Local-global properties of bifunctions

Representations of composite systems, such as bilinear programming, models of consumer/producer behavior, and sensitivity problems involve bifunctions (functions of two vector arguments). Such bifunctions are typically convex, pseudoconvex, or quasiconvex in each of their arguments, but not jointly convex, pseudoconvex, or quasiconvex. These functions do not in general possess the strong local-global property, namely, that every stationary point is a global minimum. In this paper, we define conditions that ensure that a bifunction possesses only a global minimum. In exploring this question, we use P-convexity and pseudo P-convexity, which are classes of bifunctions that generalize quasiconvexity and pseudoconvexity.