In this paper which will appear as a chapter in the Handbook ofGeneralized Convexity we discuss the basic ideas ofconvex and quasiconvex analysis in finite dimensional Euclideanspaces. To illustrate the usefulness of this branchof mathematics also applications to optimization theory...

In this paper we introduce several classes of generalized convexfunctions already discussed in the literature and show the relationbetween those function classes. Moreover, for some of those functionclasses a Farkas-type theorem is proved. As such this paper unifiesand extends results existing...

In this paper we will show that the closely K-convexlike vector-valued functions with K Rm a nonempty convex cone and related classes of vector-valued functions discussed in the literature arise naturally within the theory of biconjugate functions applied to the Lagrangian perturbation scheme in...

In the first chapter of this book the basic results within convex and quasiconvex analysis are presented. In Section 2 we consider in detail the algebraic and topological properties of convex sets within Rn together with their primal and dual representations. In Section 3 we apply the results...