Duality results for interval-valued semiinfinite optimization problems with equilibrium constraints using convexificators

Abstract

Abstract This paper deals with the study of interval-valued semiinfinite optimization problems with equilibrium constraints (ISOPEC) using convexificators. First, we formulate Wolfe-type dual problem for (ISOPEC) and establish duality results between the (ISOPEC) and the corresponding Wolfe-type dual under the assumption of ∂ ∗ $\partial ^{*} $ -convexity. Second, we formulate Mond–Weir-type dual problem and propose duality results between the (ISOPEC) and the corresponding Mond–Weir-type dual under the assumption of ∂ ∗ $\partial ^{*} $ -convexity, ∂ ∗ $\partial ^{*} $ -pseudoconvexity, and ∂ ∗ $\partial ^{*} $ -quasiconvexity.