Variational inequalities characterizing weak minimality in set optimization
Optimization and Control
2016-12-02 v1
Abstract
We introduce the notion of weak minimizer in set optimization. Necessary and sufficient conditions in terms of scalarized variational inequalities of Stampacchia and Minty type, respectively, are proved. As an application, we obtain necessary and sufficient optimality conditions for weak efficiency of vector optimization in infinite dimensional spaces. A Minty variational principle in this framework is proved as a corollary of our main result.
Cite
@article{arxiv.1407.4292,
title = {Variational inequalities characterizing weak minimality in set optimization},
author = {Giovanni P. Crespi and MatteoRocca and Carola Schrage},
journal= {arXiv preprint arXiv:1407.4292},
year = {2016}
}
Comments
Includes an appendix summarizing results which are submitted but not published at this point