A Family of Least Change Diagonally Quasi-Newton Methods for Nonlinear Equations

机译：非线性方程组的最小变化对角拟牛顿法

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摘要

A new family of least-change weak-secant methods for solving systems of nonlinear algebraic equations is introduced. This class of methods belongs to that of quasi-Newton family, except for which the approximation to the Jacobian, at each step, is updated by means of a diagonal matrix. The approach underlying such approximation is based upon the commonly used least change updating strategy with the added restriction that full matrices are replaced by diagonal matrices. Using some appropriate matrix norms, some members of this family are introduced. Convergence results are proved, and particular members of the family that seem to be of practical usefulness are also considered.

机译：介绍了一种求解非线性代数方程组的新的最小变化弱割线方法。这类方法属于拟牛顿族的方法，所不同的是，在每一步骤中，通过对角矩阵更新对雅可比方程的近似。这种近似的基础是基于常用的最小变化更新策略，并增加了对角矩阵替换完整矩阵的限制。使用一些适当的矩阵规范，介绍了该族的一些成员。证明了收敛结果，并且还考虑了似乎有用的特定家庭成员。

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来源
《The 8th international conference on optimization: Techniques and Applications》|2010年|315-316|共2页
会议地点 Shanghai(CN)
作者
Wah June Leong; Malik Abu Hassan;
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作者单位

Department of Mathematics,University Putra Malaysia, 43400 Serdang, Malaysia;

Institute for Mathematical Research,University Putra Malaysia, 43400 Serdang, Malaysia;

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会议组织
原文格式 PDF
正文语种 eng
中图分类系统优化;
关键词
nonlinear equations; quasi-Newton methods; weak-secant updates; diagonal approximation;

机译：非线性方程；拟牛顿法；弱割线更新；对角线近似;

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专利

1. A modified quasi-Newton diagonal update algorithm for total variation denoising problems and nonlinear monotone equations with applications in compressive sensing [J] . Zhang Benxin, Zhu Zhibin Numerical linear algebra with applications . 2015,第3期

机译：改进的拟牛顿对角线更新算法，用于总变化降噪和非线性单调方程组及其在压缩传感中的应用
2. Broyden’s quasi-Newton methods for a nonlinear system of equations and unconstrained optimization: a review and open problems [J] . Mehiddin Al-Baali, Emilio Spedicato, Francesca Maggioni Optimization methods & software . 2014,第4a6期

机译：非线性方程组和无约束优化的Broyden拟牛顿法：回顾和开放性问题
3. Recent Applications and Numerical Implementation of Quasi-Newton Methods for Solving Nonlinear Systems of Equations [J] . Rosana Perez, Vera Lucia Rocha Lopes Numerical algorithms . 2004,第2a4期

机译：拟牛顿法求解非线性方程组的最新应用和数值实现
4. A Family of Least Change Diagonally Quasi-Newton Methods for Nonlinear Equations [C] . Wah June Leong, Malik Abu Hassan International conference on optimization: Techniques and Applications . 2010

机译：一个最不改变对角线准牛顿的非线性方程方法的家庭
5. SEQUENTIAL QUADRATIC PROGRAMMING METHODS BASED ON APPROXIMATING A PROJECTED HESSIAN MATRIX (UPDATING METHOD, QUASI-NEWTON, NONLINEAR CONSTRAINTS). [D] . GURWITZ, CHAYA BLEICH. 1986

机译：基于逼近投影Hessian矩阵的顺序二次编程方法（更新方法，拟牛顿法，非线性约束）。
6. A quasi-Newton algorithm for large-scale nonlinear equations [O] . Linghua Huang -1

机译：大型非线性方程的拟牛顿算法
7. DESCENT DIRECTIONS OF QUASI-NEWTON METHODS FOR SYMMETRIC NONLINEAR EQUATIONS∗ [O] . Guang-ze Gu, Dong-hui Li, Liqun Qi, 2016

机译：对称非线性方程拟牛顿方法的下行方向*
8. Quasi-Newton Methods for Large Scale Nonlinear Equations and Constrained Optimization: Progress Report, July 1, 1987-June 30, 1988 [R] . Dennis, J. E. , Tapia, R. A. 1988

机译：大规模非线性方程的拟牛顿方法和约束优化：进展报告，1987年7月1日 - 1988年6月30日

A Family of Least Change Diagonally Quasi-Newton Methods for Nonlinear Equations

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