Solving the L1 regularized least square problem via a box-constrained smooth minimization
This work addresses optimization challenges in sparse regression and image processing, but it appears incremental as it builds on existing proximal gradient methods.
The paper tackles the L1 regularized least square problem by proposing an equivalent smooth, convex box-constrained minimization, enabling the use of fast optimization methods. Experiments on L1 and total variation regularized problems report results, though no concrete numbers are provided.
In this paper, an equivalent smooth minimization for the 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 the property "the dual of dual is primal" holds for the L1 regularized least square problem. A solver for the smooth problem is proposed, and its affinity to the proximal gradient is shown. Finally, the experiments on L1 and total variation regularized problems are performed, and the corresponding results are reported.