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Pre-Publicación 2009-10

Fabián Flores-Bazán, Elvira Hernández:

Unifying and scalarizing vector optimization problems: a theoretical approach and optimality conditions

Abstract:

This paper introduces and analyses a general vector optimization problem which encompasses those related to efficiency, weak efficiency, and two kinds of strict efficiency, among others, in a unified framework. A corresponding approximate vector problem is also studied, and new optimality conditions for both problems are established via a nonlinear scalarizing function and subdifferentials. Generalized convexity of vector functions are characterized through generalized convexity of scalar functions. The approach sheds new light and offers an alternative to obtain several existing results in the literature.

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