Characterization of stability for cone increasing constraint mappings

Abstract

We investigate stability (in terms of metric regularity) for the specific class of cone increasing constraint mappings. This class is of interest in problems with additional knowledge on some nondecreasing behavior of the constraints (e.g. in chance constraints, where the distribution function of some measure is automatically nondecreasing). It is demonstrated, how this extra information may lead to sharper characterizations. In the first part, rather general cone increasing constraint mappings are studied by exploiting criteria for metric regularity, as recently developed by Mordukhovich. The second part focusses on genericity investigations for global metric regularity (i.e. metric regularity at all feasible points) of nondecreasing constraints in finite dimensions. Applications to chance constraints are given.