Necessary Conditions and Sufficient Conditions for Static Minmax Problems.

摘要

This paper presents necessary conditions and sufficient conditions for minmax problems. A special case of the generalized Motzkin's theorem is presented and then used to derive necessary conditions for the minmax problem. A Lagrange multiplier rule is obtained that is an equality rather than an inequality. Two sets of sufficient conditions for a minmax solution are presented. Finally, examples are given to illustrate the theory. (Author)