Iterative Hard Thresholding Methods for l_0 Regularized Convex Cone Programming
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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 minimizer of the problem.
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