Necessary optimality conditions for a semivectorial bilevel optimization problem via a revisited Charnes–Cooper scalarization

Abstract

In this paper, we investigate a multiobjective bilevel optimization problem with a vector-valued lower-level objective function. We revisit the Charnes–Cooper scalarization technique for multi-objective programs and use optimal value reformulation to transform the scalar problem into a one-level optimization problem. Using Mordukhovich's generalized differentiation calculus, a new subdifferential estimate and Lipschitz condition for the optimal value function of this problem are developed as a result of this reformulation. In addition, we construct first-order necessary optimality conditions in the smooth setting.