Solving the L1 regularized least square problem via a box-constrained smooth minimization.

In this paper, an equivalent smooth minimization for L1 regularized least square problem is proposed. The proposed problem is a convex box-constrained smooth minimization which allows applying fast optimization methods to find its solution. Further, it is investigated that property the dual of dual is primal holds for L1 regularized least square problem. A solver for smooth problem is proposed, and its affinity to proximal gradient is shown. Finally, experiments on L1 and total variation regularized problems are performed, and corresponding results are reported.