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三项记忆梯度法及其投影算法的收敛性分析
  • ISSN号：1007-6093
  • 期刊名称：《运筹学学报》
  • 时间：0
  • 分类：O221.2[理学—运筹学与控制论;理学—数学]
  • 作者机构：[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
  • 相关基金：This work is supported by National Natural Science Foundation under Grant No.10571106.Acknowledgement The authors want to express their sincere thanks to Professor Wang Changyu for his kindly help.
作者： 李梅霞[1], 刘茜[2], 孙清滢[3]
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, Operations research, Three-term memory gradient method, memory gradient projection method, non-monotone line search, global convergence property
中文摘要：

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．

英文摘要：

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 of f（＊）.

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期刊信息
  • 《运筹学学报》
  • 中国科技核心期刊
  • 主管单位:中国科学技术协会
  • 主办单位:中国运筹学会
  • 主编：胡旭东
  • 地址：上海市上大路99号上海大学期刊社
  • 邮编：200444
  • 邮箱：ort@mail.shu.edu.cn
  • 电话：021-66137605
  • 国际标准刊号：ISSN：1007-6093
  • 国内统一刊号：ISSN：31-1732/O1
  • 邮发代号:4-777
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）
  • 被引量:1362