Generalized Convexity and Vector Optimization

Mishra, Shashi Kant; Wang, Shouyang; Lai, Kin Keung

doi:10.1007/978-3-540-85671-9

Cited by 13 publications

(1 citation statement)

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“…The theory and applications of vector optimization problems have been closely tied with convex analysis. In recent years, however, there has been an increasing interest in developing sufficient optimality conditions and duality results for various classes of nonconvex vector optimization problems (see, for instance, [1,2,3,4,5,6,8,12,18,9,23,24,30,32,34,22,43], and others).…”

Section: Introductionmentioning

confidence: 99%

E-optimality conditions and Wolfe E-duality for E-differentiable vector optimization problems with inequality and equality constraints

Antczak¹,

Abdulaleem²

2019

J. Nonlinear Sci. Appl.

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In this paper, a nonconvex vector optimization problem with both inequality and equality constraints is considered. The functions constituting it are not necessarily differentiable, but they are E-differentiable. The so-called E-Fritz John necessary optimality conditions and the so-called E-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered E-differentiable multiobjective programming problems with both inequality and equality constraints. Further, the sufficient optimality conditions are derived for such nonconvex nonsmooth vector optimization problems under (generalized) E-convexity. The so-called vector E-Wolfe dual problem is defined for the considered E-differentiable multiobjective programming problem with both inequality and equality constraints and several dual theorems are established also under (generalized) E-convexity hypotheses.

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