Optimization Online


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 )


Download: [PDF]

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

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society