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A subspace-accelerated split Bregman method for sparse data recovery with joint l1-type regularizers

14 Dec 2019arXiv:1912.06805links table onlyarchive 2025-07-28

Valentina De Simone, Daniela di Serafino, Marco Viola

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We propose a subspace-accelerated Bregman method for the linearly constrained minimization of functions of the form f(𝐮)+τ₁ 𝐮₁ + τ₂ D 𝐮₁, 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 and learning of predictive models from functional Magnetic Resonance Imaging (fMRI) data, and source detection problems in electroencephalography. The use of D 𝐮₁ 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 on multi-period portfolio selection problems using real datasets show the effectiveness of the proposed method.

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