多目标最优化G-恰当有效解集的存在性和连通性

Existence and Connectedness of G-Proper Efficient Sets for Multiobjective Optimization

本文证明了非空紧凸集上拟凸多目标最优化问题的G-恰当有效解的存在性.在此基础上,得到了向量目标函数既是似凸又是拟凸的多目标最优化问题的G-恰当有效解集是连通的结论.同时,还给出一个关于Pareto有效解集连通性的新结果.

In this paper, we prove the existence of G-proper efficient solutions of like-convex multiobjective optimization problem. On the conditions that vector objective function is like-convex and quasi-convex, we obtain the connectedness of G-proper efficient so-lution set of the multiobjective optimization problem. Finally, a new result about the connectedness of Pareto efficient solution set is gained.