拓扑空间中非光滑向量极值的最优性条件  

Optimality Conditions for Nonsmooth Extremum Problems in Topological Vector Spaces

作　　者：陈修素[1] 肖志祥[2] 

机构地区：[1]重庆商学院,重庆400067 [2]重庆大学数理学院,重庆400044

出　　处：《重庆大学学报（自然科学版）》2002年第4期47-50,60,共5页Journal of Chongqing University

基　　金：国家自然科学基金资助项目 (199710 92 ;1940 10 40 )

摘　　要：提出了向量值函数的锥D-s凸 ,锥D-s拟凸 ,s右导数及锥D -s伪凸等新概念 ,讨论了锥D-s凸函数的有关性质 ,建立了约束向量极值问题 (VP)的最优性必要条件与涉及锥D-s凸 (拟凸 ,伪凸 )函数的约束极值问题 (VP)的最优性充分条件 ,揭示了 (VP)的局部最优解与整体最优解 ,(VP)的弱有效解与有效解的关系 ,所得结果推广了凸规划及部分广义凸规划的相关结论。Some new concepts of coneD_s convexity,coneD-s quasiconvexity,cone D-s pseudoconvexity,s right derivative of vector value mapping are proposed;and their related properties are discussed;the optimality necessary conditions and sufficient conditions for constrained extremum problem(VP)involving in cone D-s convex mapping are extablished;the relation between local optimal solution and global optimal solution;as well as the relation between weakly efficient solution and efficient solution for (VP) are derived;the corresponding results generalize the related results of classic convex programming.

关 键 词：锥D-s s右导数 (弱)有效解 最优性条件 

分 类 号：O221.2[理学—运筹学与控制论]