On efficiently solving the subproblems of a level-set method for fused lasso problems

Abstract

In applying the level-set method developed in [Van den Berg and Friedlander, SIAM J. on Scientific Computing, 31 (2008), pp.~890--912 and SIAM J. on Optimization, 21 (2011), pp.~1201--1229] to solve the fused lasso problems, one needs to solve a sequence of regularized least squares subproblems. In order to make the level-set method practical, we develop a highly efficient inexact semismooth Newton based augmented Lagrangian method for solving these subproblems. The efficiency of our approach is based on several ingredients that constitute the main contributions of this paper. Firstly, an explicit formula for constructing the generalized Jacobian of the proximal mapping of the fused lasso regularizer is derived. Secondly, the special structure of the generalized Jacobian is carefully extracted and analyzed for the efficient implementation of the semismooth Newton method. Finally, numerical results, including the comparison between our approach and several state-of-the-art solvers, on real data sets are presented to demonstrate the high efficiency and robustness of our proposed algorithm in solving challenging large-scale fused lasso problems.

References in corpus (3)

• Modular proximal optimization for multidimensional total-variation regularization
• On the Asymptotic Superlinear Convergence of the Augmented Lagrangian Method for Semidefinite Programming with Multiple Solutions
• On the efficient computation of a generalized Jacobian of the projector over the Birkhoff polytope

Cited by in corpus (1)

• Solving the OSCAR and SLOPE Models Using a Semismooth Newton-Based Augmented Lagrangian Method