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arXiv · 1506.02253

Existence, Pareto reducibility, and connectedness in multi-objective optimization: Elementary proofs and extension

Latif Pourkarimi·Majid Soleimani-damaneh
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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, $R^p_{\geqq}$-(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.

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Latif Pourkarimi, Majid Soleimani-damaneh. 2015-06-07. Existence, Pareto reducibility, and connectedness in multi-objective optimization: Elementary proofs and extension. https://arxiv.org/abs/1506.02253

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