# Regularity of solution mappings in nonlinear optimization

## Prof. Diethard Klatte

**Feb. 11, 2014, 12:45 p.m. S3 057**

The concepts of strong regularity and metric regularity for equations and inclusions play an important role both for the sensitivity analysis of solutions and the convergence theory of solution methods. In this talk, we first discuss these notions in the context of generalized equations (inclusions) and then present classical and recent characterizations of strong and metric regularity with respect to sets of critical points and optimal solutions of nonlinear optimization problems. This applies both to standard nonlinear programs and to cone constrained optimization problems. In particular, we are interested in conditions under which metric and strong regularity of Karush-Kuhn-Tucker (KKT) systems coincide. Further we show that the metric regularity of a KKT system implies the non-degeneracy of constraints and hence the uniqueness of the multipliers.