
Journal of Convex Analysis 06 (1999), No. 2, 235266 Copyright Heldermann Verlag 1999 GraphConvex Mappings and KConvex Functions Teemu Pennanen Dept. of Mathematics, University of Washington, Seattle, WA 981954350, U.S.A. This paper studies global and local behavior of graphconvex setvalued mappings in finitedimensional vector spaces. This is done in terms of recession mappings and graphical derivatives which are setvalued mappings whose graphs are convex cones. The main results are chain rules for computing the recession mapping and the graphical derivative of a composition of two setvalued mappings. The results on graphconvex mappings are applied to Kconvex functions which are vectorvalued generalizations of extendedrealvalued proper convex functions. Many generalizations of classical results in convex analysis are obtained, along with a generalization of subdifferential calculus, in which the differential behavior of a function is described by a sublinear mapping that resembles the classical Jacobian. A particular advantage of this approach is that it leads to simple chain rules for compositions of vectorvalued convex functions. The generality is reflected in the fact that most of the classical rules for computing recession functions and subdifferentials are obtained as special cases of the given chain rules. Some applications to mathematical programming and matrix analysis are given. [ Fulltextpdf (308 KB)] 