| 结合Armijo步长搜索的一类新记忆梯度算法及其收敛特征 |
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| 引用本文： | 孙清滢,刘新海.结合Armijo步长搜索的一类新记忆梯度算法及其收敛特征[J].中国石油大学学报(自然科学版),2003,27(5). |
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| 作者姓名： | 孙清滢 刘新海 |
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| 作者单位： | 石油大学应用数学系,山东,东营,257061 |
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| 摘 要： | 对于求解无约束规划的共轭梯度算法中的共轭梯度方向参数 ,给定一个假设条件 ,确定它的一个取值范围 ,以保证搜索方向是目标函数的充分下降方向 ,由此提出了一类新的记忆梯度算法。在去掉迭代点列有界和Armijo步长搜索下 ,讨论了算法的全局收敛性 ,同时给出了结合FR、PR、HS共轭梯度算法的修正形式。数值实验表明 ,新算法比Armijo步长搜索下的FR、PR、HS共轭梯度法更稳定、更有效。
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| 关 键 词： | 非线性规划 共轭梯度 Armijo步长搜索 收敛性 数值实验 |
Global convergence results for a new memory gradient method with generalized Armijo step size rule |
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| SUN Qing-ying and LIU Xin-hai.Global convergence results for a new memory gradient method with generalized Armijo step size rule[J].Journal of China University of Petroleum,2003,27(5). |
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| Authors: | SUN Qing-ying and LIU Xin-hai |
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| Institution: | SUN Qing-ying and LIU Xin-hai. Department of Applied Mathematics in the University of Petroleum,China,Dongying 257061 |
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| Abstract: | An assumption condition was given on the scalar to ensure that the conjugate gradient direction be a sufficient descent. A new memory gradient method was presented. The convergence properties of the new memory gradient method with Armijo step size rule were discussed without assuming that the sequence of iterates is bounded. Numerical results show that the algorithm is efficient in comparison with FR, PR, HS conjugate gradient methods with Armijo step size rule. |
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| Keywords: | non-linear programming memory gradient method Armijo step size rule convergence numerical calculation experiment |
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