Semi-$ (E, F) $-convexity in complex programming problems

Abstract

<abstract><p>Under recent circulars on the notions of convexity for real sets and functions like $ E $-convexity and $ (E, F) $-convexity, we expand the notions of $ (E, F) $ and semi-$ (E, F) $-convexity to include domains and functions in complex space. We examine their properties and interrelationships. As a consequence, we apply the associated results on a non-linear semi-$ (E, F) $-convex programming problem with cone-constraints in complex space. We discuss the existence and uniqueness of its optimal solution and establish the necessary and sufficient conditions for a feasible point to be an optimal solution to such a problem. The related results in real space can be deduced as special cases.</p></abstract>