Proceedings of the Princeton Symposium on Mathematical Programming

Harold W. Kuhn

Published by Princeton University Press 1971

Proceedings of the Princeton Symposium on Mathematical Programming

Harold W. Kuhn

Volume 1547 in the series Princeton Legacy Library

https://doi.org/10.1515/9781400869930

Overview
Contents

About this book

This volume contains thirty-three selected general research papers devoted to the theory and application of the mathematics of constrained optimization, including linear programming and its extensions to convex programming, general nonlinear programming, integer programming, and programming under uncertainty.

Originally published in 1971.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Topics

Frontmatter Publicly Available Download PDF	i
PREFACE Requires Authentication Unlicensed Licensed Download PDF	iii
CONTENTS Requires Authentication Unlicensed Licensed Download PDF	iv
PART I. LARGE SCALE SYSTEMS
TWO METHODS OF DECOMPOSITION FOR LINEAR PROGRAMMING J. Abadie and M. Sakarovitch Requires Authentication Unlicensed Licensed Download PDF	1
MATRIX GENERATORS AND OUTPUT ANALYZERS E. M. L. Beale Requires Authentication Unlicensed Licensed Download PDF	25
DECOMPOSITION APPROACHES FOR SOLVING LINKED PROGRAMS R. H. Cobb and J. Cord Requires Authentication Unlicensed Licensed Download PDF	37
LARGE SCALE SYSTEMS AND THE COMPUTER REVOLUTION G. B. Dantzig Requires Authentication Unlicensed Licensed Download PDF	51
PART II. PROGRAMMING UNDER UNCERTAINTY
STOCHASTIC GEOMETRIC PROGRAMMING M. Avriel and D. J. Wilde Requires Authentication Unlicensed Licensed Download PDF	73
THE CURRENT STATE OF CHANCE-CONSTRAINED PROGRAMMING M. J. L. Kirby Requires Authentication Unlicensed Licensed Download PDF	93
ON PROBABILISTIC CONSTRAINED PROGRAMMING A. Prekopa Requires Authentication Unlicensed Licensed Download PDF	113
STOCHASTIC PROGRAMS WITH RECOURSE: SPECIAL FORMS D. W. Walkup and R. J. B. Wets Requires Authentication Unlicensed Licensed Download PDF	139
NONLINEAR ACTIVITY ANALYSIS AND DUALITY A. C. Williams Requires Authentication Unlicensed Licensed Download PDF	163
PART III. INTEGER PROGRAMMING
DUALITY IN DISCRETE PROGRAMMING E. Balas Requires Authentication Unlicensed Licensed Download PDF	179
INTEGER PROGRAMMING: METHODS, USES, COMPUTATION M. L. Balinski Requires Authentication Unlicensed Licensed Download PDF	199
ON RECENT DEVELOPMENTS IN INTEGER PROGRAMMING M. L. Balinski Requires Authentication Unlicensed Licensed Download PDF	267
ON MAXIMUM MATCHING, MINIMUM COVERING AND THEIR CONNECTIONS M. L. Balinski Requires Authentication Unlicensed Licensed Download PDF	303
PROGRAMMES MATHETIQUES NONLINEARES A VARIABLES BIVALENTES P. Huard Requires Authentication Unlicensed Licensed Download PDF	313
ENUMERATION ALGORITHMS FOR THE PURE AND MIXED INTEGER PROGRAMMING PROBLEM G. Zoutendijk Requires Authentication Unlicensed Licensed Download PDF	323
PART IV. ALGORITHMS
ON NEWTON’S METHOD IN NONLINEAR PROGRAMMING A. Ben-Israel Requires Authentication Unlicensed Licensed Download PDF	339
EXTENDING NEWTON'S METHOD TO SYSTEMS OF LINEAR INEQUALITIES H. D. Mills Requires Authentication Unlicensed Licensed Download PDF	353
INTERIOR POINT METHODS FOR THE SOLUTION OF MATHEMATICAL PROGRAMMING PROBLEMS J. D. Roode Requires Authentication Unlicensed Licensed Download PDF	359
PART V. APPLICATIONS
THE SOLUTION OF A FIXED CHARGE LINEAR PROGRAMMING PROBLEM P. Bod Requires Authentication Unlicensed Licensed Download PDF	367
ON CLASSES OF CONVEX AND PREEMPTIVE NUCLEI FOR N-PERSON GAMES A. Charnes and K. Kortanek Requires Authentication Unlicensed Licensed Download PDF	377
WHEN IS A TEAM ”MATHEMATICALLY“ ELIMINATED? A. J. Hoffman and T. J. Rivlin Requires Authentication Unlicensed Licensed Download PDF	391
ON THE EXISTENCE OF OPTIMAL DEVELOPMENT PLANS D. McFadden Requires Authentication Unlicensed Licensed Download PDF	403
OPTIMALITY AND DUALITY IN NONLINEAR PROGRAMMING O. L. Mangasarian Requires Authentication Unlicensed Licensed Download PDF	429
GEOMETRIC PROGRAMMING: DUALITY IN QUADRATIC PROGRAMMING AND l_p -APPROXIMATION I E. L. Peterson and J. G. Ecker Requires Authentication Unlicensed Licensed Download PDF	445
CONJUGATE CONVEX FUNCTIONS IN NONLINEAR PROGRAMMING R. T. Rockafellar Requires Authentication Unlicensed Licensed Download PDF	481
PART VII. NONLINEAR PROGRAMMING
A COMPARATIVE STUDY OF NONLINEAR PROGRAMMING CODES A. R. Colville Requires Authentication Unlicensed Licensed Download PDF	487
MINIMIZATION OF A SEPARABLE FUNCTION SUBJECT TO LINEAR CONSTRAINTS V. De Angelis Requires Authentication Unlicensed Licensed Download PDF	503
DIRECT HYPERCONE UNCONSTRAINED MINIMIZATION L. Haller and I. G. T. Miller Requires Authentication Unlicensed Licensed Download PDF	511
NONLINEAR PROGRAMMING AND SECOND VARIATION SCHEMES IN CONSTRAINED OPTIMAL CONTROL PROBLEMS G. Home and G. S. Tracz Requires Authentication Unlicensed Licensed Download PDF	523
ON CONTINUOUS FINITE-DIMENSIONAL CONSTRAINED OPTIMIZATION G. Zoutendijk Requires Authentication Unlicensed Licensed Download PDF	539
PART VIII. PIVOTAL METHODS
QUADRATIC FORMS SEMI-DEFINITE OVER CONVEX CONES R.W. Cottle, G.J. Habetler and C.E. Lemke Requires Authentication Unlicensed Licensed Download PDF	551
APPLICATIONS OF PRINCIPAL PIVOTING T. D. Parsons Requires Authentication Unlicensed Licensed Download PDF	567
LEAST DISTANCE PROGRAMMING A.W. Tucker Requires Authentication Unlicensed Licensed Download PDF	583
PART IX. ABSTRACTS
MAXIMIZING STATIONARY UTILITY IN A CONSTANT TECHNOLOGY R. Beals and T. C. Koopmans Requires Authentication Unlicensed Licensed Download PDF	591
OPTIMUM ROUTING IN CONNECTING NETWORKS OVER FINITE TIME INTERVALS V. E. Benes Requires Authentication Unlicensed Licensed Download PDF	591
SECOND ORDER CHARACTERIZATION OF GENERALIZED POLYNOMIAL PROGRAMS G. E. Blau and D. J. Wilde Requires Authentication Unlicensed Licensed Download PDF	591
ORTHOGONALITY IN MATROIDS AND MATHEMATICAL PROGRAMMING C. P. Bruter Requires Authentication Unlicensed Licensed Download PDF	592
A THEORETICAL ANALYSIS OF INPUTS TAXATION UNDER LINEAR PROGRAMMING ASSUMPTIONS G. Casale Requires Authentication Unlicensed Licensed Download PDF	592
ON THE SOLUTION OF STRUCTURED LP PROBLEMS USING GENERALIZED INVERSED METHODS R. E. Cline and L. D. Pyle Requires Authentication Unlicensed Licensed Download PDF	593
A METHOD FOR CONVEX PROGRAMMING M. Courtillot Requires Authentication Unlicensed Licensed Download PDF	594
CONTINUOUS MATHEMATICAL PROGRAMMING UNDER LINEAR INTEGRAL CONSTRAINTS W. P. Drews and R. G. Segers Requires Authentication Unlicensed Licensed Download PDF	594
RECENT DEVELOPMENTS IΝ GEOMETRIC PROGRAMMING R. J. Duff and E. L. Peterson Requires Authentication Unlicensed Licensed Download PDF	595
NONCONVEX AND CONVEX PROGRAMMING BY GENERALIZED SEQUENTIAL UNCONSTRAINED METHODS A. V. Fiacco and G. P. McCormick Requires Authentication Unlicensed Licensed Download PDF	595
MATHEMATICAL PROGRAMMING BY PHYSICAL ANALOGIES O. I. Franksen Requires Authentication Unlicensed Licensed Download PDF	595
THE MAX-FLOW MIN-CUT EQUALITY AND THE LENGTH-WIDTH INEQUALITY FOR REAL MATRICES D. R. Fulkerson Requires Authentication Unlicensed Licensed Download PDF	596
IMPLICIT ENUMERATION USING AN IMBEDDED LINEAR PROGRAM A. M. Geoffrion Requires Authentication Unlicensed Licensed Download PDF	596
A PRINCIPAL PIVOTING ALGORITHM FOR LINEAR AND QUADRATIC PROGRAMS R. L. Graves Requires Authentication Unlicensed Licensed Download PDF	597
ON THE KUHN-TUCKER THEORY M. Guignard Requires Authentication Unlicensed Licensed Download PDF	597
PROGRAMMING IN INFINITE DIMENSIONAL SPACE AND CONTROL THEORY H. Halkin Requires Authentication Unlicensed Licensed Download PDF	599
A FUNCTIONAL APPROACH TO THE DESIGN AND DEVELOPMENT OF A MATHEMATICAL PROGRAMMING SYSTEM D. W. Hallene Requires Authentication Unlicensed Licensed Download PDF	600
MAGEN II C. A. Haverly Requires Authentication Unlicensed Licensed Download PDF	600
A PARTICULAR CLASS OF FINITE-TIME MARKOV-RENEWAL PROGRAMMING SITUATIONS J. R. Hemsley Requires Authentication Unlicensed Licensed Download PDF	601
A DECOMPOSITION ALGORITHM FOR SHORTEST PATHS IN A NETWORK T. C. Hu Requires Authentication Unlicensed Licensed Download PDF	601
THE DEGREE-CONSTRAINED SUBGRAPH PROBLEM E. L. Johnson, J. Edmonds and S. C. Lockhart Requires Authentication Unlicensed Licensed Download PDF	601
MATHEMATICAL PROGRAMMING AND PROJECT INTERRELATIONSHIPS IN CAPITAL BUDGETING A. K. Klevorick Requires Authentication Unlicensed Licensed Download PDF	602
OPTIMUM DESIGN OF LONG PIPE LINE NETWORKS FOR GASES USING LINEAR PROGRAMMING J. P. Kohli and F. W. Leavitt Requires Authentication Unlicensed Licensed Download PDF	603
CENTRALIZATION AND DECENTRALIZATION OF DECISION MAKING - THE DOUBLE DECOMPOSITION METHOD - GENERALIZATION AND PROOF OF CONVERGENCE T. O. M. Kronsjo Requires Authentication Unlicensed Licensed Download PDF	603
NONLINEAR PROGRAMMING AND ENGINEERING DESIGN L. S. Lasdon and A. D. Waren Requires Authentication Unlicensed Licensed Download PDF	605
NONLINEAR PROGRAMMING VIA ROTATIONAL DISCRIMINATION V. J. Law and R. H. Fariss Requires Authentication Unlicensed Licensed Download PDF	606
COMPLEMENTARY SOLUTIONS FOR SYSTEMS OF LINEAR EQUATIONS C. E. Lemke and R. W. Cottle Requires Authentication Unlicensed Licensed Download PDF	607
ON THE COMPLEXITY OF DISCRETE PROGRAMMING PROBLEMS J. Moravek Requires Authentication Unlicensed Licensed Download PDF	608
ILL-CONDITIONING OCCURRING IN PENALTY AND BARRIER FUNCTIONS W. Murray Requires Authentication Unlicensed Licensed Download PDF	608
THE SHIFTING-OBJECTIVE ALGORITHM: AN ALTERNATIVE METHOD FOR SOLVING GENERAL LINEAR PROGRAMMING PROBLEMS V. Nalbandian Requires Authentication Unlicensed Licensed Download PDF	609
THE BLOCK PRODUCT DECOMPOSITION ALGORITHM W. Orchard-Hays Requires Authentication Unlicensed Licensed Download PDF	610
ITERATIVE SOLUTION OF LARGE, SPARSE LINEAR SYSTEMS AND RELATED TOPICS L. D. Pyle and D. K. Smith Requires Authentication Unlicensed Licensed Download PDF	611
APPROXIMATE COMPUTATIONAL SOLUTION OF NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS BY LINEAR PROGRAMMING J. B. Rosen Requires Authentication Unlicensed Licensed Download PDF	612
THE SHRINKING BOUNDARY ALGORITHM FOR DIOPHANTINE PROGRAMMING R. M. Saunders and R. Schinzinger Requires Authentication Unlicensed Licensed Download PDF	612
APPLICATION OF NONLINEAR PROGRAMMING AND BAYESIAN STATISTICS TO THE THEORY OF THE FIRM L. E. Schwartz Requires Authentication Unlicensed Licensed Download PDF	613
AN ALGORITHM FOR LINEARLY CONSTRAINED NONLINEAR ESTIMATION WITH EXTENSIONS TO GENERAL NONLINEAR PROGRAMMING D. F. Shanno Requires Authentication Unlicensed Licensed Download PDF	613
ALGORITHMS FOR MINIMAL TREES AND SEMI-STEINER TREES BASED ON THE SIMPLEX METHOD J . W. Suurballe Requires Authentication Unlicensed Licensed Download PDF	614
APPLICATION OF LINEAR AND NONLINEAR PROGRAMMING IN OPTIMAL CONTROL OF NUCLEAR REACTORS D. Tabak Requires Authentication Unlicensed Licensed Download PDF	615
A NEW ALGORITHM FOR TRANSPORTATION AND ASSIGNMENT PROBLEMS G. L. Thompson Requires Authentication Unlicensed Licensed Download PDF	616
THE SOLUTION OF PROGRAMMING PROBLEMS BY GENERATING FUNCTIONS J. K. Thurber Requires Authentication Unlicensed Licensed Download PDF	616
ON SOLVING SOME CLASSES OF INTEGER LINEAR PROGRAMMING PROBLEMS C. A. Trauth and R. E. D. Woolsey Requires Authentication Unlicensed Licensed Download PDF	616
AN EXTENDED DUALITY THEOREM FOR CONTINUOUS LINEAR PROGRAMMING PROBLEMS W. F. Tyndall Requires Authentication Unlicensed Licensed Download PDF	617
THE GUIDING PERMUTATION METHOD FOR COMBINATORIAL PROBLEMS E. Valensi Requires Authentication Unlicensed Licensed Download PDF	617
MINIMIZING A CONVEX FUNCTION OVER A CONVEX HULL R. J. -B. Wets and C. Witzgall Requires Authentication Unlicensed Licensed Download PDF	618
GAMES, LINEAR PROGRAMMING AND THE TCHEBYCHEFF APPROXIMATION L. B. Willner Requires Authentication Unlicensed Licensed Download PDF	619
ON A PRIMAL INTEGER PROGRAMMING ALGORITHM R. D. Young Requires Authentication Unlicensed Licensed Download PDF	619
APPLICATIONS OF THE CONVERGENCE CONDITIONS W. I. Zangwill Requires Authentication Unlicensed Licensed Download PDF	620