On the existence of a saddle value for nonconvex and noncoercive bifunctions

We provide necessary and sufficient conditions for ensuring the existence of a saddle value for classes of nonconvex and noncoercive bifunctions. To that end, we use special classes of asymptotic (recession) directions and generalized asymptotic functions introduced and studied previously in the literature. We apply our theoretical results for providing sufficient conditions for zero duality gap for classes of quasiconvex cone constraint mathematical programming problems.