On Some Theoretical and Computational Aspects of the Minimax Problem

摘要

The report contains both a brief summary of the pertinent theory of the minimax problem in finite dimensional spaces and the development of an elimination type algorithm for the practical computation of the minimax solution. Because algorithms for finding saddle point type solutions are easier to implement it is of considerable interest to know when they can be used in minimax problems. A lemma giving sufficient conditions for the minimax to be a local saddle point is presented in the paper. However, the most interesting minimax problems do not admit saddle point solutions and other algorithms must be sought. Two lemmas are given in the paper which guarantee the convergence of the elimination algorithm proposed in the paper for the computational solution of the minimax problem. A shortcoming of the algorithm is that its application is restricted to minimax problems in which the max function is pseudo-convex. (Author)