Stability and sensitivity analysis in multiobjective nonlinear programming

In this paper some results on stability and sensitivity analysis in multiobjective nonlinear programming are surveyed. Given a family of parametrized multiobjective programming 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 an ordering convex cone. The behavior of the perturbation map is analyzed both qualitatively and quantitatively. First, some sufficient conditions which guarantee the upper and lower semicontinuity of the perburbation map are provided. The contingent derivatives of the perturbation map are also studied. Moreover, it is shown that the results can be refined in the convex case.