A trust-region method with improved adaptive radius for systems of nonlinear equations

被引：0
作者：
Hamid Esmaeili
Morteza Kimiaei
机构：
[1] Bu-Ali Sina University,Department of Mathematics
[2] Islamic Azad University,Department of Mathematics, Asadabad Branch
来源：
Mathematical Methods of Operations Research | 2016年 / 83卷
关键词：
Nonlinear equation; Trust region algorithm; Adaptive radius; Theoretical convergence; 90C30; 93E24; 34A34;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this study, a new adaptive trust-region strategy is presented to solve nonlinear systems. More specifically, we propose a new method leading to produce a smaller trust-region radius close to the optimizer and a larger trust-region radius far away from the optimizer. Accordingly, it can lead to a smaller step-size close to the optimizer and a larger one far away from the optimizer. The new strategy includes a convex combination of the maximum norm of function value of some preceding successful iterates and the current norm of function value. The global convergence of the proposed approach is established while the local q-quadratic convergence rate is proved under local error bound condition, which is weaker than the nonsingularity. Numerical results of the proposed algorithm are also reported.
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页码：109 / 125
页数：16
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