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

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.

On Semi-Infinite Optimization Problems with Vanishing Constraints Involving Interval-Valued Functions

“…An increasing number of researchers are directing their focus towards problems related to interval-valued optimization [26,27]. In this regard, Wu [28] developed duality theorems applicable to interval-valued optimization problems that involve continuous differentiability.…”

Interval Valued Vector Variational Inequalities and Vector Optimization Problems via Convexificators

“…Convexificators were recently employed by Golestani and Nobakhtian [8], Li and Zhang [19], Long and Huang [20] and Luu [21] to create the ideal circumstances for nonsmooth optimization problems. We refer to [3,4,12,16,17,18,35], and its sources for further details on convexificators.…”