Characterizations of pseudoconvex functions and semistrictly quasiconvex ones

In this paper, we provide some new necessary and sufficient conditions for pseudoconvexity and semistrict quasiconvexity of a given proper extended real-valued function in terms of the Clarke–Rockafellar subdifferential. Further, we extend to programs with pseudoconvex objective function two earlier characterizations of the solutions set of a set constrained nonlinear programming problem due to Mangasarian (Oper Res Lett 7:21–26, <CitationRef CitationID="CR37">1988</CitationRef>). A positive function p appears in the most results. It is replaced by the number 1 if the function is convex and its domain of definition is convex, too. Copyright Springer Science+Business Media, LLC. 2013