含参原始与对偶弱向量近似平衡问题的稳定性  

The Stability of Parametric Primal and Dual Weak Vector Approximate Equilibrium Problems

作　　者：李科科 彭再云 赵勇 李小兵 LI Keke PENG Zaiyun ZHAO Yong LI Xiaobing(Department of mathematics, Sichuan University, Chengdu 610064 School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331 College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074)

机构地区：[1]四川大学数学学院,成都610064 [2]重庆师范大学数学科学学院,重庆401331 [3]重庆交通大学数学与统计学院,重庆400074

出　　处：《系统科学与数学》2017年第7期1605-1619,共15页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金资助项目(11301571;11471059);重庆市自然科学基金项目(cstc2017jcyjAX0382;cstc2015jcyjBX0131);中国博士后科学基金资助项目(2016T90837);重庆市高校创新团队项目(CXTDX201601022);重庆市巴渝学者专项资助;重庆市民生创新专项(cstc2015shmszx30004)资助课题

摘　　要：借助于标量化技巧讨论了含参原始与对偶弱向量近似平衡问题的稳定性.首先,在邻近C-次似凸性假设下获得原始平衡问题近似解集的连通性和近似解集映射的Hausdorff上(下)半连续性.然后,利用标量化方法,在较弱假设下获得了含参对偶弱向量平衡问题近似解集的连通性及近似解集映射的Hausdorff连续性的充分性条件.最后,给出了在向量优化问题中的一个应用.所得结果推广和改进了已有文献中相应结论.In this paper, we discuss the stability of parametric primal and dual weak vector approximate equilibrium problems under the scalarization method. Firstly, the connectedness of approximate solutions set and the Hausdorff upper （lower） semi- continuity of approximate solution mappings to parametric primal weak equilibrium problems, under the assumption of nearly C-subcovexlikeness, are obtained. Then,under some weak assumptions, some su^cient conditions of the connectedness of approximate solutions set and the Hausdorff continuity of approximate solution map- pings to parametric dual weak vector equilibrium problems are obtained, by using the scalarization method. At last, an application in vector optimization problems is given. The obtained results improve and generalize the corresponding ones in the literature

关 键 词：含参原始弱向量平衡问题 含参对偶弱向量平衡问题 近似解集映射 Hausdorff上(下)半连续性 

分 类 号：O224[理学—运筹学与控制论]