研究了一个非光滑半无限多目标优化问题(简记为SIMOP)并讨论它的对偶性. 本文重点考虑此SIMOP的Mond-Weir型半无限多目标对偶问题, 通过对目标函数和约束函数的某种组合赋予Clarke $F$-凸性假设, 获得了弱/强/逆对偶结论. 文章的一些结论是比较新的, 并推广了已有文献的一些结果.

This paper deals with a nonsmooth semi-infinite multiobjective optimization problem (SIMOP, in brief) and discusses its duality. We focus on Mond-Weir type semi-infinite multiobjective dual problem of the SIMOP, and weak/strong/ converse duality results are obtained by imposing Clarke $F$-convexity hypotheses on some combinations of objective functions and constraint functions. Some of our results are new and generalize the conclusions in some former literatures.