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Fixed point and Bregman iterative methods for matrix rank minimization. (English) Zbl 1221.65146
The authors propose a fixed point continuation algorithm and a Bregman iterative algorithm for solving the linearly constrained nuclear norm minimization problem. The convergence of the fixed point iterative algorithm is established. A Monte-Carlo approximate singular value decomposition procedure is incorporated into the fixed-point continuation algorithm to improve the speed and its ability to recover low-rank matrices. Some numerical results are presented to show the effectively of the proposed algorithm.

65K05 Numerical mathematical programming methods
90C25 Convex programming
90C06 Large-scale problems in mathematical programming
93C41 Control/observation systems with incomplete information
68Q32 Computational learning theory
65C05 Monte Carlo methods
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