c‐efficiency in nondifferentiable vector optimization

We study the minimal solutions in a nondifferentiable multiobjective problem, using a relation induced by a cone $C$ , that is $C$ ‐efficient and $C$ ‐weakly efficient solutions. First of all, a new class of nondifferentiable vector functions, named $(C_1,C_2)$ ‐pseudoinvex, is introduced pointing out that it differs from the ones already proposed in the literature. Then, it is proved that a critical point is $C$ ‐efficient or weakly $C$ ‐efficient if and only if the vector objective function is $(C_1,C_2)$ ‐pseudoinvex. The obtained results generalize to the nondifferentiable case some known definitions and characterization theorems which appeared in the recent vector optimization literature.