Convergence analysis of the over-relaxed proximal point algorithms with errors for generalized nonlinear random operator equations

Cai L.; Lan H.-Y.

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Convergence analysis of the over-relaxed proximal point algorithms with errors for generalized nonlinear random operator equations

机译：广义非线性随机算子方程带误差的过度松弛近点算法的收敛性分析

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The purpose of this paper is to introduce and study the over-relaxed proximal point algorithms with errors for generalized nonlinear random operator equations with H-maximal monotonicity framework. Further, by using the generalized proximal operator technique associated with the H-maximal monotone operators, we discuss the approximation solvability of generalized nonlinear random operator equations in Hilbert spaces and the convergence analysis of iterative sequences generated by the over-relaxed proximal point algorithms with errors under some suit conditions, which generalize and improve the the over-relaxed proximal point algorithms due to Verma [R.U. Verma, The over-relaxed proximal point algorithm based on H-maximal monotonicity design and applications, Computers and Mathematics with Applications 55 (2008) 2673-2679].

机译：本文的目的是介绍和研究具有H-极大单调性框架的广义非线性随机算子方程的带误差的过度松弛近点算法。此外，通过使用与H-极大单调算子相关的广义近邻算子技术，我们讨论了希尔伯特空间中广义非线性随机算子方程的逼近可解性以及过度松弛的近点算法产生的带有误差的迭代序列的收敛性分析。在某些合适的条件下，归纳和改进了Verma [RU Verma，基于H极大单调性的过松弛近端点算法设计和应用，《计算机与数学及其应用》 55（2008）2673-2679]。

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《Journal of computational analysis and applications》 |2013年第7期|共10页
作者
Cai L.; Lan H.-Y.;
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正文语种 eng
中图分类应用数学;
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Convergence analysis; Generalized nonlinear random operator equation; Generalized proximal operator technique; H-maximal monotonicity; Over-relaxed proximal point algorithms with errors;

机译：收敛性分析;广义非线性随机算子方程;广义近邻算子技术;H-极大单调性;有误差的过松弛近点算法;

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1. Convergence analysis of the over-relaxed proximal point algorithms with errors for generalized nonlinear random operator equations [J] . Cai L., Lan H.-Y. Journal of computational analysis and applications . 2013,第7期

机译：广义非线性随机算子方程带误差的过度松弛近点算法的收敛性分析
2. On Over-Relaxed Proximal Point Algorithms for Generalized Nonlinear Operator Equation with (A,η,m)-Monotonicity Framework [J] . Fang Li International Journal of Modern Nonlinear Theory and Application . 2012,第3期

机译：具有（A，η，m）-单调性框架的广义非线性算子方程的过度松弛近点算法
3. A remark on significant convergence rates for the generalized over-relaxed proximal point algorithms [J] . Verma R.U. Advances in nonlinear variational inequalities . 2013,第1期

机译：关于广义过松弛近端点算法的显着收敛速度的评论
4. An Over-Relaxed (A, η, m)-Proximal Point Algorithm for System of Nonlinear Fuzzy-Set Valued Operator Equation Frameworks and Fixed Point Problems [C] . Heng-you Lan, Xiao Wang, Tingjian Xiong, Integrated uncertainty in knowledge modelling and decision making . 2011

机译：非线性模糊集值算子方程框架和不动点问题的系统的过度松弛（A，η，m）-近点算法
5. TWO GENERALIZED CONCEPTS OF ORDINARY DIFFERENTIAL EQUATIONS: M(0)-STABILITY AND MIXED MONOTONE OPERATORS. [D] . MOORE, JANE C. 1983

机译：普通微分方程的两个广义概念：M（0）-稳定性和混合单调算子。
6. Convergence Analysis and Numerical Study of a Fixed-Point Iterative Method for Solving Systems of Nonlinear Equations [O] . Na Huang, Changfeng Ma -1

机译：求解非线性方程组的不动点迭代法的收敛性分析和数值研究
7. Graph-convergent analysis of over-relaxed (A,η,m)-proximal point iterative methods with errors for general nonlinear operator equations [O] . Heng-you Lan 2014

机译：一般非线性算子方程的带误差的过松弛（A，η，m）-近点迭代方法的图收敛分析

Convergence analysis of the over-relaxed proximal point algorithms with errors for generalized nonlinear random operator equations

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