单调向量变分不等式解集的离散性与无界性
最优化与控制
2023-12-05 v2 一般拓扑
摘要
本文研究了单调向量变分不等式解集的拓扑结构。我们证明了若单调向量变分不等式的弱 Pareto 解集是离散的，则该集合的每个连通分支都是无界的。类似地，此性质对真 Pareto 解集也成立。文末提出了关于（对称）单调向量变分不等式解集拓扑结构的两个开放问题。
引用
@article{arxiv.1804.01078,
title = {Disconnectedness and unboundedness of the solution sets of monotone vector variational inequalities},
author = {Vu Trung Hieu},
journal= {arXiv preprint arXiv:1804.01078},
year = {2023}
}
备注
The 2nd and 3rd sentences in the proof of Propsition 3.3 have been replaced by "There exist an open set $U$ in $\R^n$ such that $U$ is bounded and $\A \subset U$." The author would like to thank Dr. Yu Han for pointing out the incorrect point