Valentina De Simone,
Daniela di Serafino,
Marco Viola
S. 406 - 425
doi:
10.1553/etna_vol53s406
Verlag der Österreichischen Akademie der Wissenschaften
doi:
10.1553/etna_vol53s406
Abstract:
We propose a subspace-accelerated Bregman method for the linearly constrained minimization of functions of the form$ f(\mathbf u) + \tau_1\,\|\mathbf u\|_1 + \tau_2\,\|D\,\mathbf 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 widevariety 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 $\|D\,\mathbf u\|_1$is aimed at encouraging structured sparsity in the solution. The subspaces where the acceleration is performed are selected so that the restrictionof the objective function is a smooth function in a neighborhood of the current iterate. Numerical experiments for multi-period portfolioselection problems using real data sets show the effectiveness of the proposed method.
split Bregman method, subspace acceleration, joint $\ell_1$-type regularizers, multi-period portfolio optimization
Published Online:
2020/05/20 14:04:33
Object Identifier:
0xc1aa5576 0x003b85a4
Rights:All rights reserved.For questions regarding copyright and copies please contact us by email.
Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.
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