Perturbation Theory And The Estimation Of The Neighborhood For Metric Regularity

Metric regularity has been extensively studied since it is widely applied in optimization and control theory.This thesis mainly studies the perturbation theory of metric regularity and estimates the neighborhood on which metric regularity holds for the quadratic functions.There are two kinds of perturbations for metric regularity.The addition-type perturbation theory studies metric regularity of the sum mapping of a metrically regular mapping and a perturbation mapping.For local metric regularity,this thesis proves a set-valued perturbation result,which improves a known result by relaxing the assumption and simplifying the argument.Moreover,a perturbation result for semi-local metric regularity is also obtained.The metric-type perturbation theory studies whether a mapping is metrically regular when it is close enough to a metrically regular mapping.This thesis improves a known result of the metric-type perturbation theory by strengthening its conclusion.It is helpful to estimate the neighborhood of metric regularity for applications.However,to the best of our knowledge,there is little study for the estimation of the neighborhood.This thesis estimates the neighborhood on which metric regularity holds for a kind of convex quadratic functions.