Optimality via generalized approximate convexity and quasiefficiency

Optimality via generalized approximate convexity and quasiefficiency

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Article ID: iaor2013258
Volume: 7
Issue: 1
Start Page Number: 127
End Page Number: 135
Publication Date: Jan 2013
Journal: Optimization Letters
Authors: , ,
Keywords: programming: convex
Abstract:

In this article, we look beyond convexity and introduce the four new classes of functions, namely, approximate pseudoconvex functions of type I and type II and approximate quasiconvex functions of type I and type II. Suitable examples illustrating the non emptiness of the newly defined classes and distinguishing them from the existing classical notions of pseudoconvexity and quasiconvexity are provided. These newly defined concepts are then employed to establish sufficient optimality conditions for the quasi efficient solutions of a vector optimization problem.

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