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

Valentina De Simone (valentina.desimone***at***unicampania.it)
Daniela di Serafino (daniela.diserafino***at***unicampania.it)
Marco Viola (marco.viola***at***unicampania.it)

Abstract: 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 ||D*u||_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 and learning of predictive models from functional Magnetic Resonance Imaging (fMRI) data, and source detection problems in electroencephalography. The use of ||D*u||_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 on multi-period portfolio selection problems using real datasets show the effectiveness of the proposed method.

Keywords: split Bregman method, subspace acceleration, joint l1-type regularizers, multi-period portfolio optimization.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 3: Applications -- OR and Management Sciences (Finance and Economics )

Citation:

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Entry Submitted: 12/13/2019
Entry Accepted: 12/13/2019
Entry Last Modified: 03/23/2020

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