Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Variational analysis
  • metric regularity
  • optimization
  • optimal control

Mathematics Subject Classification

49K40, 90C31, 49M05

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Suggested citation

N. A. Jork, N. P. Osmolovskii, V. M. Veliov. “Strong Metric (Sub)Regularity in Optimal Control.” Journal of Convex Analysis 32 (2025), No. 2, 375–398. https://doi.org/10.68381/jca32019

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Published by Heldermann Verlag, 2025. Rights now held by Banach Press.