Derivatives and Codifferentials of Maps with Closed Convex Graphs and Convex Operators

摘要

We complete the study of contingent cones to a subset K and of the contingent derivatives of a set valued map F when K and the graph of F are closed and convex. In this case, the contingent cone is a closed convex cone (called the tangent cone) and the contingent derivative is a convex process (a set-valued map whose graph is a closed convex cone). The transpose of the contingent derivative is another convex process, called the codifferential, which plays a quite important role. We present a calculus of tangent cones to closed convex sets and we adopt the basic results of convex analysis to the case of set-valued maps with closed convex graph. This study is motivated by the crucial role played by convex cones in optimization, fixed-point theory and flow-invariance of dynamical systems. (Author)