Journal of Convex Analysis 32 (2025), No. 2, 375--398
Copyright Heldermann Verlag 2025
Strong Metric (Sub)Regularity in Optimal Control
Nicolai A. Jork
Fachbereicht Mathematik, University of Tübingen, Germany
nicolai.jork@uni-tuebingen.de
Nikolai P. Osmolovskii
Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland
osmolov@ibspan.waw.pl
Vladimir M. Veliov
Institute of Statistics and Mathematical Methods in Economics, Technische Universität, Wien, Austria
vladimir.veliov@tuwien.ac.at
This is mainly a survey on the properties of Strong Metric Regularity (SMR) and Strong Metric subRegularity (SMsR) of mappings representing first order optimality conditions (so-called optimality mappings) of optimization problems in infinite dimensional spaces. The focus is on the optimality mappings associated with optimal control problems for ODE systems or PDEs. We especially emphasize an extension of the concepts of SMR and SMsR which involves two metrics either in the domain or in the image spaces. The paper shows the relevance of this extension in optimal control.
Keywords: Variational analysis, metric regularity, optimization, optimal control.
MSC: 49K40, 90C31, 49M05.
[ Fulltext-pdf (189 KB)] for subscribers only.