| 一个新的带误差项的记忆梯度算法 |
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| 引用本文： | 孙清滢,谷亚丽,王长钰. 一个新的带误差项的记忆梯度算法[J]. 工程数学学报, 2007, 24(5): 813-818 |
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| 作者姓名： | 孙清滢 谷亚丽 王长钰 |
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| 作者单位： | 中国石油大学数学与计算科学学院,东营,257061;曲阜师范大学(日照校区)运筹与管理学院,日照,276826 |
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| 基金项目： | 国家自然科学基金(10571106)． |
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| 摘 要： | 对无约束规划问题,本文提出了结合Armijo步长搜索规则的一类带误差项的记忆梯度求解算法,并在目标函数的梯度一致连续的条件下,证明了算法的全局收敛性。同时给出带误差项的结合拟-Newton方程的记忆梯度算法。数值例子表明算法是有效的。
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| 关 键 词： | 无约束最优化 记忆梯度法 广义Armijo步长搜索规则 收敛 |
| 文章编号： | 1005-3085（2007）05-0813-06 |
| 修稿时间： | 2005-12-08 |
A New Memory Gradient Method with Errors |
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| SUN Qing-ying,GU Ya-li,WANG Chang-yu. A New Memory Gradient Method with Errors[J]. Chinese Journal of Engineering Mathematics, 2007, 24(5): 813-818 |
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| Authors: | SUN Qing-ying GU Ya-li WANG Chang-yu |
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| Affiliation: | 1. School of Mathematics and Computational Sciences, China University of Petroleum, Dongying 257061; 2. College of Operations Research and Management, Qufu Normal University (Rizhao Campus |
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| Abstract: | We consider the convergence properties of a new memory gradient method with errors and Armijo step size rule for unconstrained optimization problem,under the assumption that the gradient of the function is uniformly continuous.Combining the quasi-Newton equation with our new method, quasi-Newton method with errors is modified to achieve the global convergence property.Numerical results show that the new algorithms are efficient. |
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| Keywords: | unconstrained optimization memory gradient method Armijo step size rule convergence |
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