REGULARIZED JACOBI-TYPE ADMM-METHOD FOR FINDING SOLUTIONS TO GENERALIZED NASH EQUILIBRIUM PROBLEM - Akaligwo, Emmanuel; Opara, Pius; Boniface, Aharanwa (FUDMA JOURNAL OF SCIENCES, 2023)
In this paper, we extended the well-known alternating direction method of multipliers (ADMM) for optimization problems to generalized Nash equilibrium problems (GNEP) with shared constraints. We developed an ADMM-type algorithm with fixed regularization to tackle the problem (GNEP) where an upper estimate for the operator norm is not known and then we apply a multiplier-penalty in order to get rid of the joint constraints. We equipped the Hilbert space with an appropriate weighted scalar product and it turns out to be weakly convergent under a lipschitz and monotonicity assumption. A proximal term is then added to improve the convergence properties. Furthermore, a comparative analysis of quasi-variational inequality method, interior point method, penalty method and the proposed method are discussed.
Keywords: convex optimization; weak convergence; monotonicity; hilbert space