集值映射的超次梯度及其应用  

Super subgradient for set-valued map and its applications

作　　者：徐义红[1] 张小荣[1] 汪涛[1] 段五朵[1] 

机构地区：[1]南昌大学数学系,江西南昌330031

出　　处：《山东大学学报（理学版）》2012年第12期10-13,共4页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(10461007);江西省自然科学基金资助项目(2009GZS0021);江西省教育厅科技项目(GJJ12010)

摘　　要：引进了集值映射的非导数型超次梯度概念,在某种条件下证明了该梯度的存在性。作为应用,在近似锥次类凸假设下,给出了用该次梯度刻画集值优化问题取得超有效元的充分必要条件。A type of nonderivative super subgradient was introduced for a set-valued map.Under some condition,its existence theorem was proved.As an application,under the assumption of near-subconvexlikeness,the sufficient and necessary optimality conditions were established for set-valued optimization problem to obtain super efficient elements.

关 键 词：超次梯度 超有效元 集值映射 

分 类 号：O224[理学—运筹学与控制论]