Abstract
For a vector optimization problem that depends on a parameter vector, the sensitivity analysis of perturbation, proper perturbation, and weak perturbation maps is dealth with. Each of the perturbation maps is defined as a set-valued map which associates to each parameter value the set of all minimal, properly minimal, and weakly minimal points of the perturbed feasible set in the objective space with respect to a fixed ordering cone. Using contingent cones in a finite-dimensional Euclidean space, we investigate the relationship between the contingent derivatives of the three types of perturbation maps and three types of minimal point sets for the contingent derivative of the feasible-set map in the objective space. These results provide quantitative informations on the behavior of the perturbation maps.
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Communicated by P. L. Yu
The authors would like to thank the referees for their valuable comments and suggestions.
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Kuk, H., Tanino, T. & Tanaka, M. Sensitivity analysis in vector optimization. J Optim Theory Appl 89, 713–730 (1996). https://doi.org/10.1007/BF02275356
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DOI: https://doi.org/10.1007/BF02275356