| 摘要: |
| 本文在相关文献考虑MP 问题的基础上, 增加了等式约束条件, 即本文考虑了VP 问题,并将已有文献中的凸性假设改为半凸性假设, 得到VP 问题的ε-拟弱有效解的相应最优性条件. 接着, 本文定义了VP 问题的拉格朗日函数及其ε-拟弱鞍点, 得到VP 问题的ε-拟弱鞍点相应定理.最后, 本文考虑了VP 问题的对偶问题, 获得了VP 问题的弱对偶和强对偶定理. |
| 关键词: 多目标优化 ε-拟弱有效解 优性条件 半凸函数 对偶定理 |
| DOI： |
| 分类号:O221.6 |
| 基金项目:国家自然科学基金资助(11071109). |
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| OPTIMALITY CONDITIONS AND DUALITY THEOREM FOR ε-QUASI WEAKLY EFFICIENT SOLUTION IN SEMI-CONVEX MULTI-OBJECTIVE OPTIMIZATION PROBLEMS |
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ZHANG Cong-jun1, CHEN Yi-ping1, ZHOU Guang-hui2
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1.School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210046, China;2.School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, China
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| Abstract: |
| We consider the VP problem in this paper. By comparing with MP problems in existing literature, we add the equality constraints and change the convex assumptions into semi-convex ones. The optimal conditions for ε-quasi weakly efficient solution for VP problem are obtained. Further, we define the Lagrange function and ε-quasi weakly saddle points of the VP problem and obtain corresponding theorems. Finally we consider the duality of the VP problem and obtain its weak duality and strong duality theorems. |
| Key words: multi-objective optimization ε-quasi weakly efficient solution optimality conditions semi-convex function duality theorems |
