Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient sparse semismooth Newton methods for the clustered lasso
  problem   We focus on solving the clustered lasso problem, which is a least squares
problem with the $\ell_1$-type penalties imposed on both the coefficients and
their pairwise differences to learn the group structure of the regression
parameters. Here we first reformulate the clustered lasso regularizer as a
weighted ordered-lasso regularizer, which is essential in reducing the
computational cost from $O(n^2)$ to $O(n\log (n))$. We then propose an inexact
semismooth Newton augmented Lagrangian ({\sc Ssnal}) algorithm to solve the
clustered lasso problem or its dual via this equivalent formulation, depending
on whether the sample size is larger than the dimension of the features. An
essential component of the {\sc Ssnal} algorithm is the computation of the
generalized Jacobian of the proximal mapping of the clustered lasso
regularizer. Based on the new formulation, we derive an efficient procedure for
its computation. Comprehensive results on the global convergence and local
linear convergence of the {\sc Ssnal} algorithm are established. For the
purpose of exposition and comparison, we also summarize/design several
first-order methods that can be used to solve the problem under consideration,
but with the key improvement from the new formulation of the clustered lasso
regularizer. As a demonstration of the applicability of our algorithms,
numerical experiments on the clustered lasso problem are performed. The
experiments show that the {\sc Ssnal} algorithm substantially outperforms the
best alternative algorithm for the clustered lasso problem.

19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin