Optimality and duality results for $\left( h,\varphi \right) $% -nondifferentiable multiobjective programming problems with $\left( h,\varphi \right) $-$\left( b,F,\rho \right) $-convex functions

Abstract

Generalized algebraic operations introduced by Ben-Tal \cite{bental} are used to define new classes of generalized convex functions, namely $\left(

h,\varphi \right) $-$\left( b,F,\rho \right) $-convex functions and

generalized $\left( h,\varphi \right) $-$\left( b,F,\rho \right) $-convex

functions in the vectorial case. Further, optimality and duality results are

proved for the considered $\left( h,\varphi \right) $-nondifferentiable

multiobjective programming problem under assumptions that the functions

involved are (generalized) $\left( h,\varphi \right) $-$\left( b,F,\rho

\right) $-convex.