Abstract
© 2014, Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society. We introduce a partial proximal point algorithm for solving nuclear norm regularized matrix least squares problems with equality and inequality constraints. The inner subproblems, reformulated as a system of semismooth equations, are solved by an inexact smoothing Newton method, which is proved to be quadratically convergent under a constraint non-degeneracy condition, together with the strong semi-smoothness property of the singular value thresholding operator. Numerical experiments on a variety of problems including those arising from low-rank approximations of transition matrices show that our algorithm is efficient and robust.
Original language | English |
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Pages (from-to) | 281-325 |
Number of pages | 45 |
Journal | Mathematical Programming Computation |
Volume | 6 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Sept 2014 |
Externally published | Yes |
Keywords
- 65F10
- 90C06
- 90C22
- 90C25
ASJC Scopus subject areas
- Theoretical Computer Science
- Software