CAJ | 학술논문

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.
본문정의료분편선성NCP함수,병대비선성약속우화문제,제출료대유저분편NCP함수적QP-free비가행역산법.이용우화문제적일계KKT조건,승자화NCP함수,득도대응적비광활방정조.본문급출해저비광활방정조산법,타포함원시-대우변량,재국부의의하,가간성관우동우돈-의우돈질대산법.재선성수색시,저산법채용려자방법.본문급출적산법시가실현적병구유전국수렴성,재괄당가설하산법구유초선성수렴성.
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.