Iterative Hard Thresholding Methods for $l_0$ Regularized Convex Cone Programming

Zhaosong Lu

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arXiv · 1211.0056

Iterative Hard Thresholding Methods for $l_0$ Regularized Convex Cone Programming

Zhaosong Lu

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Abstract

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 $\epsilon$-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 $\epsilon$-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 minimizer of the problem.

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BibTeX RIS

Zhaosong Lu. 2012-10-31. Iterative Hard Thresholding Methods for $l_0$ Regularized Convex Cone Programming. https://arxiv.org/abs/1211.0056

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