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

Zhaosong Lu (zhaosong***at***sfu.ca)

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.

Keywords: Sparse approximation, iterative hard thresholding method, $l_0$ regularization, box constrained convex programming, convex cone programming

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Combinatorial Optimization

Citation: Manuscript, Department of Mathematics, Simon Fraser University, Canada

Download: [PDF]

Entry Submitted: 10/30/2012
Entry Accepted: 10/31/2012
Entry Last Modified: 11/01/2012

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