Nonsmooth calculus, minimality, and monotonicity of convexificators

Abstract

Noncompact convexificators, which provide upper convex and lower concave approximations for a continuous function, are defined. Various calculus rules, including extremality and mean-value properties, are presented. Regularity conditions are given for convexi ficators to be minimal. A characterization of quasiconvexity of a con tinuous function is obtained in terms of the quasimonotonicity of convexificators.