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中文摘要：
本文定义一个3-分片线性的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．根据优化问题的一阶KKT条件，利用乘子和NCP函数，得到非光滑方程，本文给出一个非光滑方程的迭代算法．这算法包含原始一对偶变量，在局部意义下，可看成关于一阶KKT最优条件的的扰动拟牛顿迭代算法．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，且在适当假设下具有超线性收敛性．
英文摘要：
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 optimality conditions. Locally, each iteration of this method can be viewed as a perturbation of a mixed 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 line searches. This method is implementable and globally convergent. We also prove that the method has superlinear convergence rate under some mild conditions.
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