On a nonsmooth version of Newton’s method using locally lipschitzian operators

Ioannis K. Argyros

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On a nonsmooth version of Newton’s method using locally lipschitzian operators

机译：在使用局部Lipschitzian算子的牛顿方法的非光滑版本中

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摘要

In this study we are concerned with the problem of approximating a locally unique solution of an operator equation in Banach space using Newton’s method. The differentiability of the operator involved is not assumed. We provide a semilocal convergence analysis utilized to solve problems that were not covered before. Numerical examples are also provided to justify our approach.

机译：在这项研究中，我们关注的是使用牛顿法在Banach空间中逼近算子方程的局部唯一解的问题。不假定涉及的操作者的可区分性。我们提供了一个半局部收敛分析，用于解决以前未涵盖的问题。还提供了数字示例来证明我们的方法是正确的。

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来源
《Rendiconti del Circolo Matematico di Palermo》 |2007年第1期|5-16|共12页
作者
Ioannis K. Argyros;
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作者单位

Department of Mathematical Sciences Cameron University 73505 Lawton OK USA;

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原文格式 PDF
正文语种 eng
中图分类
关键词
65G99; 47H10; 49M15; Newton’s method; Banach space; Banach Lemma on invertible operators; Point-Based-Approximation;

机译：65G99;47H10;49M15;牛顿法;Banach空间;可逆算符上的Banach引理;基于点的逼近;

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1. On Lifting Operators and Regularity of Nonsmooth Newton Methods for Optimal Control Problems of Differential Algebraic Equations [J] . Chen Jinhai, Rabitz Herschel Journal of Optimization Theory and Applications . 2019,第2期

机译：关于差分代数方程最优控制问题的升降算子和规律性
2. On Newton's Method for Solving Equations Containing Nonsmooth Operators [J] . Ioannis K. Argyros, Said Hilout Panamerican mathematical journal . 2013,第1期

机译：牛顿法求解包含非光滑算子的方程
3. On the convergence of Newton's method for a class of nonsmooth operators [J] . Ioannis K. Argyros Journal of Computational and Applied Mathematics . 2007,第1期

机译：一类非光滑算子的牛顿方法的收敛性
4. A smoothing stochastic quasi-newton method for non-lipschitzian stochastic optimization problems [C] . Farzad Yousefian, Angelia Nedić, Uday V. Shanbhag Simulation Conference . 2017

机译：非Lipschitzian随机优化问题的平滑随机拟牛顿法
5. Smooth Quasi-Newton Methods for Nonsmooth Optimization [D] . Guo, Jiayi. 2018

机译：非光滑优化的光滑拟牛顿法
6. REMARKS ON SPECTRA OF OPERATORS ON A LOCALLY CONVEX SPACE [O] . Fumiyuki Maeda 1961

机译：关于局部凸空间上算子谱的备注
7. On the convergence of Newton's method for a class of nonsmooth operators [O] . Argyros Ioannis K. 2007

机译：一类非光滑算子的牛顿方法的收敛性

On a nonsmooth version of Newton’s method using locally lipschitzian operators

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