Optimality Conditions and Regularity Properties in Infinite-Dimensional Optimal Control Problems

The core message of this article is to present a survey on the properties of Strong Metric Regularity (SMR) and Strong Metric subRegularity (SMsR) of mappings representing first order optimality conditions (optimality mappings) in infinite dimensional spaces, with a focus on optimal control problems for ODE systems or PDEs. The authors emphasize an extension of these concepts involving two metrics either in the domain or in the image spaces, and show the relevance of this extension in optimal control.