A nonmonotone filter trust region method for the system of nonlinear equations

Hua Wang; Dingguo Pu

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A nonmonotone filter trust region method for the system of nonlinear equations

机译：非线性方程组的非单调滤波器信赖域方法

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摘要

In this paper, we present a nonmonotone filter trust region method to attack the system of nonlinear equations. The system of nonlinear equations is transformed into a constrained nonlinear programming problem at each step: some equations are treated as constraints while the others act as objective functions. Compared with the traditional filter strategies, our algorithm is flexible to accept trail steps by means of the nonmonotone filter technique. Moreover, the restoration phase is not needed so that the scale of the calculation is decreased in a certain degree. Global convergence is proven under some suitable conditions. Numerical experiments also show the efficiency of the algorithm.

机译：在本文中，我们提出了一种非单调滤波器信赖域方法来攻击非线性方程组。非线性方程组在每一步都转化为约束非线性规划问题：一些方程被视为约束，而另一些则充当目标函数。与传统的滤波策略相比，我们的算法通过非单调滤波技术可以灵活地接受步长。而且，不需要恢复阶段，因此计算规模在一定程度上减小了。在某些适当条件下证明了全球趋同。数值实验也证明了该算法的有效性。

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来源
《Applied Mathematical Modelling》 |2013年第2期|498-506|共9页
作者
Hua Wang; Dingguo Pu;
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作者单位

School of Mathematics and Information, Shanghai Lixin University of Commerce, Shanghai 201620, PR China;

Department of Mathematics, Tongji University, Shanghai 200092, PR China;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
filter; trust region; equality constraints; the system of nonlinear equations; global convergence;

机译：过滤;信任区域平等约束;非线性方程组;全球趋同;

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1. A new class of nonmonotone adaptive trust-region methods for nonlinear equations with box constraints [J] . Kimiaei Morteza Calcolo . 2017,第3期

机译：具有框限制的非线性方程的新类非单调自适应信任区域方法
2. Nonmonotone trust-region methods for bound-constrained semismooth equations with applications to nonlinear mixed complementarity problems [J] . Ulbrich M. SIAM Journal on Optimization: A Publication of the Society for Industrial and Applied Mathematics . 2001,第4期

机译：有界约束半光滑方程的非单调信赖域方法及其在非线性混合互补问题中的应用
3. A BFGS trust-region method with a new nonmonotone technique for nonlinear equations [J] . Wang Hua, Gu Chao, Pu Dingguo Optimization: A Journal of Mathematical Programming and Operations Research . 2015,第4a6期

机译：新的非单调技术的非线性方程组的BFGS信赖域方法
4. Nonmonotone AdaptiveTrust-region Method for Nonlinear Equations [C] . CHENG Huifang, QIU Jin yue, ZENG Zhangji International Symposium on Distributed Computing and Applications for Business Engineering and Science . 2008

机译：非线性方程的非单调AdaptiveTrust-区域方法
5. Solving large sparse systems of nonlinear equations and nonlinear least squares problems using tensor methods on sequential and parallel computers*. [D] . Bouaricha, Ali. 1992

机译：在连续和并行计算机上使用张量法来求解非线性方程和非线性最小二乘问题的大型稀疏系统。
6. A modified filter nonmonotone adaptive retrospective trust region method [O] . Xianfeng Ding, Quan Qu, Xinyi Wang 2021

机译：修改过滤器非单调的自适应回顾性信任区域方法
7. A nonmonotone filter trust region method for nonlinear constrained optimization [O] . Su Ke, Pu Dingguo 2009

机译：非线性约束优化的非单调滤波器信赖域方法

A nonmonotone filter trust region method for the system of nonlinear equations

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