An algorithm for solving the variational inequality problem over the fixed point set of a quasi-nonexpansive operator in Euclidean space
Optimization and Control
2013-04-03 v1
Abstract
This paper is concerned with the variational inequality problem (VIP) over the fixed point set of a quasi-nonexpansive operator. We propose, in particular, an algorithm which entails, at each step, projecting onto a suitably chosen half-space, and prove that the sequences it generates converge to the unique solution of the VIP. We also present an application of our result to a hierarchical optimization problem.
Cite
@article{arxiv.1304.0690,
title = {An algorithm for solving the variational inequality problem over the fixed point set of a quasi-nonexpansive operator in Euclidean space},
author = {Andrzej Cegielski and Aviv Gibali and Simeon Reich and Rafał Zalas},
journal= {arXiv preprint arXiv:1304.0690},
year = {2013}
}
Comments
Accepted for publication in Numerical Functional Analysis and Optimization