Quasinonexpansive Iterations on the Affine Hull of Orbits: From Mann's Mean Value Algorithm to Inertial Methods
Optimization and Control
2017-08-15 v3
Abstract
Fixed point iterations play a central role in the design and the analysis of a large number of optimization algorithms. We study a new iterative scheme in which the update is obtained by applying a composition of quasinonexpansive operators to a point in the affine hull of the orbit generated up to the current iterate. This investigation unifies several algorithmic constructs, including Mann's mean value method, inertial methods, and multi-layer memoryless methods. It also provides a framework for the development of new algorithms, such as those we propose for solving monotone inclusion and minimization problems.
Keywords
Cite
@article{arxiv.1704.03563,
title = {Quasinonexpansive Iterations on the Affine Hull of Orbits: From Mann's Mean Value Algorithm to Inertial Methods},
author = {Patrick L. Combettes and Lilian E. Glaudin},
journal= {arXiv preprint arXiv:1704.03563},
year = {2017}
}