集值映射的次微分的性质及其应用(英文)

本文讨论了文章Subgradient of S-convex set-valued mappings and weak efficientsolutions(Appl.Math.J.Chinese Univ.1998,13(4):463-472)中引入的集值映射的次微分的性质及应用.利用相依导数的性质,讨论次微分的性质,并得到了两个集值映射的和、复合以及交的次微分的运算法则.最后,通过这种次微分得到了集值优化问题最优性条件的充要条件,同时推广了此文中的定理7.

The Properties of Subdifferential for Set-Valued Mappings and Applications

In this paper,some difierent properties of the subdifierential for set-valued mappings.which has been introduced inSubgradient of S-convex set-valued map-pings and weak efficient solutions(Appl.Math.J.Chinese Univ.,1998,13(4):463.472)are discussed.Moreover,in virtue of the property of the contingent derivative,some exact calculus rules of the subdiirerential for calculating the subdiiTerential for the sum,com-position and intersection of two set-valued mappings.Finally.a necessary and sufficient optimality condition of set-valued optimization problems is discussed.