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| 三项记忆梯度法及其投影算法的收敛性分析 | |
| 引用本文： | 李梅霞,刘茜,孙清滢.三项记忆梯度法及其投影算法的收敛性分析[J].运筹学学报,2007,11(1):23-32. |
| 作者姓名： | 李梅霞 刘茜 孙清滢 |
| 作者单位： | 1. 潍坊学院数学系,潍坊,261061 2. 内蒙古大学应用数学系,呼和浩特,010021 3. 石油大学应用数学系,山东东营,257061 |
| 摘 要： | 对于无约束优化问题,提出了一类新的三项记忆梯度算法．这类算法是在参数满足某些假设的条件下,确定它的取值范围,从而保证三项记忆梯度方向是使目标函数充分下降的方向．在非单调步长搜索下讨论了算法的全局收敛性．为了得到具有更好收敛性质的算法,结合Solodov and Svaiter(2000)中的部分技巧,提出了一种新的记忆梯度投影算法,并证明了该算法在函数伪凸的情况下具有整体收敛性． |
| 关 键 词： | 运筹学 三项记忆梯度算法 忆忆梯度投影算法 非单调步长搜索 全局收敛性 |
| 修稿时间： | 2004-04-13 |
Convergence Property of the Three-term Memory Gradient Method and Its Projection Method |
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| Li Meixia,Liu Qian,Sun Qingying.Convergence Property of the Three-term Memory Gradient Method and Its Projection Method[J].OR Transactions,2007,11(1):23-32. | |
| Authors: | Li Meixia Liu Qian Sun Qingying |
| Institution: | Department of Mathematics, Weifang University, Weifang 261061, China; Department of Applied Mathematics, Inner Mongolia University, Hohhot 010021, China;Department of Applied Mathematics, University of Petroleum, Dongying Shandong 257061, China |
| Abstract: | In this paper, we propose a new kind of three-term memory gradient method for unconstrained optimization problem. We discuss the global convergence property of the method with non-monotone line search technique. At the same time, a new kind of memory gradient projection method is also presented. The convergence property in the sense that the whole sequence of iterates converges to a solution of the problem is proved under no assumption other than pseudo-convexity and continuous differentiability f(·). |
| Keywords: | Operations research Three-term memory gradient method memory gradient projection method non-monotone line search global convergence property |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ | |