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| 一类新的求解无约束优化问题的记忆梯度法 | |
| 引用本文： | 汤京永,贺国平,董丽.一类新的求解无约束优化问题的记忆梯度法[J].数学杂志,2011,31(2):362-368. |
| 作者姓名： | 汤京永 贺国平 董丽 |
| 作者单位： | 1. 信阳师范学院数学与信息科学学院,河南,信阳,464000;上海交通大学数学系,上海,200240 2. 山东科技大学信息科学与工程学院,山东,青岛,266510 3. 信阳师范学院数学与信息科学学院,河南,信阳,464000 |
| 基金项目： | 国家自然科学基金，山东省自然科学基金，信阳师范学院青年科研基金 |
| 摘 要： | 本文研究了无约束优化问题.利用当前和前面迭代点的信息产生下降方向以及Armijo线性搜索确定步长,得到了一类新的记忆梯度法.在较弱条件下证明了算法具有全局收敛性和线性收敛速率.数值试验表明算法是有效的. |
| 关 键 词： | 无约束优化 记忆梯度法 全局收敛性 线性收敛速率 |
A NEW CLASS OF MEMORY GRADIENT METHODS FOR UNCONSTRAINED OPTIMIZATION PROBLEMS |
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| TANG Jing-yong,HE Guo-ping,DONG Li.A NEW CLASS OF MEMORY GRADIENT METHODS FOR UNCONSTRAINED OPTIMIZATION PROBLEMS[J].Journal of Mathematics,2011,31(2):362-368. | |
| Authors: | TANG Jing-yong HE Guo-ping DONG Li |
| Institution: | TANG Jing-yong~(1,2),HE Guo-ping~3,DONG Li~1 (1.College of Mathematics and Information Science,Xinyang Normal University,Xinyang 464000,China) (2.Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240,China) (3.College of Information Science and Engineering,Shandong University of Science and Technology,Qingdao 266510,China) |
| Abstract: | In this article,the unconstrained optimization problem is concerned.By using the current and previous iterative information and applying Armijo linear search,a new memory gradient method is presented.Meanwhile,we generate a descending direction and deflne the step-size.The global convergence and linear convergence rate are proved under some mild conditions.Numerical experiments show that the new method is efficient in practical computation. |
| Keywords: | unconstrained optimization memory gradient method global convergence linear convergence rate |
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