Convex KKM maps, monotone operators and Minty variational inequalities
Optimization and Control
2015-03-24 v1
Abstract
It is known that for convex sets, the KKM condition is equivalent to the finite intersection property. We use this equivalence to obtain a characterisation of monotone operators in terms of convex KKM maps and in terms of the existence of solutions to Minty variational inequalities. The latter result provides a converse to the seminal theorem of Minty.
Cite
@article{arxiv.1503.06363,
title = {Convex KKM maps, monotone operators and Minty variational inequalities},
author = {Marc Lassonde},
journal= {arXiv preprint arXiv:1503.06363},
year = {2015}
}