Regularitaetskonzepte fuer nichtglatte Gleichungen und ihre Anwendungen auf Optimierungs- und Gleichgewichtsprobleme

For studying critical points of optimization and equilibrium problems with inequality constraints and (more or less) smooth data, the traditional way is to consider them as solutions of Kuhn-Tucker type systems or of normal cone inclusions. We prefer to use a direct, analytical approach for characterizing such points: namely as zeros of certain locally Lipshitz properties of critical point and stationary/optimal solution mappings. In particular, we give characterizations of strong regularity and of local upper Lipshitz behavior by certain properties of associated quadratic auxiliary problems and outline the interconnection with injectivity properties of suitable generalized directional derivatives. Applications of these regularity concepts in the analysis of marginal values and iterated minimization schemes are presented.

Reference:
D. Klatte and B. Kummer. Nonsmooth Equations in Optimization - Regularity, Calculus, Methods and Applications, Kluwer, 2002; in particular, Chapter 7 and 8.