Optimization problems with nonconvex multiobjective generalized Nash equilibrium problem constraints

This work discusses a category of optimization problems in which the lower-level problems include multiobjective generalized Nash equilibrium problems. Despite the fact that it has various possible applications, there has been little research into it in the literature. We provide a single-level reformulation for these types of problems and highlight their equivalence in terms of global and local minimizers. Our method consists of transforming our problem into a one-level optimization problem, utilizing the kth-objective weighted-constraint and optimal value reformulation. The Mordukhovich generalized differentiation calculus is then used to derive completely detailed first-order necessary optimality conditions in the smooth setting.