The forward-backward algorithm and the normal problem

DOI10.1007/S10957-017-1113-4arXiv1608.02240MaRDI QIDQ6276299

Publication date: 7 August 2016

Abstract: The forward-backward splitting technique is a popular method for solving monotone inclusions that has applications in optimization. In this paper we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions using the forward-backward operator. We also provide a formula for the range of the displacement map of the forward-backward operator. Several examples illustrate our theory.

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Numerical methods involving duality (49M29) Numerical optimization and variational techniques (65K10) Monotone operators and generalizations (47H05) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Duality theory (optimization) (49N15) Decomposition methods (49M27) Perturbations of nonlinear operators (47H14)

This page was built for publication: The forward-backward algorithm and the normal problem

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6276299)