Sensitivity Analysis in Multiobjective Optimization

Sensitivity analysis is both theoretically and practically useful in optimization. However, only a few results in this direction have been obtained for multiobjective optimization. In this paper, the issue of sensitivity analysis in multiobjective optimization is dealt with. 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 with respect to a fixed ordering convex cone. The behavior of the perturbation map is analyzed quantitatively by using the concept of contingent derivative for set-valued maps. Particularly it is shown that the contingent derivative of the perturbation map for multiobjective programming problems with parametrized inequality Constraints is closely related to the corresponding Lagrange multipliers