Abstract:
In this paper we introduce notions of inhomogeneous upper convex and lower concave approximations of the increment of a nonsmooth function defined in a normed space and study exhaustive families of these approximations. In terms of the introduced notions we establish optimality conditions for various constrained and unconstrained extremum problems.
Keywords:nonsmooth analysis, inhomogeneous upper convex approximation, inhomogeneous lower concave approximation, exhaustive family of approximations, coexhauster.