New approximate optimality conditions of strong type in multiobjective generalized Nash equilibrium problems

This paper aims to derive optimality conditions for a multiobjective generalized Nash equilibrium problem (MGNEP) involving constraints in multiobjective games.We demonstrate that any efficient solution satisfies the standard approximate strong Karush-Kuhn-Tucker (KKT) condition.However, recognizing that these conditions may be overly stringent, we propose a new approximate strong KKT condition specifically tailored for MGNEPs, named MGNEP-ASKKT.To ensure the convergence of an MGNEP-ASKKT sequence towards an MGNEP-SKKT point, we introduce the concept of conecontinuity regularity, adapted for MGNEPs.Under this framework, we present an enhanced Lagrangiantype algorithm for solving MGNEPs and establish its global convergence to an MGNEP-SKKT point.