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.

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

Valentina De Simone;Daniela di Serafino
;
Marco Viola
2020

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 || 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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11591/429928
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? ND
social impact