Dini集值方向导数和广义预不变凸向量优化问题(英文)  

Dini Set-valued Directional Derivatives and Generalized Preinvex Vector Optimization

作　　者：余国林[1] 刘三阳[2] 

机构地区：[1]北方民族大学信息与系统科学研究所,银川750021 [2]西安电子科技大学数学系,西安710071

出　　处：《工程数学学报》2012年第6期945-948,共4页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation for the Youth(10901004);the Zizhu Science Foundation of Beifang University of Nationalities(2011ZQY024);the Key Project of Science and Technology of Ministry of Education(212204)

摘　　要：文讨论拓扑向量空间中非光滑广义凸向量优化的最优性条件问题.利用映射的Dini集值方向导数,建立了广义预不变凸向量优化问题关于强有效解和弱有效解的充分和必要最优性条件.所得结果丰富并深化了优化理论和应用的内容.In topological vector spaces, the optimality condition of non-smooth vector optimization problems involving generalized convexity are studied. By using the concept of Dini set- valued directional derivatives, the necessary and sufficient optimality conditions are estab- lished for weak and strong minimal solutions, respectively, in generalized preinvex vector optimization problems. It is proved that the weak efficiency and strong efficiency of a gen- eralized preinvex vector optimization problem can be characterized by a unified condition. These results deepen and enrich the current optimization theory.

关 键 词：向量优化 Dini集值方向导数 预不变凸函数 最优性条件 

分 类 号：O221.4[理学—运筹学与控制论]