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一类Lagrangian对偶问题的零对偶间隙性质及其最优路径的收敛性
  • ISSN号：1007-6093
  • 期刊名称：《运筹学学报》
  • 时间：0
  • 分类：O175.2[理学—数学;理学—基础数学]
  • 作者机构：[1]上海大学数学系,上海200444, [2]曲阜师范大学运筹管理学院,山东273165
  • 相关基金：Project supported by the National Natural Science Foundation （No. 10571106） of China
作者： 刘丙状[1], 王长钰[2]
关键词： 运筹学, 对偶间隙, Lagrangian函数, 收敛性, 最优路径, Operations research, duality gap, Lagrangian function, convergence, optimal path
中文摘要：

针对一般的非线性规划问题，利用某些Lagrange型函数给出了一类Lagrangian对偶问题的一般模型，并证明它与原问题之间存在零对偶间隙．针对具体的一类增广Lagrangian对偶问题以及几类由非线性卷积函数构成的Lagrangian对偶问题，详细讨论了零对偶间隙的存在性．进一步，讨论了在最优路径存在的前提下，最优路径的收敛性质．

英文摘要：

In this paper, we propose a general model of a class of Lagrangian dual problem for the general nonlinear programming problem with respect to some Lagrangetype functions. We obtain that the zero duality gap exists between this class of Lagrangian dual problem and the primal problem. We discuss detailedly the existence of the zero duality gap for a class of augmented Lagrangian problem, and several classes of nonlinear convolution Lagrangian dual problems. Finally, we discuss the convergence of optimal path.

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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