A Vectorization for Nonconvex Set-valued Optimization
Optimization and Control
2017-06-09 v1
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.
Cite
@article{arxiv.1706.02579,
title = {A Vectorization for Nonconvex Set-valued Optimization},
author = {Emrah Karaman and İlknur Atasever Güvenç and Mustafa Soyertem and Didem Tozkan and Mahide Küçük and Yalçın Küçük},
journal= {arXiv preprint arXiv:1706.02579},
year = {2017}
}