广义凸性假设下的集合最优化解的性质  

On properties of the optimal solutions in set optimization under the assumptions of generalized convexities

作　　者：李毛亲[1] 李杉林[2] 

机构地区：[1]太原师范学院数学系,山西太原030012 [2]台州学院数学系,浙江临海317000

出　　处：《浙江师范大学学报（自然科学版）》2011年第1期22-27,共6页Journal of Zhejiang Normal University:Natural Sciences

基　　金：山西省回国留学人员科研资助项目(2010087);台州学院培育基金资助项目(2010PY011)

摘　　要：集合最优化与向量最优化同属于多目标最优化的范畴,后者依赖于目标空间向量之间的序关系,而前者则依赖于集合之间的序关系.介绍了由Kuroiwa引入的拓扑线性空间中集合之间的序关系(下关系和上关系)及与此相关的集合最优化问题;探讨了其最优解和弱最优解的性质,并把向量最优化问题的相关结论推广到集合最优化;在一些广义凸性假设下,得到了集合最优化问题的最优解与弱最优解的关系以及局部最优解和全局最优解的关系.Set optimization problem and vector optimization problem are both the branches of multiobjective optimization problem.The optimal solutions to the later one depend on the partial order relation between vectors;the solutions to the former one depend on the partial order relations between sets in the objective space.The partial order relations,called set relations given by Kuroiwa,were introduced in topological linear space.Properties of the optimal solutions and weak optimal solutions were discussed.Conclusions for vector optimization problems were extended to set optimization problems.Under assumptions of some generalized convexities,the relation between optimal solutions and weak optimal solutions,the relation between local optimal solutions and global optimal solutions to set optimization problem were presented.

关 键 词：集合最优化 下关系 上关系 l(u)-(弱)最优解 局部l(u)-(弱)最优解 全局l(u)-(弱)最优解 

分 类 号：O221.6[理学—运筹学与控制论] C931.1[理学—数学]