| 无线搜索共轭梯度法的全局收敛性 |
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| 引用本文： | 陈翠玲,陈玉. 无线搜索共轭梯度法的全局收敛性[J]. 数学研究及应用, 2018, 38(5): 541-550 |
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| 作者姓名： | 陈翠玲 陈玉 |
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| 作者单位： | 广西师范大学数学与统计学院, 广西 桂林 541004; 匹兹堡大学计算与信息学院, 美国宾州 匹兹堡 15238,广西师范大学数学与统计学院, 广西 桂林 541004 |
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| 摘 要： |
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| 收稿时间： | 2017-10-27 |
| 修稿时间： | 2018-06-06 |
Global Convergence of Conjugate Gradient Methods without Line Search |
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| Cuiling CHEN and Yu CHEN. Global Convergence of Conjugate Gradient Methods without Line Search[J]. Journal of Mathematical Research with Applications, 2018, 38(5): 541-550 |
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| Authors: | Cuiling CHEN and Yu CHEN |
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| Abstract: | In this paper, a new steplength formula is proposed for unconstrained optimization,which can determine the step-size only by one step and avoids the line search step. Global convergence of the five well-known conjugate gradient methods with this formula is analyzed,and the corresponding results are as follows:(1) The DY method globally converges for a strongly convex LC~1 objective function;(2) The CD method, the FR method, the PRP method and the LS method globally converge for a general, not necessarily convex, LC~1 objective function. |
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| Keywords: | unconstrained optimization conjugate gradient method line search global convergence |
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