Characterization of the optimal set of the multicriterion optimization problem

The use of the sensitivity function in multicriterion optimization is considered. An analogy is established between the sensitivity function of the non-linear programming (NLP) problem and the optimal set of the multicriterion optimization problem. Using the properties of the sensitivity function, efficiency conditions are derived for Pareto, Slater, and Geoffrion optimal sets, as well as the conditions for the Pareto-optimal set to be connected. The necessary and sufficient conditions for the continuity of the sensitivity function of the NLP problem are given.