Prederivatives of gamma paraconvex set-valued maps and Pareto optimality conditions for set optimization problems

Abstract

Prederivatives play an important role in the research of set optimization problems. First, we establish several existence theorems of prederivatives for γ-paraconvex set-valued mappings in Banach spaces with . Then, in terms of prederivatives, we establish both necessary and sufficient conditions for the existence of Pareto minimal solution of set optimization problems.

An extension of the Rådström cancellation theorem to cornets

“…This lemma turned out to be a basic tool in various fields and hundreds of papers have used it by now. For instance, in nonsmooth analysis [7][8][9]14,[18][19][20]34], optimization theory [15,36,38], theory of convex sets and functions [10,12,16,17,[23][24][25][26][27][28][29][30][31][32][33]35,40,59,60], set-valued analysis [2,13,37,39,41,[44][45][46]48], set-valued differential equations [3,4,11,22,43,49], set-valued functional equations [6,42,[51][52][53]…”

An extension of the Rådström Cancellation Theorem to Cornets

“…This lemma turned out to be a basic tool in various fields and hundreds of papers have used it by now. For instance, in nonsmooth analysis [7][8][9]14,[18][19][20]34], optimization theory [15,36,38], theory of convex sets and functions [10,12,16,17,[23][24][25][26][27][28][29][30][31][32][33]35,40,59,60], set-valued analysis [2,13,37,39,41,44,45,47,48], set-valued differential equations [3,4,11,22,43,49], set-valued functional equations [6,42,[51][52]…”