Parametric Set Mathematical Programming Problem Over Cone Using Ρ-K-Locally Connected Set Maps

Abstract

In this paper, we investigate a set-valued mathematical programming problem with parameters (PSVP), where set-valued functions are used for the constraints and objective functions. Set valued ρ-locally connected maps over cone (ρ-k-LC) are introduced and using these maps and contingent epiderivatives, the Karush-Kuhn-Tucker criteria of sufficiency is investigated for the above-mentioned problem. Lastly, using the same presumptions, the Mond-Weir dual is developed and duality theorems are demonstrated.

Primary 26B25; Secondary 49N15