## Metric Regularity

- March 26, 2010
- 2:30 p.m.
- LeConte 312

## Abstract

Metric regularity has its roots in the Banach open mapping principle and in the subsequent works of Lyusternik and Graves, and has been recognized as a basic property in the general area of the theory of extremum. It serves as a constraint qualification condition in deriving optimality conditions, and more importantly, is very instrumental in obtaining error bounds for perturbed minima and proving convergence of algorithms for solving optimization problems and beyond. In this talk we move into a wider territory in establishing a link between metric regularity and set-valued contractions. As applications we discuss what metric regularity means for Newton's iteration and for approximations in optimal control.