Strong metric (sub)regularity in optimal control

TL;DR

This survey explores strong metric regularity and subregularity of optimality mappings in infinite-dimensional optimal control problems, emphasizing metric extensions and their significance.

Contribution

It extends the concepts of SMR and SMsR with dual metrics and highlights their importance in optimal control of ODEs and PDEs.

Findings

Extension of SMR/SMsR with dual metrics enhances analysis.

Relevance of metric extensions in optimal control problems.

Survey consolidates properties of optimality mappings in infinite dimensions.

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.