期刊
SIAM JOURNAL ON OPTIMIZATION
卷 28, 期 2, 页码 1842-1866出版社
SIAM PUBLICATIONS
DOI: 10.1137/17M1136390
关键词
level-set method; fused lasso; convex composite programming; generalized Jacobian; semismooth Newton method
资金
- Hong Kong Polytechnic University
- Ministry of Education, Singapore [R-146-000-256-114]
In applying the level-set method developed in [E. Van den Berg and M. P. Friedlander, SIAM J. Sci. Comput., 31 (2008), pp. 890-912] and [E. Van den Berg and M. P. Friedlander, SIAM J. Optim., 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. First, an explicit formula for constructing the generalized Jacobian of the proximal mapping of the fused lasso regularizer is derived. Second, 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.
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