Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2012-007 (September 24, 2012)

An Inexact Coordinate Descent Method for the Weighted L1-regularized Convex Optimization Problem
by Xiaoqin Hua, and Nobuo Yamashita

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The purpose of this paper is to propose an inexact coordinate descent (ICD) method for solving the weighted L1-regularized convex optimization problem with a box constraint. The proposed algorithm solves a one dimensional subproblem inexactly at each iteration. We give criteria of the inexactness under which the sequence generated by the proposed method converges to an optimal solution and its convergence rate is at least R-linear without assuming the uniqueness of solutions.