Farkas' theorem of nonconvex type and its application to a min-max problem (Q1089906)

This note is concerned with the generalization of Farkas' theorem and its application to derive optimality conditions for a min-max problem. Farkas' theorem is generalized to a system of inequalities described by sup-min type positively homogeneous functions. This generalization allows us to deal with optimization problems consisting of objective and constraint functions whose directional derivatives are not necessarily convex with respect to the directions. As an example of such problems, we formulate a min-max problem and derive its optimality conditions.