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.
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Proceedings of the Princeton Symposium on Mathematical Programming
By Harold W. KuhnPRINCETON UNIVERSITY PRESS
Copyright © 1970 Princeton University Press
All rights reserved.
ISBN: 978-0-691-08088-8Contents
Page,
Preface, iii,
PART I. LARGE SCALE SYSTEMS, 1,
J. ABADIE and M. SAKAROVITCH: Two Methods of Decomposition for Linear Programming, 1,
E. M. L. BEALE: Matrix Generators and Output Analyzers, 25,
R. H. COBB and J. CORD: Decomposition Approaches for Solving Linked Programs, 37,
G. B. DANTZIG: Large Scale Systems and the Computer Revolution, 51,
PART II. PROGRAMMING UNDER UNCERTAINTY, 73,
M. AVRIEL and D. J. WILDE: Stochastic Geometric Programming, 73,
M. J. L. KIRBY: The Current State of Chance-Constrained Programming, 93,
A. PREKOPA: On Probabilistic Constrained Programming, 113,
D. W. WALKUP and R. J. B. WETS: Stochastic Programs with Recourse: Special Forms, 139,
A. C. WILLIAMS: Nonlinear Activity Analysis and Duality, 163,
PART III. INTEGER PROGRAMMING, 179,
E. BALAS: Duality in Discrete Programming, 179,
M. L. BALINSKI: Integer Programming: Methods, Uses, Computation, 199,
M. L. BALINSKI: On Recent Developments in Integer Programming, 267,
M. L. BALINSKI: On Maximum Matching, Minimum Covering and Their Connections, 303,
P. HUARD: Programmes Mathematiques Nonlineares a Variables Bivalentes, 313,
G. ZOUTENDIJK: Enumeration Algorithms for the Pure and Mixed Integer Programming Problem, 323,
PART IV. ALGORITHMS, 339,
A. BEN-ISRAEL: On Newton's Method in Nonlinear Programming, 339,
H. D. MILLS: Extending Newton's Method to Systems of Linear Inequalities, 353,
J. D. ROODE: Interior Point Methods for the Solution of Mathematical Programming Problems, 359,
PART V. APPLICATIONS, 367,
P. BOD: The Solution of a Fixed Charge Linear Programming Problem, 367,
A. CHARNES and K. KORTANEK: On Classes of Convex Preemptive Nuclei for N-Person Games, 377,
A. J. HOFFMAN and T. J. RIVLIN: When is a Team "Mathematically" Eliminated?, 391,
D. MCFADDEN: On the Existence of Optimal Development Plans, 403,
PART VI. THEORY, 429,
O. L. MANGASARIAN: Optimality and Duality in Nonlinear Programming, 429,
E. L. PETERSON and J. G. ECKER: Geometric Programming:,
Duality in Quadratic Programming and Ip-Approximation I., 445,
R. T. ROCKAFELLAR: Conjugate Convex Functions in Nonlinear Programming, 481,
PART VII. NONLINEAR PROGRAMMING,
A. R. COLVILLE: A Comparative Study of Nonlinear Programming Codes, 487,
V. DE ANGELIS: Minimization of a Separable Function Subject to Linear Constraints, 503,
L. HALLER and I. G. T. MILLER: Direct Hypercone Unconstrained Minimization, 511,
G. HORNE and G. S. TRACZ: Nonlinear Programming and Second Variation Schemes in Constrained Optimal Control Problems, 523,
G. ZOUTENDIJK: On Continuous Finite-Dimensional Constrained Optimization, 539,
PART VIII. PIVOTAL METHODS, 551,
R. W. COTTLE, G. J. HABETLER, and C. E. LEMKE: Quadratic Forms Semi-Definite Over Convex Cones, 551,
T. D. PARSONS: Applications of Principal Pivoting, 567,
A. W. TUCKER: Least Distance Programming, 583,
PART IX. ABSTRACTS, 591,
CHAPTER 1
TWO METHODS OF DECOMPOSITION FOR LINEAR PROGRAMMING
J. Abadie and M. Sakarovitch
I. Introduction
Consider a linear program having the following structure:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where x is an n1, vector, y is an n2-vector, ..., z is an nt-vector
p is an m1-vector, q is an m2-vector, ..., R is an m