Necessary optimality conditions for a semivectorial bilevel problem under a partial calmness condition
Stephan Dempe, Nazih Abderrazzak Gadhi, Mohammed El Idrissi, Khadija Hamdaoui · Optimization · 2020
In this paper, we are concerned with a semivectorial bilevel optimization problem P. Using a partial calmness suitable for bilevel semivectorial problems, we formulate its necessary optimality conditions. Our approach consists of reformulating our problem into a one level optimization problem using successively the kth-objective weighted-constraint and the optimal value reformulation. Our main results are given in terms of the limiting subdifferentials and the limiting normal cones. Completely detailed first-order necessary optimality conditions are then derived in the smooth setting while using the generalized differentiation calculus of Mordukhovich.