Abstract
A vector optimization problem is given by a feasible setZ⊑ℝn, a vector-valued objective functionf: ℝn→ℝl, and an ordering coneCℝℝl. We perturb the ordering cone in such a way that the weakly efficient points of the “perturbed” vector optimization problem given byZ, 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, we apply this algorithm to a structural optimization problem.
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Helbig, S. Approximation of the efficient point set by perturbation of the ordering cone. ZOR - Methods and Models of Operations Research 35, 197–220 (1991). https://doi.org/10.1007/BF01415907
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DOI: https://doi.org/10.1007/BF01415907