- Iterative Hard Thresholding Methods for $l_0$ Regularized Convex Cone Programming Zhaosong Lu (zhaosongsfu.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: 10/30/2012Entry Accepted: 10/31/2012Entry Last Modified: 11/01/2012Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.