-

 

 

 




Optimization Online





 

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

Xudong Li(lixudong***at***u.nus.edu)
Defeng Sun(matsundf***at***nus.edu.sg)
Kim-Chuan Toh(mattohkc***at***nus.edu.sg)

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.

Keywords: Level-set method, fused lasso, convex composite programming, generalized Jacobian, semismooth Newton method

Category 1: Convex and Nonsmooth Optimization

Citation:

Download: [PDF]

Entry Submitted: 06/28/2017
Entry Accepted: 06/28/2017
Entry Last Modified: 06/28/2017

Modify/Update this entry


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

 

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