Abstract
Sensitivity analysis in multiobjective optimization is dealt with in this paper. Given a family of parametrized multiobjective optimization problems, the perturbation map is defined as the set-valued map which associates to each parameter value the set of minimal points of the perturbed feasible set in the objective space with respect to a fixed ordering convex cone. The behavior of the perturbation map is analyzed quantitatively by using the concept of contingent derivatives for set-valued maps. Particularly, it is shown that the sensitivity is closely related to the Lagrange multipliers in multiobjective programming.
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Communicated by P. L. Yu
This research was made while the author stayed at the International Institute for Applied Systems Analysis, Laxenburg, Austria.
The author would like to thank an anonymous referee for his helpful suggestions; particularly, he pointed out that Proposition 2.2 and Theorem 2.1 are valid also in infinite-dimensional spaces.
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Tanino, T. Sensitivity analysis in multiobjective optimization. J Optim Theory Appl 56, 479–499 (1988). https://doi.org/10.1007/BF00939554
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DOI: https://doi.org/10.1007/BF00939554