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.