Resolvent splitting with minimal lifting for composite monotone inclusions
Abstract
In this paper we propose a resolvent splitting with minimal lifting for finding a zero of the sum of maximally monotone operators involving the composition with a linear bounded operator. The resolvent of each monotone operator, the linear operator, and its adjoint are computed exactly once in the proposed algorithm. In the case when the linear operator is the identity, we recover the resolvent splitting with minimal lifting developed in Malitsky-Tam (2021). We also derive a new resolvent splitting for solving the composite monotone inclusion in the case with minimal fold lifting.
Cite
@article{arxiv.2111.09757,
title = {Resolvent splitting with minimal lifting for composite monotone inclusions},
author = {Luis M. Briceño-Arias},
journal= {arXiv preprint arXiv:2111.09757},
year = {2022}
}
Comments
There is a mistake in the main Theorem. Even if the derived algorithm is convergent, we cannot ensure its convergence to a solution to the main problem. We are now trying to fix this. The author thanks F. Arag\'on-Artacho for noting and communicating this issue