| 一类新的具有充分下降条件和强收敛性的共轭梯度法 |
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| 引用本文： | 董晓亮,何郁波,孔翔宇,李卫军.一类新的具有充分下降条件和强收敛性的共轭梯度法[J].数学杂志,2017,37(2):231-238. |
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| 作者姓名： | 董晓亮 何郁波 孔翔宇 李卫军 |
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| 作者单位： | 北方民族大学数学与信息学院, 宁夏 银川 750021;怀化学院数学与应用数学系, 湖南 怀化 418008,北方民族大学网络信息技术中心, 宁夏 银川 750021,北方民族大学数学与信息学院, 宁夏 银川 750021,北方民族大学数学与信息学院, 宁夏 银川 750021 |
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| 基金项目： | Supported by National Natural Science Foundation of China (11601012; 11661002); Ningxia Natural Science Foundation (NZ13095; NZ16093); Scientiflc Research Foundation of the Higher Education Institutions of Ningxia (NGY2016134); Beifang University of Nationalities Foundation (2016SXKY06; 2014XBZ09; 2014XBZ01; 2013XYZ028). |
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| 摘 要： | 本文研究了求解无约束优化问题的WYL共轭梯度法.利用修正迭代格式，得到了算法在每步迭代能产生不依赖于搜索条件的充分下降方向.同时，在原算法中关于Wolfe条件中参数去掉的情况下，获得了本文算法是强收敛的.数值实验说明本文算法可以有效求解测试问题.
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| 关 键 词： | 共轭梯度法 充分下降条件 强收敛性 Wolfe搜索 |
| 收稿时间： | 2014/5/2 0:00:00 |
| 修稿时间： | 2015/3/16 0:00:00 |
A NEW CONJUGATE GRADIENT METHOD WITH STRONGLY GLOBAL CONVERGENCE AND SUFFICIENT DESCENT CONDITION |
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| DONG Xiao-liang,HE Yu-bo,KONG Xiang-yu and LI Wei-jun.A NEW CONJUGATE GRADIENT METHOD WITH STRONGLY GLOBAL CONVERGENCE AND SUFFICIENT DESCENT CONDITION[J].Journal of Mathematics,2017,37(2):231-238. |
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| Authors: | DONG Xiao-liang HE Yu-bo KONG Xiang-yu and LI Wei-jun |
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| Institution: | School of Mathematics and Information, Beifang University of Nationalities, Yinchuan, 710021, China;Department of Mathematics and Application Mathematics, Huaihua University, Huaihua, 418008, China,Network Information Technology Center, Beifang University of Nationalities, Yinchuan, 710021, China,School of Mathematics and Information, Beifang University of Nationalities, Yinchuan, 710021, China and School of Mathematics and Information, Beifang University of Nationalities, Yinchuan, 710021, China |
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| Abstract: | In this paper,we study the WYL conjugate gradient method for unconstrained optimization problems.By making use of the modified iterative scheme,the sufficient descent conditions are satisfied at each iteration independent of the line search used.Also,by removing the original restriction on the parameter of the Wolfe conditions,we establish the strongly global convergence property for the general function.Numerical results illustrate that our method is efficient for the test problems. |
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| Keywords: | conjugate gradient method sufficient descent condition strongly global convergence Wolfe line search |
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