非线性方程组的一个不使用罚函数和filter的算法  

An Algorithm without A Penalty Function or A Filter for Nonlinear Equations

作　　者：房月华[1] FANG Yue-hua(Mathematics and computer Department , Hengshui University, Hebei 053000, Chin)

机构地区：[1]衡水学院数学与计算机科学系,河北衡水053000

出　　处：《西南师范大学学报（自然科学版）》2018年第5期23-30,共8页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：衡水学院院级课题(2010009)

摘　　要：给出了求解非线性方程组的一个新算法,首先将非线性方程组转化为一个非线性规划,再使用一个不使用罚函数和filter的算法求解这个非线性规划,在Jacobi矩阵一致列满秩的条件下证明由算法产生序列的极限点是非线性方程组的解.通过在算法中引进二阶校正技术来克服可能的Maratos效应,可以证明这个方法是局部超线性收敛的.We present a new algorithm for solving a system of nonlinear equations. The system of nonlinear equations is reformulated into a nonlinear programming problem firstly, and then we solve the problem by a method without a penalty function or a filter. Under the standard assumption that Jacobi matrices are uniformly full rank, it is proved that every limit point of the sequence generated by the algorithm is a solution of the system of nonlinear equations. Introducing the second-order correction technique to the algorithm for overcoming the so-called Maratos effect, this algorithm will locally have superlinear convergence.

关 键 词：罚函数 filter技术 线搜索 超线性收敛 

分 类 号：O221[理学—运筹学与控制论]