非单调QP-free非可行域方法

Nonmonotone Line Search Technique for QP-free Infeasible Method

摘要:

本文提出带有Fischer-Burmeister 非线性互补(NCP)函数的非单调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，本文给出解这个非光滑方程的迭代算法.这算法包含原始-对偶变量，在局部意义下，可看成关于一阶KKT最优条件的的扰动牛顿-拟牛顿迭代算法.在线性搜索时，这算法采用非单调方法. 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.

Abstract:

In this paper, a new QP-free infeasible method with nonmonotone line search techniqueis and the Fischer-Burmeister NCP function is proposed for minimizing a smooth function subject to smooth inequality constraints. This iterative method is based on the solution of nonsmooth equations which are obtained by the multiplier function and the Fischer-Burmeister NCP function for the KKT first-order optimality conditions. We use nonmonotone line search techniqueis on line searches. This method is implementable and globally convergent without assuming the strict complementarity condition, isolatedness of the accumulation point and linear independence of the gradients of active constrained functions at the solution. We also prove that the method has superlinear convergence rate under some mild conditions.