Necessary optimality conditions and a new approach to multiobjective bilevel optimization problems
A multiobjective bilevel optimization problem using the optimistic approach is investigated. It is assumed that the leader presupposes cooperation of the follower in the sense that the latter will choose in each time that solution in the solution set of his/her parametric optimization problem which is best suited with respect to the leader's objective function. Using the concept of Pareto optimality, together with a special scalarization function introduced in [\textit{J.-B. Hiriart-Urruty}, Math. Oper. Res. 4, 79--97 (1979; Zbl 0409.90086); \textit{J.-B. Hiriart-Urruty} and \textit{C. Lemaréchal}, Convex analysis and minimization algorithms. Part 1: Fundamentals. Grundlehren der Mathematischen Wissenschaften 305. Berlin: Springer-Verlag (1993; Zbl 0795.49001)], the authors give necessary optimality conditions. Several intermediate optimization problems are introduced to help in the investigation.
scientific article; zbMATH DE number 6132211
scientific article