An implicit multifunction theorem for the hemiregularity of mappings with application to constrained optimization
Optimization and Control
2017-04-06 v2
Abstract
The present paper contains some investigations about a uniform variant of the notion of metric hemiregularity, the latter being a less explored property obtained by weakening metric regularity. The introduction of such a quantitative stability property for set-valued mappings is motivated by applications to the penalization of constrained optimization problems, through the notion of problem calmness. As a main result, an implicit multifunction theorem for parameterized inclusion problems is established, which measures the uniform hemiregularity of the related solution mapping in terms of problem data. A consequence on the exactness of penalty functions is discussed.
Cite
@article{arxiv.1703.10552,
title = {An implicit multifunction theorem for the hemiregularity of mappings with application to constrained optimization},
author = {Amos Uderzo},
journal= {arXiv preprint arXiv:1703.10552},
year = {2017}
}