ON CONTINUOUS PROGRAMMING WITH GENERALIZED CONVEXITY

Converse Kuhn-Tucker and duality results for constrained continuous programming, under generarlized convex hypotheses, have often been proved independently of the known results for programming in finite dimensions. It is shown here that a large class of such results follow immediately from known results with the standard definitions of pseudoconvex, quasiconvex, pseudoinvex, and quasiinvex, by using Frechet derivatives and integral formulas describing them. Both Wolfe and Mond-Weir duals are included, and both pointwise and integral constraints in a continuous program. Also sufficient conditions, simpler than those previously given, are obtained for a minimax problem, or a minsup problem of continuous programming.