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一个充分下降的有效共轭梯度法

简金宝1,2, 尹江华1, 江羡珍2   

  1. 1. 广西大学数学与信息科学学院, 南宁 530004;
    2. 玉林师范学院数学与信息科学学院, 广西高校复杂系统优化与大数据处理重点实验室, 广西玉林 537000
  • 收稿日期:2014-10-30 出版日期:2015-11-15 发布日期:2015-11-19
  • 通讯作者: 简金宝,E-mail: jianjb@gxu.edu.cn.
  • 基金资助:

    广西自然科学基金(2013GXNSFAA019009,2014GXNSFFA118001);广西高校科研项目(2013YB196);广西高校人才小高地创新团队专项资助.

简金宝, 尹江华, 江羡珍. 一个充分下降的有效共轭梯度法[J]. 计算数学, 2015, 37(4): 415-424.

Jian Jinbao, Yin Jianghua, Jiang Xianzhen. An efficient conjugate gradient method with sufficient descent property[J]. Mathematica Numerica Sinica, 2015, 37(4): 415-424.

An efficient conjugate gradient method with sufficient descent property

Jian Jinbao1,2, Yin Jianghua1, Jiang Xianzhen2   

  1. 1. School of Mathematics and Information Science, Guangxi University, Nanning 530004, China;
    2. School of Mathematics and Information Science, Guangxi Colleges and Universities Key Lab of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, Guangxi, China
  • Received:2014-10-30 Online:2015-11-15 Published:2015-11-19
对于大规模无约束优化问题, 本文提出了一个充分下降的共轭梯度法公式, 并建立相应的算法. 该算法在不依赖于任何线搜索条件下, 每步迭代都能产生一个充分下降方向. 若采用标准Wolfe非精确线搜索求步长, 则在常规假设条件下可获得算法良好的全局收敛性. 最后, 对算法进行大规模数值试验, 并采用Dolan和Moré的性能图对试验效果进行刻画, 结果表明该算法是有效的.
In this paper, a sufficient descent conjugate gradient method is proposed for solving large-scale optimal problems and built the algorithm accordingly. The presented method can generate sufficient descent directions at every iteration depending on no any line search, therefore, the global convergence of the proposed method is proved under the standard Wolfe inexact line search condition. Some elementary numerical experiments are reported, which show that the proposed method is promising.

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