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山东大学学报(理学版) ›› 2016, Vol. 51 ›› Issue (4): 86-89.doi: 10.6040/j.issn.1671-9352.0.2015.384

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仿射约束矩阵秩最小问题与无约束矩阵秩最小问题的等价性

崔安刚,李海洋*   

  1. 西安工程大学理学院, 陕西 西安 710048
  • 收稿日期:2015-08-04 出版日期:2016-04-20 发布日期:2016-04-08
  • 通讯作者: 李海洋(1975— ),男,博士,教授,研究方向为稀疏信息处理、量子逻辑、格上拓扑学等. E-mail:fplihaiyang@126.com E-mail:cuiangang@163.com
  • 作者简介:崔安刚(1989— ),男,硕士研究生,研究方向为稀疏信息处理. E-mail:cuiangang@163.com
  • 基金资助:
    国家自然科学基金资助项目(11271297);陕西省自然科学基础研究计划(2015JM1012);西安工程大学研究生创新基金资助项目(CX2015012)

Equivalence between the affine matrix rank minimization problem and the unconstrained matrix rank minimization problem

CUI An-gang, LI Hai-yang*   

  1. School of Science, Xian Polytechnic University, Xian 710048, Shaanxi, China
  • Received:2015-08-04 Online:2016-04-20 Published:2016-04-08

摘要: 证明了仿射约束矩阵秩最小问题与无约束矩阵秩最小问题的等价性,即存在λ0>0,对于任意的λ∈(00),无约束矩阵秩最小问题与仿射约束矩阵秩最小问题有相同的最优解。通过求解无约束罚函数矩阵秩最小问题的最优解来近似替代仿射约束矩阵秩最小问题的最优解是可行的。

关键词: 仿射约束矩阵秩最小问题, 无约束罚函数矩阵秩最小问题, 无约束矩阵秩最小问题

Abstract: Equivalence between the affine matrix rank minimization problem and the unconstrained matrix rank minimization problem is proved; i.e., there is a λ0>0 such that, for any λ∈(00), the affine matrix rank minimization problem and the unconstrained matrix rank minimization problem have the same optimal solution. Based on this, it is feasible to use the optimal solution to the unconstrained penalty function matrix rank minimization problem to approximate the optimal solution to the affine matrix rank minimization problem.

Key words: the unconstrained penalty function matrix rank minimization problem, the unconstrained matrix rank minimization problem, the affine matrix rank minimization problem

中图分类号: 

  • O242.2
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