Methods and Applications of Analysis

Volume 26 (2019)

Number 3

Special Issue in Honor of Roland Glowinski (Part 2 of 2)

Guest Editors: Xiaoping Wang (Hong Kong University of Science and Technology) and Xiaoming Yuan (The University of Hong Kong)

A Douglas–Rachford method for sparse extreme learning machine

Pages: 217 – 234



Tommi Kärkkäinen (University of Jyväskylä, Faculty of Information Technology, Jyväskylä, Finland)

Roland Glowinski (Department of Mathematics, University of Houston, Texas, U.S.A.)


Operator-splitting methods have gained popularity in various areas of computational sciences, including machine learning. In this article, we present a novel nonsmooth and nonconvex formulation and its efficient associated solution algorithm to derive a sparse predictive machine learning model. The model structure is based on the so-called extreme learning machine with randomly generated basis. Our computational experiments confirm the efficiency of the proposed method, when a bold selection of the timestep is made. Comparative tests also indicate interesting results concerning the use of the $l_0$ seminorm for ultimate sparsity.


operator-splitting, Douglas–Rachford, extreme learning machine, sparse regularization

2010 Mathematics Subject Classification


Received 21 December 2017

Accepted 12 April 2019

Published 2 April 2020