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| 一类新的多步曲线搜索下的超记忆梯度法 | |
| 引用本文： | 汤京永,贺国平,董丽.一类新的多步曲线搜索下的超记忆梯度法[J].应用数学学报,2011,34(2). |
| 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,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,青岛,2665103 3. 信阳师范学院数学与信息科学学院,信阳,464000 |
| 基金项目： | 国家自然科学基金，山东省自然科学基金，高等学校博士学科点专项科研基金 |
| 摘 要： | 研究一类新的求解无约束优化问题的超记忆梯度法,分析了算法的全局收敛性和线性收敛速率.算法利用一种多步曲线搜索准则产生新的迭代点,在每步迭代时同时确定下降方向和步长,并且不用计算和存储矩阵,适于求解大规模优化问题.数值试验表明算法是有效的. |
| 关 键 词： | 无约束优化 曲线搜索 全局收敛 线性收敛速率 |
A New Class of Supermemory Gradient Methods with Multi-step Curve Search Rule |
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| TANG JINGYONG,HE GUOPING,DONG LI.A New Class of Supermemory Gradient Methods with Multi-step Curve Search Rule[J].Acta Mathematicae Applicatae Sinica,2011,34(2). | |
| Authors: | TANG JINGYONG HE GUOPING DONG LI |
| Institution: | TANG JINGYONG (College of Mathematics and Information Science,Xinyang Normal University,Xinyang 464000) (Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240) HE GUOPING (College of Information Science and Engineering,Shandong University of Science and Technology,Qingdao 266510) DONG LI (College of Mathematics and Information Science,Xinyang 464000) |
| Abstract: | The paper presents a new class of supermemory gradient methods for unconstrained optimization problems,and analyzes its global convergence and linear convergence rate.The algorithm generates new iterative points by means of a multi-step curve search rule.The search direction and the stepsize are determined simultaneously at each iteration of the new algorithm.It avoids the computation and storage of some matrices and is suitable to solve large scale optimization problems.Numerical results show that the new ... |
| Keywords: | unconstrained optimization curve search global convergence linear convergence rate |
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