Sensitivity analysis in multiobjective optimization (Q1090247)

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.