Most Maximally Monotone Operators Have a Unique Zero and a Super-regular Resolvent
Optimization and Control
2013-01-29 v1
Abstract
Maximally monotone operators play important roles in optimization, variational analysis and differential equations. Finding zeros of maximally monotone operators has been a central topic. In a Hilbert space, we show that most resolvents are super-regular, that most maximally monotone operators have a unique zero and that the set of strongly monotone mapping is of first category although each strongly monotone operator has a unique zero. The results are established by applying the Baire Category Theorem to the space of nonexpansive mappings.
Cite
@article{arxiv.1301.6443,
title = {Most Maximally Monotone Operators Have a Unique Zero and a Super-regular Resolvent},
author = {Xianfu Wang},
journal= {arXiv preprint arXiv:1301.6443},
year = {2013}
}