Optimality and duality results for (h,φ)-nondifferentiable multiobjective programming problems with (h,φ) – (b,f,ρ) -convex functions

Abstract

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 generalized (h,?)?(b,F,?)-convex functions in the vectorial case. Further, optimality and duality results are proved for the considered (h,?)- nondifferentiable multiobjective programming problem under assumptions that the functions involved are (generalized) (h,?)- (b,F,?)-convex.