caa a22 4500 445331739 CHVBK 20180317142739.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s10208-011-9084-6 doi (NATIONALLICENCE)springer-10.1007/s10208-011-9084-6 Convergence of Fixed-Point Continuation Algorithms for Matrix Rank Minimization [Elektronische Daten] [Donald Goldfarb, Shiqian Ma] The matrix rank minimization problem has applications in many fields, such as system identification, optimal control, low-dimensional embedding, etc. As this problem is NP-hard in general, its convex relaxation, the nuclear norm minimization problem, is often solved instead. Recently, Ma, Goldfarb and Chen proposed a fixed-point continuation algorithm for solving the nuclear norm minimization problem (Math. Program., doi:10.1007/s10107-009-0306-5, 2009). By incorporating an approximate singular value decomposition technique in this algorithm, the solution to the matrix rank minimization problem is usually obtained. In this paper, we study the convergence/recoverability properties of the fixed-point continuation algorithm and its variants for matrix rank minimization. Heuristics for determining the rank of the matrix when its true rank is not known are also proposed. Some of these algorithms are closely related to greedy algorithms in compressed sensing. Numerical results for these algorithms for solving affinely constrained matrix rank minimization problems are reported. SFoCM, 2011 Matrix rank minimization nationallicence Matrix completion nationallicence Greedy algorithm nationallicence Fixed-point method nationallicence Restricted isometry property nationallicence Singular value decomposition nationallicence Goldfarb Donald Department of Industrial Engineering and Operations Research, Columbia University, 10027, New York, NY, USA aut Ma Shiqian Department of Industrial Engineering and Operations Research, Columbia University, 10027, New York, NY, USA aut Foundations of Computational Mathematics Springer-Verlag 11/2(2011-04-01), 183-210 1615-3375 11:2<183 2011 11 10208 https://doi.org/10.1007/s10208-011-9084-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10208-011-9084-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Goldfarb Donald Department of Industrial Engineering and Operations Research, Columbia University, 10027, New York, NY, USA aut NATIONALLICENCE 700 1- Ma Shiqian Department of Industrial Engineering and Operations Research, Columbia University, 10027, New York, NY, USA aut NATIONALLICENCE 773 0- Foundations of Computational Mathematics Springer-Verlag 11/2(2011-04-01), 183-210 1615-3375 11:2<183 2011 11 10208 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer