一类非光滑分式优化问题的最优性条件和对偶

Optimality conditions and duality for a class of non-smooth fractional optimization problems

研究了一类非光滑多目标分式优化问题,利用变分分析和广义微分中的工具,在新的凸性假设下,建立了此类优化问题有效解的必要条件和充分条件.这些结果都是用极限次微分来刻画的,这在非光滑多目标分式优化问题的研究中是一个比较新的结果,而对于极限次微分的研究是近年来国内外优化领域的研究学者比较关注的一个课题.此外,文中第二部分提出了此类优化问题的Mond-Weir对偶模型,并研究了弱对偶、强对偶的结果.

This paper studies a class of non-smooth multi-objective fractional optimization problems,using the tools in variational analysis and the generalized differential,and establishes necessary conditions and sufficient conditions under some new convexity.These results,which are relatively new in the study of non-smooth multi-objective fractional optimization problems,are characterized by limiting subdifferential.And the study of limiting subdifferential is a pretty hot subject in recent years.In addition,the weak duality and the strong duality results have been obtained in Mond-Weir type duality.