Abstract
In this paper we consider general rank minimization problems with rank appearing either in the objective function or as a constraint. We first establish that a class of special rank minimization problems has closed-form solutions. Using this result, we then propose penalty decomposition (PD) methods for general rank minimization problems in which each subproblem is solved by a block coordinate descent method. Under some suitable assumptions, we show that any accumulation point of the sequence generated by the PD methods satisfies the first-order optimality conditions of a nonlinear reformulation of the problems. Finally, we test the performance of our methods by applying them to the matrix completion and nearest low-rank correlation matrix problems. The computational results demonstrate that our methods are generally comparable or superior to the existing methods in terms of solution quality.
Original language | English (US) |
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Pages (from-to) | 531-558 |
Number of pages | 28 |
Journal | Optimization Methods and Software |
Volume | 30 |
Issue number | 3 |
DOIs | |
State | Published - May 4 2015 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2014 Taylor & Francis.
Keywords
- matrix completion
- nearest low-rank correlation matrix
- penalty decomposition methods
- rank minimization