Paris, October 25th-26th, 2011

The theory of metric regularity is a rapidly developing area motivated by various applications in optimisation and control. It is useful both for theoretical studies and in numerical analysis.

In particular, metric regularity is very instrumental as a tool for handling fundamental problems such as controllability, normality of necessary optimality conditions, feasibility, as well as implicit mapping theorems, sensitivity and robustness. It plays a major role in proving convergence of numerical methods for solving problems of optimal control, optimization, equilibrium, and beyond. Specifically, the metric regularity property reflects the idea of a posteriori error bounds for constraint systems. For discrete approximations of extremals in optimal control it leads to a posteriori error estimates. There is a natural relationship between metric regularity and convergence of a broad range of algorithms, such as Newton-type methods, providing also the rate of convergence.