REGULARIZED JACOBI-TYPE ADMM-METHOD FOR FINDING SOLUTIONS TO GENERALIZED NASH EQUILIBRIUM PROBLEM
DOI:
https://doi.org/10.33003/fjs-2023-0704-1815Keywords:
convex optimization, weak convergence, monotonicity, hilbert spaceAbstract
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.
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