多目标优化ε-拟弱有效解的最优性条件

Optimality Conditions forε-quasi Weakly Efficient Solution in Multiobjective Optimization Problems

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.