2019/12/14 by Valentina De Simone, De Simone, Valentina, Daniela di Serafino +3
Engineering · Mathematics · #65K05 #90C25 #FOS: Mathematics #G.1.6 #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1912.06805
openalex publication_date 2019/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a subspace-accelerated Bregman method for the linearly constrained\nminimization of functions of the form f(\u)+\τ1 \‖\u\‖1 +\n\τ2 \‖D ,\u\‖1, where f is a smooth convex function and D\nrepresents a linear operator, e.g. a finite difference operator, as in\nanisotropic Total Variation and fused-lasso regularizations. Problems of this\ntype arise in a wide variety of applications, including portfolio optimization\nand learning of predictive models from functional Magnetic Resonance Imaging\n(fMRI) data, and source detection problems in electroencephalography. The use\nof \‖D ,\u\‖1 is aimed at encouraging structured sparsity in the\nsolution. The subspaces where the acceleration is performed are selected so\nthat the restriction of the objective function is a smooth function in a\nneighborhood of the current iterate. Numerical experiments on multi-period\nportfolio selection problems using real datasets show the effectiveness of the\nproposed method.\n