A SUBSPACE-ACCELERATED SPLIT BREGMAN METHOD FOR SPARSE DATA RECOVERY WITH JOINT L1-TYPE REGULARIZERS

We propose a subspace-accelerated Bregman method for the linearly constrained minimization of functions of the form f (u) + tau_1 ||u ||_1 + tau_2 || Du ||_1, where f is a smooth convex function and D represents a linear operator, e.g., a finite difference operator, as in anisotropic total variation and fused lasso regularizations. Problems of this type arise in a wide variety of applications, including portfolio optimization, learning of predictive models from functional magnetic resonance imaging (fMRI) data, and source detection problems in electroencephalography. The use of || Du ||_1 is aimed at encouraging structured sparsity in the solution. The subspaces where the acceleration is performed are selected so that the restriction of the objective function is a smooth function in a neighborhood of the current iterate. Numerical experiments for multi-period portfolio selection problems using real data sets show the effectiveness of the proposed method.