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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 andits variant for solving $l_0$ regularized box constrained convex programming.We show that the sequence generated by these methods converges to a localminimizer. Also, we establish the iteration complexity of the IHT method forfinding an $\epsilon$-local-optimal solution. We then propose a method forsolving $l_0$ regularized convex cone programming by applying the IHT method toits quadratic penalty relaxation and establish its iteration complexity forfinding an $\epsilon$-approximate local minimizer. Finally, we propose avariant of this method in which the associated penalty parameter is dynamicallyupdated, and show that every accumulation point is a local minimizer of theproblem.

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