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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