Introduction to Linear Programming and the Theory of Games

by Glicksman, Abraham M.

• ISBN13: 9780486417103
• ISBN10: 0486417107
• Format: Paperback
• Copyright: 2001-03-22
• Publisher: Dover Publications

Summary

Simple exposition of linear programming and matrix games covers convex sets in the Cartesian plane and the fundamental extreme point theorem for convex polygons; the simplex method in linear programming; the fundamental duality theorem and its corollary, von Neumann's minimax theorem; more. Easily understood problems and illustrative exercises. 1963 edition.

Table of Contents

Part I Elementary Aspects of Linear Programming	1	(21)
Preliminary Remarks	1	(2)
Graphical Solution of Linear Programming Problems	3	(10)
Alternate Optimal Solutions	13	(9)
Part II Convex Sets in the Cartesian Plane and the Fundamental Extreme Point Theorem	22	(36)
Preliminary Remarks	22	(1)
The Linear Relation in the Cartesian Plane	23	(6)
Convex Sets in the Cartesian Plane	29	(9)
Convex Subsets of a Line	38	(2)
Polygonal Convex Sets and Linear Forms	40	(9)
The Fundamental Extreme Point Theorem	49	(9)
Part III The Simplex Method in Linear Programming	58	(26)
Preliminary Remarks	58	(1)
The Gauss-Jordan Complete Elimination Procedure	59	(4)
The Extended Simplex Tableau	63	(7)
The Use of Artificial Variables	70	(4)
The Condensed Simplex Tableau	74	(4)
Degeneracy	78	(6)
Part IV Elementary Aspects of the Theory of Games	84	(27)
Preliminary Remarks	84	(1)
2 x 2 Matrix Games	85	(12)
Graphical Analysis of m x 2 and 2 x n Matrix Games	97	(14)
Part V Matrix Games and Linear Programming	111	(16)
The Solution of Matrix Games by Linear Programming	111	(6)
Duality and the Minimax Theorem	117	(10)
References	127	(2)
Index	129