| 李 景，景书杰，牛海峰.一类改进的谱共轭梯度法[J].海南师范大学学报自科版,2021,34(3):269-273 |
| 一类改进的谱共轭梯度法 |
| A Kind of Improved Spectral Conjugate Gradient Method |
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| DOI：10.12051/j.issn.1674-4942.2021.03.003 |
| 中文关键词: 无约束优化 谱共轭梯度法 Wolfe线搜索 全局收敛性 |
| 英文关键词: unconstrained optimization spectral conjugate gradient method Wolfe line search global convergence |
| 基金项目:国家自然科学基金项目（U1504104） |
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| 摘要点击次数: 949 |
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| 中文摘要: |
| 谱共轭梯度法是在共轭梯度法基础上发展起来的新型算法，其特点是有两个方向控制
参数，是解决大规模无约束优化问题的有效方法，也是优化工作者研究的热点。本文基于已有的
非线性谱共轭梯度法提出了一类新的谱共轭梯度法，利用新构造的共轭方向调控参数βk构建了新
的算法，并保证了该算法在任何线搜索下都满足共轭条件，进而在迭代时产生的搜索方向都是充
分下降的。在Wolfe线搜索下，该方法的全局收敛性得以验证。 |
| 英文摘要: |
| The spectral conjugate gradient method is a new algorithm developed on the basis of the conjugate gradient
method. Its characteristic is to control parameters in two directions. It is an effective method to solve large-scale uncon⁃
strained optimization problems and a hot topic for optimization workers. In this paper, based on the existing nonlinear spec⁃
tral conjugate gradient method, a new class of spectral conjugate gradient method was proposed. Using the newly construct⁃
ed conjugate direction control parameter βk , a new algorithm was constructed, and it is guaranteed that the algorithm meets
the conjugate condition under any line search, and the search direction generated during iteration is fully reduced. Under
the Wolfe line search, the global convergence of the method was verified. |
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