Existence, Pareto reducibility, and connectedness in multi-objective optimization: Elementary proofs and extension
Optimization and Control
2018-04-25 v3
Abstract
This paper is divided to two parts. In the first part, we provide elementary proofs for some important results in multi-objective optimization. The given proofs are so simple and short in compared to the existing ones. Also, a Pareto reducibility result is extended from efficiency to proper efficiency. The second part is devoted to the connections between nonemptiness, -(semi)compactness, external stability and connectedness of the set of nondominated solutions in multi-objective optimization. Furthermore, it is shown that some assumption in an important result, concerning connectedness, is redundant and should be removed.
Cite
@article{arxiv.1506.02253,
title = {Existence, Pareto reducibility, and connectedness in multi-objective optimization: Elementary proofs and extension},
author = {Latif Pourkarimi and Majid Soleimani-damaneh},
journal= {arXiv preprint arXiv:1506.02253},
year = {2018}
}