KT-E-invexity in E-differentiable vector optimization problems

Abstract

Abstract In this paper, a new concept of generalized convexity is introduced for E-differentiable vector optimization problems. Namely, the concept of KT-E-invexity is defined for (not necessarily) differentiable vector optimization problems in which the functions involved are E-differentiable. The sufficiency of the so-called E-Karush-Kuhn-Tucker optimality conditions is established for the considered E-differentiable multiobjective programming problem under assumption that is KT-E-invex at an E-Karush-Kuhn-Tucker point. Further, the examples of KT-E-invex optimization problems with E-differentiable functions are constructed to illustrate the aforesaid results. Moreover, the so-called vector Mond-Weir E-dual problem is also derived for the considered E-differentiable vector optimization problem and several E-duality theorems in the sense of Mond-Weir are derived under KT-E-invexity hypotheses. 2020 Mathematics Subject Classification: 90C26, 90C29, 90C30, 90C46.