带凸约束的非线性方程组的无导数记忆法  

A Derivative-free Memory Method for Systems of Nonlinear Equations with Convex Constraints

作　　者：许琼[1] 林海婵[1] 欧宜贵[1] 

机构地区：[1]海南大学信息学院数学系,海南海口570228

出　　处：《应用数学》2016年第3期686-696,共11页Mathematica Applicata

基　　金：国家自然科学基金(11261015);海南省自然科学基金(111001;114002)

摘　　要：基于无导数线搜索技术和投影方法,本文提出了一种新的求解带凸约束的非线性方程组的无导数记忆法.该方法在每步迭代时不需要计算和贮存任何矩阵,因而适合求解大规模非线性方程组问题.在较弱条件下,该算法具有全局收敛性.数值试验结果及其相关的比较表明该算法是比较有效的.Based on a derivative-free line search technique and the projection method, this paper presents a new derivative-free memory method for solving a system of nonlinear equations with convex constraints. The proposed method does not calculate and store any matrix, thus it is suitable for solving large scale nonlinear equations. Under mild assumptions, the proposed algorithm is proven to be globally convergent. Preliminary numerical results and related comparisons indicate that this algorithm is effective.

关 键 词：非线性方程组 无导数记忆法 投影法 整体收敛性 数值试验 

分 类 号：O221[理学—运筹学与控制论] O241[理学—数学]