Regularity of solution mappings in nonlinear optimization

Prof. Diethard Klatte

Feb. 11, 2014, 1:45 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.