IMPROVED NONMONOTONE ADAPTIVE TRUST-REGION METHOD TO SOLVE GENERALIZED NASH EQUILIBRIUM PROBLEMS

Abstract

The generalized Nash equilibrium problems (GNEP) are typically challenging to solve by Newtonian methods because the problems generally have locally nonunique solutions. To overcome these difficulties, we propose an improved nonmonotone adaptive trust region (INATR) method for constrained optimization problems under fairly loose error-bound conditions. Also, we solve GNEPs using the INATR method and provide its numerical performances. The INATR method maintains the local convergence properties of its nonmonotone counterpart, and also it is proven that the proposed INATR method has global convergence properties. The numerical results indicate that the INATR method performs better compared to the nonmonotone trust region method. © 2024 Yokohama Publications. All rights reserved.