一种序列线性方程组滤子算法的收敛性分析

Convergence Analysis of a Sequential Systems of Linear Equations Filter Algorithm

摘要:

笔者曾提出一种不可行序列线性方程组滤子方法.它将不可行无需二次规划(QPfree)方法与滤子技巧结合，可以避免罚参数的选取.只需求解两个具有相同系数矩阵的线性方程组以得到搜索方向.在一定程度上克服了序列二次规划方法的缺点.在以上算法的基础上，增加了一个同系数矩阵的线性方程组以计算二阶校正步，使得算法避免了Maratos效应.在一定的条件下，证明了该算法的局部超线性收敛性.

Abstract:

An infeasible sequential systems of linear equations filter algorithm was proposed by author.It combines QPfree methods and filter technique so that it is unnecessary to choose the problematic penalty parameter.That algorithm only needs to solve two systems of linear equations with the same nonsingular coefficient matrix. To some extent,the deficiency of the current SQPtype filter algorithms can be overcome.Based on the algorithm,the second order correction step is computated by adding a system of linear equation,and the Maratos effect can be avoided. Under suitable conditions, the locally superlinear convergence is proved.