向量集值优化中的二次最优性条件  

Second-order Optimality Conditions in Vector Set-valued Optimization

作　　者：刘敬华[1] 龚循华[1] 何鸽[1] 

机构地区：[1]南昌大学数学系,江西南昌330031

出　　处：《南昌大学学报（理科版）》2007年第2期103-109,共7页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(10561007);江西省自然科学基金资助项目(01110067)

摘　　要：考虑集值向量优化中的二次最优性条件。引进了新的集值映射的二次切上导数概念,并利用这个概念给出了在无约束条件下弱有效点对,Henig有效点对,整体有效点对和f-有效点对的充分和必要条件,以及Benson有效点必要条件;还给出了有约束条件前四种有效点对的必要条件。This paper considers second - order optimality conditions in vector set - valued optimization. It proposes new second - order epiderivatives for set - valued maps. By these concepts, it presents a few necessary and sufficient conditions for a weakly efficient solution, a Henig efficient solution, a global efficient solution, an f - efficient solution, respectively, to a vector set -valued optimizaition problem without constraints, and a necessary condition for a Benson efficient solution;moreover,it presents a few necessary conditions for a weakly efficient solution, a Henig efficient solution, a global efficient solution, an f-efficient solution, respectively, to a vector set -valued optimizaition problem with constraints.

关 键 词：集值向量优化 二次切上导数 最优性条件 

分 类 号：O221[理学—运筹学与控制论]