互补约束问题的部分增广Lagrange罚函数方法及其收敛性分析

CONVERGENCE ANALYSIS OF A PARTIAL AUGMENTEDLAGRANGIAN PENALTY METHOD FOR MPCC

本文受文献[3]的启发,对一般互补约束问题,提出了一种部分增广Lagrange罚函数法,该方法仅把较难处理的互补约束条件作了惩罚对象。通过改进的证明方法,比文献[3]所采用条件更弱的条件下,即假设在相应的罚问题对应的拉格朗日函数的Hesse矩阵在其切平面上关于α下有界的条件下,得到了算法所产生的迭代序列收敛到原互补约束问题的一个B-稳定点的收敛性结果。

In the paper,enlightened from the reference[3],a partial augmented Lagrangian penalty method for MPCC was proposed.The method only incorporatedthe complementarity constraints into the objective function of the partial augmented Lagrangian penalty problem.Under the condition that the Hessian matrices of the Lagrangian function of the partial augmented Lagrangian penalty problem is bounded below with constant on the corresponding tangent space,the convergent result that the limit point of the sequence of iterates generated by the algorithm is a B-stationary point of the original MPCC was proved.Obviously,the assumption is weaker than that used in paper[3].