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arXiv · 1706.02579

A Vectorization for Nonconvex Set-valued Optimization

Emrah Karaman·İlknur Atasever Güvenç·Mustafa Soyertem·Didem Tozkan·Mahide Küçük·Yalçın Küçük
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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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Emrah Karaman, İlknur Atasever Güvenç, Mustafa Soyertem, Didem Tozkan, Mahide Küçük, Yalçın Küçük. 2017-06-08. A Vectorization for Nonconvex Set-valued Optimization. https://arxiv.org/abs/1706.02579

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