Generalized Convexity and Generalized Derivatives
Sándor Komlósi · Kluwer Academic Publishers eBooks · 2006
This chapter is devoted to the study of nonsmooth generalized convex functions with the help of special classes of generalized derivatives. Several results are presented on the links between generalized monotonicity of the generalized derivatives and generalized convexity of the functions under discussion. The abundance of the different notions of generalized derivatives has motivated an axiomatic treatment resulting, among others, in the concept of first order approximation. The usefulness of quasiconvex first order approximations in optimization theory is investigated, in particular, generalized upper quasidifferentiable functions are studied, quasiconvex Farkas Theorems and KKT-type optimality conditions are elaborated.