A primal-dual splitting algorithm for composite monotone inclusions with minimal lifting
From MaRDI portal
Publication:6391592
DOI10.1007/S11075-022-01405-9arXiv2202.09665MaRDI QIDQ6391592
Radu Ioan Boţ, David Torregrosa-Belén, Francisco J. Aragón Artacho
Publication date: 19 February 2022
Abstract: In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators. Our main contribution is establishing the first primal-dual splitting algorithm for composite monotone inclusions with minimal lifting. Specifically, the proposed scheme reduces the dimension of the product space where the underlying fixed point operator is defined, in comparison to other algorithms, without requiring additional evaluations of the resolvent operators. We prove the convergence of this new algorithm and analyze its performance in a problem arising in image deblurring and denoising. This work also contributes to the theory of resolvent splitting algorithms by extending the minimal lifting theorem recently proved by Malitsky and Tam to schemes with resolvent parameters.
Nonlinear programming (90C30) Numerical optimization and variational techniques (65K10) Monotone operators and generalizations (47H05) Numerical analysis (65-XX)
This page was built for publication: A primal-dual splitting algorithm for composite monotone inclusions with minimal lifting
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6391592)
