求解对称非线性方程组的MPRP型Derivative-Free算法  

An MPRP Type Derivative-Free Method for Symmetric Nonlinear Equations

作　　者：李灿[1] 

机构地区：[1]红河学院数学学院,云南蒙自661199

出　　处：《西南大学学报（自然科学版）》2014年第1期67-71,共5页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11161020);云南省教育厅科学研究基金资助项目(2013Y064)

摘　　要：通过将对称非线性方程组转化为等价的无约束优化问题,并借助求解无约束优化问题的共轭梯度法的思想,提出了一种用于求解对称非线性方程组的MPRP型Derivative-Free算法.该算法保留了共轭梯度法存储量少的优点,适用于求解大规模的对称非线性方程组.同时,该算法始终能产生下降方向,并且在适当的条件下具有全局收敛性.数值试验结果表明该算法是求解对称非线性方程组的一种有效算法.In this paper, based on the conjugate gradient method for solving unconstrained optimization problems, we propose an MPRP type Derivative Free method for solving the symmetric nonlinear equation by converting it into an equivalent unconstrained optimization problem. This method can be applied to solve large-scale symmetric nonlinear equations due to its low storage requirement. The directions genera- ted by the method are descent for the residual ~unction, and the proposed method is globally convergent under appropriate conditions. Finally, the results of a numerical experiment is presented to show the effectiveness of the proposed method.

关 键 词：对称非线性方程组 DerivativeFree算法 MPRP算法 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]