Optimality conditions and Mond–Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints

Abstract

In this paper, the class of differentiable semi-infinite multiobjective programming problems with vanishing constraints is considered. Both Karush–Kuhn–Tucker necessary optimality conditions and, under appropriate invexity hypotheses, sufficient optimality conditions are proved for such nonconvex smooth vector optimization problems. Further, vector duals in the sense of Mond–Weir are defined for the considered differentiable semi-infinite multiobjective programming problems with vanishing constraints and several duality results are established also under invexity hypotheses.

A linearized approach for solving differentiable vector optimization problems with vanishing constraints

“…In recent years, many researchers developed different types of algorithms and optimization techniques for solving vector optimization problems. Particular attention has been devoted to the development of new methods that solve the original mathematical (multiobjective) programming problem by means of an associated (vector) optimization problem which, in general, is easier for solving (see, e.g., Antczak [9], Chen et al [10], Duca and Duca [11,12], Miettinen [13], Ruzika and Wiecek [14], and others).…”

“…Mishra et al [27] established the Karush-Kuhn-Tucker-type necessary optimality conditions for Pareto solutions in vector optimization problems with vanishing constraints in which the functions involved are continuously differentiable and studied the relationships between various constraint qualifications in such multiobjective programming problems. Quite recently, Antczak [9] considered the class of differentiable semi-infinite multiobjective programming problems with vanishing constraints for which he proved the Karush-Kuhn-Tucker necessary optimality conditions and, under appropriate invexity hypotheses, sufficient optimality conditions and various Mond-Weir duality results.…”

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

“…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. However, KKT necessary optimality conditions for nonsmooth semi-infinite programming problems with vanishing constraints have not yet considered in [21].…”