Generalized algebraic operations introduced by Ben-Tal [5] are used to define new classes of generalized convex functions, namely (h,?)?(b,F,?) -convex functions and (h,?)?(b,F,?)-convex in the vectorial case. Further, optimality duality results proved for considered (h,?)- nondifferentiable multiobjective programming problem under assumptions that involved (generalized) (b,F,?)-convex.

We study some classes of generalized convex functions, using a generalized di¤erential approach. By this we mean a set-valued mapping which stands either for a derivative, a subdi¤erential or a pseudodi¤erential in the sense of Jeyakumar and Luc. We establish some links between the corresponding classes of pseudoconvex, quasiconvex and another class of generalized convex functions we introduced...

There exists a calculus for general nondifferentiable functions that englobes a large part of the familiar subdifferential calculus for convex nondifferentiable functions [1]. This development started with F.H. Clarke, who introduced a generalized gradient for functions that are locally Lipschitz, but (possibly) nondifferentiable. Generalized gradients turn out to be the subdifferentials, in th...