Sensitivity analysis in convex vector optimization
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We consider a parametrized convex vector optimization problem with a parameter vectoru. LetY(u) be the objective space image of the parametrized feasible region. The perturbation mapW(u) is defined as the set of all minimal points of the setY(u) with respect to an ordering cone in the objective space. The purpose of this paper is to investigate the relationship between the contingent derivativeDW ofW and the contingent derivativeDY ofY. Sufficient conditions for MinDW=MinDY andDW=W minDY are obtained, respectively. Therefore, quantitative information on the behavior of the perturbation map is provided.
Key WordsConvex vector optimization perturbation maps contingent derivatives
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- 1.Tanino, T.,Sensitivity Analysis in Multiobjective Optimization, Journal of Optimization Theory and Applications, Vol. 56, pp. 479–499, 1988.Google Scholar
- 2.Shi, D. S.,Contingent Derivative of the Perturbation in Multiobjective Optimization, Journal of Optimization Theory and Applications, Vol. 70, pp. 351–362, 1991.Google Scholar
- 3.Tanino, T.,Stability and Sensitivity Analysis in Convex Vector Optimization, SIAM Journal on Control and Optimization, Vol. 26, pp. 521–536, 1988.Google Scholar
- 4.Yu, P. L.,Cone Convexity, Cone Extreme Points, and Nondominated Solutions in Decision Problems with Multiobjectives, Journal of Optimization Theory and Applications, Vol. 14, pp. 319–377, 1974.Google Scholar
- 5.Benson, P.,An Improved Definition of Proper Efficiency for Vector Maximization with Respect to Cones, Journal of Mathematical Analysis and Applications, Vol. 71, pp. 232–241, 1979.Google Scholar
- 6.Henig, M. I.,Proper Efficiency with Respect to Cones, Journal of Optimization Theory and Applications, Vol. 36, pp. 387–407, 1982.Google Scholar
- 7.Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1972.Google Scholar
- 8.Sawaragi, Y., Nakayama, H., andTanino, T.,Theory of Multiobjective Optimization, Academic Press, New York, New York, 1985.Google Scholar