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- Title
Two-stage convex relaxation approach to low-rank and sparsity regularized least squares loss.
- Authors
Han, Le; Bi, Shujun
- Abstract
In this paper we consider the rank and zero norm regularized least squares loss minimization problem with a spectral norm ball constraint. For this class of NP-hard optimization problems, we propose a two-stage convex relaxation approach by majorizing some suitable locally Lipschitz continuous surrogates. Furthermore, the Frobenius norm error bound for the optimal solution of each stage is characterized and the theoretical guarantee is established for the two-stage convex relaxation approach by showing that the error bound of the first stage convex relaxation (i.e., the nuclear norm and $$\ell _1$$ -norm regularized minimization problem), can be reduced much by the second stage convex relaxation under a suitable restricted eigenvalue condition. Also, we verify the efficiency of the proposed approach by applying it to some random test problems and some real problems.
- Subjects
NP-hard problems; CONVEX functions; LEAST squares; PROBLEM solving; LIPSCHITZ spaces; GLOBAL optimization
- Publication
Journal of Global Optimization, 2018, Vol 70, Issue 1, p71
- ISSN
0925-5001
- Publication type
Article
- DOI
10.1007/s10898-017-0573-2