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,...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.展开更多
基金the Natural Science Foundation of China(Grant No.10471159,No.10171118)the key project of the Chinese Ministry of Education,Supported by Program for New Century Excellent Talents in University,Education Commission project Research Foundation of Chongqing(Grant No.K J060818,KJ060804)+1 种基金the Research Fund for the Doctoral Program of Chongqing Normal University(Grant No.06XLB023)the project supported by Chongqing Key Laboratory of Operations Research and System Engineering.
基金Supported by the National Natural Science Foundation of China(11071053)the Natural Science Foundation of Hebei Province(A2014207010)+1 种基金the Key Project of Science and Research of Hebei Educational Department(ZH2012080)the Key Project of Science and Research of Hebei University of Economics and Business(2015KYZ03)
基金This research was partially supported by the National Natural Science Foundation of China(Grant number:10871216)the Fundamental Research Funds for the Central Universities(Grant number: CDJXS10 100009).
文摘本文讨论了文章"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.
