On Multilevel optimization

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Bilevel programming is a tool for modelling two level hierarchical decision making. This class of programs constitutes a branch of mathematical programming in which the constraints are, partially, determined by another optimisation problem. The deci sion maker at the upper level is termed as the leader, and at the lower level the follower. The control of variables is partitioned between the decision makers who attempt to optimise their individual objectives. The leader goes first in order to optimise his/her objective function. The follower observes the leader's decision and constructs his/her decision. Bilevel programs are non-convex problems and have been proved to be NP-hard problems even in the simplest case where the objective and constraint functions are all linear. In this document, we study an extension of these problems. Precisely, we are concerned with Multiobjective bilevel optimization problems.