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Iterative hard thresholding methods for l0 regularized convex cone programming
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Journal Article
Iterative hard thresholding methods for l0 regularized convex cone programming
2014
Overview
In this paper we consider
l
0
regularized convex cone programming problems. In particular, we first propose an iterative hard thresholding (IHT) method and its variant for solving
l
0
regularized box constrained convex programming. We show that the sequence generated by these methods converges to a local minimizer. Also, we establish the iteration complexity of the IHT method for finding an
ϵ
-local-optimal solution. We then propose a method for solving
l
0
regularized convex cone programming by applying the IHT method to its quadratic penalty relaxation and establish its iteration complexity for finding an
ϵ
-approximate local minimizer. Finally, we propose a variant of this method in which the associated penalty parameter is dynamically updated, and show that every accumulation point is a local izer of the problem.
Publisher
Springer Berlin Heidelberg
