications ................... 1 S4 Adi Ben-Israel Cost-flow Networks and Generali zed Inverses . . . . . 187 Yuji Ijiri x The Weighted Generalized Inverse in Nonlinear Programming--Active Set Selection Using a Variable- metric Generalization of the Simplex Algorithm 197 L. Duane Pyle Convergence Properties of Powers of Matrices with Applications to Iterative Methods for Solving Linear Systems . . . . . . . . . . . . . . . . . . . . . .. 231 Uriel G. Rothblum PART V TRANSPORTATION AND NETWORKS A Network Augmenting Path Basis Algorithm for Transshipment Problems 250 Richard Barr, Joyce Elam, Fred Glover, and Darwin Klingman More on the More for Less Paradox in the Distribution Model. . . . . . . . . . . . . . .. 275 Michael J. Ryan PART VI GAME THEORY The Nash Solution as a Model of Rational Bargaining. 306 Al vin E. Roth Computing the Core of a Market Game. . . . . . . .. 312 Gerald L. Thompson PART VII MATHEMATICAL PROGRAMMING THEORY Second Order Theory of Extremum Problems 336 Aharon Ben-Tal An Elementary Treatment of Lagrange Multipliers 357 R. J. Duffin Representation of Convex Sets. . . . . . . . . . .. 374 Ulrich Eckhardt On One-row Linear Programs 384 Christoph Witzgall Duality in Fuzzy Linear Programming ... 415 Wilhelm Radder and Hans-Jurgen Zimmermann PART VIII MATHEMATICAL PROGRAMMING COMPUTATIONS Fractional Programming with Zero-one Variables 430 E. M. L. Beale Quadratic Termination of Conjugate Gradient Algori thms . . . . . . . . . . . 433 D. F. Shanno XI Rectilinear Distance Location-Allocation Problem: A Simplex Based Algorithm . . . . . . . . . . . . 442 C. M. Shetty and H. D. Sherali PART IX COMPLEMENTARITY AND FIXED POINT THEORY Recent and Past Developments in the Simplicial Approximation Approach to Solving Nonlinear Equations-A Subjective View . . . . . . . . . 466 F. J. Gould Global Continuation Methods for Finding All Solutions to Polynomial Systems of Equations in N Variables. 481 C. B. Garcia and W. I. Zangwill Worst-case Behavior of Local Fixed-point Algorithms. 498 Charles E. Blair PART X STOCHASTIC, DYNAMIC, AND MARKOV MODELS I Quality Control and Free Boundary Problems 506 Avner Friedman The Use of Stochastic Programming for the Solution of Some Problems in Statistics and Probability. . . .• 522 Andras Prekopa AUTHORS, PARTICIPANTS, AND AFFILIATIONS 539 ACTING ASSOCIATE EDITORS 545 THE SYMPOSIUM COMMITTEE . 545
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