Separable conditions and scalarization of Benson proper efficiency

Under the assumption that the ordering cone has a nonempty interior and is separable (or the feasible set has a nonempty interior and is separable), we give scalarization theorems on Benson proper efficiency. Applying the results to vector optimization problems with nearly cone-subconvexlike set-valued maps, we obtain scalarization theorems and Lagrange multiplier theorems for Benson proper efficient solutions.