Optimality conditions for a unified vector optimization problem with not necessarily preordering relations

Optimality conditions for a unified vector optimization problem with not necessarily preordering relations

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Article ID: iaor20134040
Volume: 56
Issue: 2
Start Page Number: 299
End Page Number: 315
Publication Date: Jun 2013
Journal: Journal of Global Optimization
Authors: ,
Keywords: vector optimization
Abstract:

This paper studies a general vector optimization problem which encompasses those related to efficiency, weak efficiency, strict efficiency, proper efficiency and approximate efficiency among others involving non necessarily preordering relations. Based on existing results about complete characterization by scalarization of the solution set obtained by the same authors, several properties of (generalized) convexity and lower semicontinuity of the composition of the scalarizing functional and the objective vector function are studied. Finally, some optimality conditions are presented through subdifferentials in the convex and nonconvex case.

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