Set-valued minimax programming problems under higher-order σ-arcwisely connectivity

Abstract

In this work, a set-valued minimax programming problem (MP) is taken into account. In the broad sense of higher-order arcwisely connected set-valued maps, we introduce the concept of higher-order σ-arcwisely connectedness of set-valued maps. Under higher-order contingent epidifferentiation and higher-order σ-arcwisely connectivity suppositions, the higher-order sufficient criteria for Karush-Kuhn-Tucker (KKT) optimality are constructed for the problem (MP). Additionally, we develop the higher-order Mond-Weir, Wolfe, and mixed kinds of duality and demonstrate the higher-order strong, weak, and converse theorems of duality among our main problem (MP) and the associated duals under higher-order σ-arcwisely connectivity supposition. Mathematics Subject Classification (2000) 26B25 · 49N15