分片线性NCP函数滤子QP-free算法

本文定义了分片线性NCP函数,并对非线性约束优化问题,提出了带有这分片NCP函数的QP-free非可行域算法.利用优化问题的一阶KKT条件,乘子和NCP函数,得到对应的非光滑方程组.本文给出解这非光滑方程组算法,它包含原始-对偶变量,在局部意义下,可看成关扰动牛顿-拟牛顿迭代算法.在线性搜索时,这算法采用滤子方法.本文给出的算法是可实现的并具有全局收敛性,在适当假设下算法具有超线性收敛性.

Filter QP-free Method with Piecewise Linear NCP Function

In this paper, we define a piecewise linear NCP function and propose a filter QP-free infeasible method with this NCP function for constrained nonlinear optimization problems. This iterative method is based on the solution of nonsmooth equations which are obtained by the multipliers and the NCP function for the KKT first-order opti-mality conditions. Locally, each iteration of this method can be viewed as a perturbation of a Newton-quasi Newton iteration on both the primal and dual variables for the solution of the KKT optimality conditions. We also use the filter on linear searches. This method is implementable and globally convergent. We also prove that the method has superlinear convergence rate under some mild conditions.