A NOTE ON MINIMAX (MAXIMIN) PROGRAMMING.

Charnes [2] has established the equivalence between the linear programming and the constrained rectangular game. An attempt is made here to establish a similar equivalence between the linear programming and a more general class of decision problems which may be referred to as the "minimax (or maximin) programming problems." This class includes as its special cases the constrained rectangular games and the goal programming [3]. The generalized equivalence theorems are shown to imply the theorem due to Goldman and Tucker [5] on the mutually dual linear programming problems. A brief proof of the existence of a saddle point to the constrained rectangular game is also given as a corollary to these theorems. [ABSTRACT FROM AUTHOR]