Sensitivity analysis in multiobjective differential programming

In this paper we deal with sensitivity analysis in multiobjective differential programs with equality constraints. We analyze the quantitative behavior of the optimal solutions according to changes of right-hand side values included in the original optimization problem. One of the difficulties lies in the fact that the efficient solution in multiobjective optimization in general becomes a set. If the preference of the decision maker is represented by a scalar utility which transforms optimal solutions in optima, we may apply existing methods of sensitivity analysis. However, when dealing with a subset of optimal points, the existence of a Fréchet differentiable selection of such a set-valued map is usually assumed. The aim of the paper is to investigate the derivative of certain set-valued maps of efficient points. We show that the sensitivity depends on a set-valued map associated to the T-Lagrange multipliers and a projection of its sensitivity.