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非线性优化修正Frisch函数方法的乘子映射
  • ISSN号：1007-6093
  • 期刊名称：《运筹学学报》
  • 时间：0
  • 分类：O224[理学—运筹学与控制论;理学—数学] O174[理学—数学;理学—基础数学]
  • 作者机构：[1]呼伦贝尔学院数学系,黑龙江海拉尔021008, [2]大连理工大学数学科学学院,辽宁大连116024
  • 相关基金：The research is also supported by the National Natural Science Foundation of China under project grant No.10771026.
作者： 孔德宝[1], 张立卫[2]
关键词： 运筹学, 修正Frisch函数方法, 非线性优化, 乘子映射, 收敛率, Operations research, the modified Frisch function method, nonlinear optimization, multiplier mapping, rate of convergence
中文摘要：

对于同时含有等式与不等式约束的非线性优化问题的修正Frisch函数方法，给出其乘子映射和解映射的导数的估计。将得到的估计用于建立修正Frisch函数方法的线性收敛速率。在线性无关的约束规范，严格互补条件和二阶充分性条件成立的前提下，证得该收敛率与1／c成正比。本文的收敛性分析依赖于矩阵的奇异值分解，其方法可以用来分析其他的修正Lagrange方法。

英文摘要：

We estimate the derivatives of the multiplier mapping and the solution mapping of the modified Frisch function method for nonlinear optimization problems with both equality and inequality constraints. The estimates are used to establish the linear rate of convergence of the the modified Frisch function method, which is proportionalto 1/c with the penalty parameter c exceeding a threshold ^-c〉 0, under the linear independence constraint qualification, the strict complementarity condition and the second order sufficient condition. The analysis is based on the singular value decompositions of matrices and the methodology in this paper can be used to analyze other modified Lagrange methods.

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非凸半定规划与二阶锥约束优化的算法研究及应用
期刊论文 41 著作 2
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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:
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  • 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