| Banach空间上一类非凸向量最优规划的对偶性 |
| |
| 引用本文： | 杜廷松,杨静俐,彭锐.Banach空间上一类非凸向量最优规划的对偶性[J].四川师范大学学报(自然科学版),2012(1):25-28. |
| |
| 作者姓名： | 杜廷松 杨静俐 彭锐 |
| |
| 作者单位： | 三峡大学理学院数学系 |
| |
| 基金项目： | 国家自然科学基金数学天元基金(10726016);湖北省教育厅优秀中青年科技创新团队项目(T201103和T200809);湖北省自然科学基金(2008CDZ047)资助项目 |
| |
| 摘 要： | 讨论了一般Banach空间上一类非凸向量最优规划,提出了Banach空间上一类非凸向量最优规划的一个Mond-Weir型对偶问题.基于问题自身的结构特点和利用定义在Banach空间之间的映射不变凸性,获得了对偶问题新的弱(强)对偶结果.在满足Slater型约束品性条件假设下,严格证明了对偶问题新的弱(强)对偶结果.所获得的对偶性研究结果涉及的是一类多目标规划建立在一般Banach空间上,且目标函数及约束函数为不可微强紧Lipschitz.
|
| 关 键 词： | 多目标规划 (弱)强对偶 Banach空间 |
Duality Theorems for a Class of Nonconvex Vector Optimization Programming in Banach Spaces |
| |
| DU Ting-song,YANG Jing-li,PENG Rui.Duality Theorems for a Class of Nonconvex Vector Optimization Programming in Banach Spaces[J].Journal of Sichuan Normal University(Natural Science),2012(1):25-28. |
| |
| Authors: | DU Ting-song YANG Jing-li PENG Rui |
| |
| Institution: | (Department of Mathematics,Science College,China Three Gorges University,Yichang 443002,Hubei) |
| |
| Abstract: | In this paper,a class of nonconvex vector optimization programming in general Banach spaces is discussed.A Mond-Weir-Like dual mathematical programming problem for a class of nonconvex vector optimization programming in Banach spaces is proposed on the basis of some scholars’ research results.Some new weak(strong) duality results are obtained by means of their inherent properties and by using an invexity notion for mappings defined between Banach spaces.The proposed weak(strong) duality results have been strictly shown under a Slater-type constraint qualification condition.We obtain some new weak(strong) duality results on which a class of multiobjective optimization problem is defined on general Banach spaces,and the objective and constraint functions are nondifferentiable strongly compact Lipschitz. |
| |
| Keywords: | multiobjective optimization weak(strong) duality Banach spaces |
| 本文献已被 CNKI 等数据库收录！ |
