Abstract:
Abstract: We study a class of variational inclusion problems in Hilbert spaces and propose a simple modification of Tseng’s forward-backward-forward splitting method for solving such problems. The algorithm is obtained via a regularization procedure and uses self-adaptive step sizes. We show that the approximating sequences generated by our algorithm converge strongly to a solution under some suitable assumptions on the regularization parameters. Moreover, we apply our results to the elastic net penalty problem in statistical learning theory and to bilevel optimization problems.
Based on a joint work with Simeon Reich.