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解凸约束非线性单调方程组的无导数谱PRP投影算法

刘金魁   

  1. 非线性科学与系统结构重点实验室, 重庆三峡学院, 重庆万州 404100
  • 收稿日期:2015-02-06 出版日期:2016-04-15 发布日期:2016-05-13
  • 基金资助:

    东南大学高校基本科研业务费专项资金,重庆市教委科学技术研究项目(KJ1501003),重庆三峡学院重点项目(14ZD-14).

刘金魁. 解凸约束非线性单调方程组的无导数谱PRP投影算法[J]. 计算数学, 2016, 38(2): 113-124.

Liu Jinkui. DERIVATIVE-FREE SPECTRAL PRP PROJECTION METHOD FOR SOLVING NONLINEAR MONOTONE EQUATIONS WITH CONVEX CONSTRAINTS[J]. Mathematica Numerica Sinica, 2016, 38(2): 113-124.

DERIVATIVE-FREE SPECTRAL PRP PROJECTION METHOD FOR SOLVING NONLINEAR MONOTONE EQUATIONS WITH CONVEX CONSTRAINTS

Liu Jinkui   

  1. Key Laboratory for Nonlinear Science and System Structure, Chongqing Three Gorges University, Wanzhou 404100, Chongqing, China
  • Received:2015-02-06 Online:2016-04-15 Published:2016-05-13
本文在著名PRP共轭梯度算法的基础上研究了一种无导数谱PRP投影算法,并证明了算法在求解带有凸约束条件的非线性单调方程组问题的全局收敛性.由于无导数和储存量小的特性,它更适应于求解大规模非光滑的非线性单调方程组问题.数值试验表明,新算法对给定的测试问题是有效的和稳定的.
In this paper, based on the famous PRP conjugate gradient method, a derivative-free spectral PRP projection method is proposed for solving nonlinear monotone equations with convex constraints. The global convergence of the proposed method is also established with some suitable conditions. Due to the derivative-free feature and lower storage requirement, the proposed method is very suitable to solve large-scale non-smooth nonlinear monotone equations. Numerical experiments show that the proposed method is efficient and robust.

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