  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.

Optimization and Control;Machine Learning;Numerical Analysis;Computation;Machine Learning