Approximation of the efficient point set by perturbation of the ordering cone

A vector optimization problem is given by a feasible set Z⊆ℝⁿ, a vector-valued objective function f:ℝⁿ⇒ℝ^l, and an ordering cone C⊆ℝ^l. The ordering cone is perturbed in such a way that the weakly efficient points of the ‘perturbed’ vector optimization problem given by Z, f, and the perturbed cone are efficient points of the original problem. Especially this means that scalarization methods, which compute in general only weakly efficient points, determine efficient points of the original problem, when they were applied to the perturbed problem. It turns out that the efficient points are the limits of weakly efficient points of the perturbed problems, letting the perturbation tend to zero. On the basis of this, a reference point algorithm is formulated. Finally, this algorithm is applied to a structural optimization problem.