Sensitivity analysis in multiobjective optimization
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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.
Key WordsSensitivity analysis multiobjective optimization perturbation maps contingent derivatives
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- 1.Fiacco, A. V.,Introduction to Sensitivity and Stability Analysis in Nonlinear Programming, Academic Press, New York, New York, 1983.Google Scholar
- 2.Rockafellar, R. T.,Lagrange Multipliers and Subderivatives of Optimal Value Functions in Nonlinear Programming, Mathematical Programming Study, Vol. 17, pp. 28–66, 1982.Google Scholar
- 3.Tanino, T., andSawaragi, Y.,Stability of Nondominated Solutions in Multicriteria Decision-Making, Journal of Optimization Theory and Applications, Vol. 30, pp. 229–253, 1980.Google Scholar
- 4.Aubin, J. P.,Contingent Derivatives of Set-Valued Maps and Existence of Solutions to Nonlinear Inclusions and Differential Inclusions, Advances in Mathematics, Supplementary Studies, Edited by L. Nachbin, Academic Press, New York, New York, pp. 160–232, 1981.Google Scholar
- 5.Aubin, J. P., andEkeland, I.,Applied Nonlinear Analysis, John Wiley, New York, New York, 1984.Google Scholar
- 6.Sawaragi, Y., Nakayama, H., andTanino, T.,Theory of Multiobjective Optimization, Academic Press, New York, New York, 1985.Google Scholar
- 7.Holmes, R. B.,Geometric Functional Analysis and Its Applications, Springer-Verlag, New York, New York, 1975.Google Scholar
- 8.Rockafellar, R. T.,Lipschitzian Properties of Multifunctions, Nonlinear Analysis, Theory, Methods, and Applications, Vol. 9, pp. 867–885, 1985.Google Scholar
- 9.Borwein, J.,Proper Efficient Points for Maximizations with Respect to Cones, SIAM Journal on Control and Optimization, Vol. 15, pp. 57–63, 1977.Google Scholar
- 10.Malanowski, K.,Differentiability with Respect to Parameters of Solutions to Convex Programming Problems, Mathematical Programming, Vol. 33, pp. 352–361, 1985.Google Scholar