The Vector-Valued Variational Principle in Banach Spaces Ordered by Cones with Nonempty Interiors

We prove sharpness of efficient solutions $x_k$ to vector optimization problems resulting from Ekeland vector variational principles. We achieve this by sharpening some of the existing vector variational principles and showing that $x_k$ remains efficient not only for perturbations in the direction $k$ but also for other directions of perturbations.