| 拓扑空间中非光滑向量极值的最值性条件 |
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| 引用本文： | 陈修素 肖志祥. 拓扑空间中非光滑向量极值的最值性条件[J]. 重庆大学学报(自然科学版), 2002, 25(4): 47-50,60 |
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| 作者姓名： | 陈修素 肖志祥 |
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| 作者单位： | [1]重庆商学院，重庆400067 [2]重庆大学数理学院，重庆400044 |
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| 基金项目： | 国家自然科学基金资助项目 (199710 92，1940 10 40 ) |
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| 摘 要： | 提出了向最值函数的锥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。
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| 关 键 词： | 锥D－s s右导数 （弱）有效解 最优性条件 |
| 文章编号： | 1000-582X(2002)04-0047-04 |
Optimality Conditions for Nonsmooth Extremum Problems in Topological Vector Spaces |
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| CHEN Xiu su,XIAO Zhi xiang. Optimality Conditions for Nonsmooth Extremum Problems in Topological Vector Spaces[J]. Journal of Chongqing University(Natural Science Edition), 2002, 25(4): 47-50,60 |
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| Authors: | CHEN Xiu su XIAO Zhi xiang |
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| Affiliation: | CHEN Xiu su 1,XIAO Zhi xiang 2 |
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| Abstract: | 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. |
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| Keywords: | cone D-s convexity s right derivative (weakly)efficient solution optimality conditions |
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