超线性与二次收敛的序列方程组可行方法

A Feasible Method for Superlinearly and Quadratically Convergent Sequential Systems of Equations

本文讨论不等式约束规划问题,给出一个线性方程组与辅助方向相结合的新可行算法,算法用一种新型的直线搜索产生步长.在一定条件下,当k充分大后,求方向dk每次只需解一个线性方程组.文中证明了算法的全局收敛性与超线性的收敛速度以及二次收敛性,并给出了方法初步的数值试验.

Abstract In this paper, inequality constrained programming problems are discussed, based on a combination technique of a system of linear equations and an auxiliary direction, a new feasible algorithm is presented, where the step size is found by a new line search. Under suitable conditions, only one system of linear equations needs to be solved for finding the direction dk when k is large enough. The algorithm isproved to possess global convergence, rate of superlinear convergence and quadratical convergence. Some preliminary numerical results are reported.