集序约束集值优化问题的最优性条件  

Optimality conditions for constrained set-valued optimization problems with set relations

作　　者：赵素平[1] 朱胜坤[1] 

机构地区：[1]重庆大学数学与统计学院,重庆401331

出　　处：《四川大学学报（自然科学版）》2013年第5期913-916,共4页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11171362);中央高校基本科研业务费资助项目(CDJXS12100019)

摘　　要：首先,我们给出了集序关系意义下集值映射有效解与弱有效解的关系,并通过实例加以验证.其次,借助集值映射的各种导数,我们对集序约束集值优化问题的最优性条件进行了研究,得到了集序约束集值优化问题存在有效解的充分与必要条件.最后,根据有效解和弱有效解的关系,我们得到了此集序约束集值优化问题存在弱有效解的充分与必要条件.First, the relation between efficient and weak efficient solutions for set-valued maps with set relations is given. And some examples are given to verify the relation. Next, by different kinds of derivatives of set-valued maps, the optimality conditions for constrained set-valued optimization problems are studied. The sufficient and necessary conditions for this constrained set-valued optimization problem existing efficient solutions are concluded. Finally, according to the relation between efficient and weak ef- ficient solutions, the sufficient and necessary conditions for this constrained set-valued optimization problem existing weak efficient solutions are concluded.

关 键 词：集序关系 导数 集值优化 有效解 弱有效解 最优性条件 

分 类 号：O221.6[理学—运筹学与控制论]