Optimization and Flow Invariance via First and Second Order Tangent Cones

Abstract

This is a survey paper on optimization problems via the technique of first and second order tangent cones to a nonempty subset of a Banach space X. Such a technique is also used in the study of the flow invariance of a closed set with respect to a second order differential equation (motion on a given orbit in a force field). Many of the known results in these areas are included here.