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Lie群上的最速下降算法
  • ISSN号：1005-3085
  • 期刊名称：《工程数学学报》
  • 时间：0
  • 分类：O152.5[理学—数学;理学—基础数学]
  • 作者机构：[1]合作民族师范专科学校数学系,甘肃合作747000
  • 相关基金：国家自然科学基金项目（10531030）
作者： 夏跃华[1], 席进华[1], 贺志朋[1]
关键词： LIE群, LIE代数, 下降方向, 收敛, Lie group, Lie algebra, descent direction , convengence
中文摘要：

通过对Lie群及其Lie代数的基本性质及特殊结构的分析，提出了求解一般Lie群上优化问题的最速下降算法，并对算法的收敛性作了一定的分析．得到了该算法全局收敛的两个充分条件，并在一般框架下证明了该算法至少线性收敛．通过上Riernann质心的计算问题，证明该算法可行有效．

英文摘要：

Through analyzing special properties and structures of Lie group and its Lie algebra, a new steepest descent algorithm on Lie groups is developed. The convergence of the proposed algorithm is analyzed and achieve two sufficient conditions for the global convergence. Moreover, this paper proves that this algorithm is at least linearly convergent under the general framework. In order to show the feasibility and validity, the spacial rotation group is selected as the experimental subject.

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期刊信息
  • 《工程数学学报》
  • 北大核心期刊（2011版）
  • 主管单位:教育部
  • 主办单位:西安交通大学
  • 主编：李大潜
  • 地址：西宁市咸宁西路28号西安交通大学数学与统计学院
  • 邮编：710049
  • 邮箱：jgsx@mail.xjtu.edu.cn
  • 电话：029-82667877
  • 国际标准刊号：ISSN：1005-3085
  • 国内统一刊号：ISSN：61-1269/O1
  • 邮发代号:
  • 获奖情况:
  • 《中文核心期刊要目总览》核心期刊,《中国科学引文数据库》核心期刊,《中国数学文摘》核心期刊,陕西省优秀科技期刊
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,荷兰文摘与引文数据库,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（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:6741