多目标最优化中的存在性、Pareto约简和连通性：初等证明和推广
Existence, Pareto reducibility, and connectedness in multi-objective optimization: Elementary proofs and extension
摘要：
本文分为两个部分。在第一部分中，我们对多目标最优化中的一些重要结果进行了初步的证明。与现有的证明相比，给出的证明是如此简单和简短。同时，将一个Pareto约简结果从有效性推广到真有效性.第二部分研究了多目标最优化非支配解集的非空性、$R^p_{\geqq}$ -（半）紧性、外部稳定性和连通性之间的关系。此外，它表明，一些重要的结果，有关连通性的假设，是多余的，应该删除。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
