运筹学学报
運籌學學報
운주학학보
OR TRANSACTIONS
2010年
4期
32-40
,共9页
运筹学%集值映射的次微分%相依导数%次微分性质%最优性条件
運籌學%集值映射的次微分%相依導數%次微分性質%最優性條件
운주학%집치영사적차미분%상의도수%차미분성질%최우성조건
Operations research%subdifferential of set-valued mappings%contingentderivative%property of subdifierential%optimality condition
本文讨论了文章"Subgradient of S-convex set-valued mappings and weak effi.cient 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.
本文討論瞭文章"Subgradient of S-convex set-valued mappings and weak effi.cient 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質及應用.利用相依導數的性質,討論次微分的性質,併得到瞭兩箇集值映射的和、複閤以及交的次微分的運算法則.最後,通過這種次微分得到瞭集值優化問題最優性條件的充要條件,同時推廣瞭此文中的定理7.
본문토론료문장"Subgradient of S-convex set-valued mappings and weak effi.cient solutions"(Appl.Math.J.Chinese Univ.1998,13(4):463-472)중인입적집치영사적차미분적성질급응용.이용상의도수적성질,토론차미분적성질,병득도료량개집치영사적화、복합이급교적차미분적운산법칙.최후,통과저충차미분득도료집치우화문제최우성조건적충요조건,동시추엄료차문중적정리7.
In this paper,some difierent properties of the subdifierential for set-valued mappings.which has been introduced in"Subgradient 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.
