JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (4): 86-89.doi: 10.6040/j.issn.1671-9352.0.2015.384

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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

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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∈(0,λ0), 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

CLC Number: 

  • O242.2
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