Metric regularity: characterizations, nonsmooth variations and successive approximation ∗
Bernd Kummer · Optimization · 1999
Metric regularity of (multi-) functions is characterized in terms of some uniform lower semicontinuity as well as by means of Ekeland points of related functionals. Specializations and consequences are studied for stability conditions via co-derivatives and contingent derivatives. Under metric regularity, we show that persistence and Lipschitzian behavior of parametric solutions can be constructively handled by a successive approximation scheme. This permits a simple approach to implicit functions with multi valued inverse and connects iteration methods of quite different types. Particularly, successive approximation may be trivially applied for solving regular piecewise smooth equations