摘要
本文研究了多目标优化问题的ε-拟弱有效解.通过Hadamard(上、下)方向导数和极限次微分给出了ε-拟弱有效解存在的充分和必要条件.提出了一种ε-拟弱鞍点的概念,给出了鞍点存在的条件.最后,建立了拉格朗日对偶模型,证明了对偶定理.
In this paper,necessary and sufficient conditions are obtained for the existence ofε-quasi weakly efficient solution in multiobjective optimization problem in terms of Hadamard directional derivatives and limiting subdifferentials.The notion ofε-quasi weakly saddle point is introduced,and necessary and sufficient conditions are obtained for the existence ofε-quasi weakly saddle point.At last,a Lagrange dual problem is considered and duality theorems are given.
出处
《应用数学学报》
CSCD
北大核心
2010年第6期1061-1071,共11页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金(No.10831009
No.10771228)
重庆师范大学博士启动基金(No.10XLB015)
重庆市自然科学基金(No.CSTC.2010BB2090)资助项目