A penalty method for rank minimization problems in symmetric matrices

Xin Shen () and John E. Mitchell ()
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Xin Shen: Rensselaer Polytechnic Institute
John E. Mitchell: Rensselaer Polytechnic Institute

Computational Optimization and Applications, 2018, vol. 71, issue 2, No 3, 353-380

Abstract: Abstract The problem of minimizing the rank of a symmetric positive semidefinite matrix subject to constraints can be cast equivalently as a semidefinite program with complementarity constraints (SDCMPCC). The formulation requires two positive semidefinite matrices to be complementary. This is a continuous and nonconvex reformulation of the rank minimization problem. We investigate calmness of locally optimal solutions to the SDCMPCC formulation and hence show that any locally optimal solution is a KKT point. We develop a penalty formulation of the problem. We present calmness results for locally optimal solutions to the penalty formulation. We also develop a proximal alternating linearized minimization (PALM) scheme for the penalty formulation, and investigate the incorporation of a momentum term into the algorithm. Computational results are presented.

Keywords: Rank minimization; Penalty methods; Alternating minimization; 90C33; 90C53 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-018-0010-6

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