A Vectorization for Nonconvex Set-valued Optimization

2017/06/08 by Emrah Karaman, İlknur Atasever Güvenç, Karaman, Emrah +9
Mathematics · #80M50 #90C26 #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:80M50 #msc:90C26

paper · pdf · doi:10.48550/arxiv.1706.02579

arxiv created 2017/06/08 · arxiv updated 2017/06/09

Abstract

Vectorization is a technique that replaces a set-valued optimization problem with a vector optimization problem. In this work, by using an extension of Gerstewitz function [1], a vectorizing function is defined to replace a given set-valued optimization problem with respect to set less order relation. Some properties of this function are studied. Also, relationships between a set-valued optimization problem and a vector optimization problem, derived via vectorization of this set-valued optimization problem, are examined. Furthermore, necessary and sufficient optimality conditions are presented without any convexity assumption.

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