On strong KKT type sufficient optimality conditions for multiobjective semi-infinite programming problems with vanishing constraints

Abstract

In this paper, we consider a nonsmooth multiobjective semi-infinite programming problem with vanishing constraints (MOSIPVC). We introduce stationary conditions for the MOSIPVCs and establish the strong Karush-Kuhn-Tucker type sufficient optimality conditions for the MOSIPVC under generalized convexity assumptions.

Karush-Kuhn-Tucker optimality conditions and duality for semi-infinite programming problems with vanishing constraints

“…In the line of [5], we consider the following semi-infinite programming with vanishing constraints (P):…”

“…For some recent results in this direction; see, e.g., the papers [11,12,13,18,19,21,22,23,24] and references therein. In [5], KKT sufficient optimality conditions for semi-infinite programming problems with vanishing constraints were investigated. However, KKT necessary optimality conditions for semi-infinite programming problems with vanishing constraints have not considered yet in [5].…”

“…In [5], KKT sufficient optimality conditions for semi-infinite programming problems with vanishing constraints were investigated. However, KKT necessary optimality conditions for semi-infinite programming problems with vanishing constraints have not considered yet in [5]. Moreover, to the best of our knowledge, there is no paper dealing with duality for semi-infinite programming problems with vanishing constraints.…”

Karush-Kuhn-Tucker optimality conditions and duality for nonsmooth multiobjective semi-infinite programming problems with vanishing constraints

“…In addition, the semi-infinite programming problems, the optimization with an infinite number of constraints, have been recently studied by many authors; see, e.g., [11,12,13,14,15,16,17,18,19,20] and the references therein. Employing the Clarke subdifferentials, the KKT sufficient optimality conditions for nonsmooth semi-infinite programming problems with vanishing constraints were investigated in [21]. The papers [22,23,24] investigated KKT necessary and sufficient optimality conditions and duality for smooth semi-infinite programming problems with vanishing constraints.…”

“…The papers [22,23,24] investigated KKT necessary and sufficient optimality conditions and duality for smooth semi-infinite programming problems with vanishing constraints. However, KKT necessary optimality conditions for nonsmooth semi-infinite programming problems with vanishing constraints have not yet considered in [21]. Moreover, to the best of our knowledge, there is no paper dealing with duality for nonsmooth semi-infinite programming problems with vanishing constraints.…”