题名 | On convergence of augmented lagrangian method for inverse semi-definite quadratic programming problems |
作者 | |
发表日期 | 2009 |
会议名称 | 13th Latin-Ibero-American Conference on Operations Research |
会议录名称 | Journal of Industrial and Management Optimization
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ISSN | 1547-5816 |
卷号 | 5 |
期号 | 2 |
页码 | 319-339 |
会议日期 | 2006 |
会议地点 | Montevideo, URUGUAY |
摘要 | We consider an inverse problem raised from the semi-definite quadratic programming (SDQP) problem. In the inverse problem, the parameters in the objective function of a given SDQP problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a minimization problem with a positive semi-definite cone constraint and its dual is a linearly positive semi-definite cone constrained semismoothly differentiable (SC) convex programming problem with fewer variables than the original one. We demonstrate the global convergence of the augmented Lagrangian method for the dual problem and prove that the convergence rate of primal iterates, generated by the augmented Lagrange method, is proportional to 1/t, and the rate of multiplier iterates is proportional to 1/√t, where t is the penalty parameter in the augmented Lagrangian. The numerical results are reported to show the effectiveness of the augmented Lagrangian method for solving the inverse semi-definite quadratic programming problem. |
关键词 | Inverse optimization Newton method Quadratic programming Rate of convergence The augmented Lagrangian method The cone of positive semi-definite matrices |
DOI | 10.3934/jimo.2009.5.319 |
URL | 查看来源 |
收录类别 | SCIE |
语种 | 英语English |
WOS研究方向 | Engineering ; Operations Research & Management Science ; Mathematics |
WOS类目 | Engineering, Multidisciplinary ; Operations Research & Management Science ; Mathematics, Interdisciplinary Applications |
WOS记录号 | WOS:000265190800010 |
Scopus入藏号 | 2-s2.0-67649460926 |
引用统计 | |
文献类型 | 会议论文 |
条目标识符 | https://repository.uic.edu.cn/handle/39GCC9TT/6644 |
专题 | 北师香港浸会大学 |
通讯作者 | Xiao, Xiantao |
作者单位 | 1.Department of Applied Mathematics,Dalian University of Technology,Dalian 116024 Liaoning,China 2.BJNU-HKBU United International College,Zhuhai,China |
推荐引用方式 GB/T 7714 | Xiao, Xiantao,Zhang, Liwei,Zhang, Jianzhong. On convergence of augmented lagrangian method for inverse semi-definite quadratic programming problems[C], 2009: 319-339. |
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