A note on subdifferential of composed convex operator

Abstract

The aim of this paper is to establish the strong vector subdifferential of the convex operator f +g•h when f, g and h are vector valued convex mappings and g is nondecreasing. An application to a cone-constrained vector optimization problem is also given.

Strong subdifferential calculus for convex set-valued mappings and applications to set optimization

“…In [1], Théra established a formula for the strong vector subdifferential of the sum of two vector valued mappings in the framework of ordered complete topological vector spaces by using the so-called sandwich theorem. Recently, Laghdir et al in [5] established the strong vector subdifferential calculus of the composed convex operator f + g • h when f , g, and h are vector valued convex mappings, and g is nondecreasing. Our main objective in this paper is to establish the sum and composition rules for the strong vector subdifferential in the setting of set-valued convex mappings.…”