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Rachid El Idrissi, El Mostafa Kalmoun, Lahoussine Lafhim, New approximate optimality conditions of strong type in multiobjective generalized Nash equilibrium problems

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DOI: 10.23952/asvao.8.2026.1.05
Volume 8, Issue 1, 1 April 2026, Pages 85-101

 

Abstract. 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 cone-continuity regularity, adapted for MGNEPs. Under this framework, we present an enhanced Lagrangian-type algorithm for solving MGNEPs and establish its global convergence to an MGNEP-SKKT point.

 

How to Cite this Article:
R. El Idrissi, E.M. Kalmoun, L. Lafhim, New approximate optimality conditions of strong type in multiobjective generalized Nash equilibrium problems, Appl. Set-Valued Anal. Optim. 8 (2026), 85-101.