集值映射的次微分的性质及其应用(英)

本文讨论了文章``Subgradient of S-convex set-valued mappings and weak efficient solutions"(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 different properties of the subdifferential for set-valued mappings, which has been introduced in ``Subgradient of S-convex set-valued mappings 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 subdifferential for calculating the subdifferential for the sum, composition and intersection of two set-valued mappings. Finally, anecessary and sufficient optimality condition of set-valued optimization problems is discussed.