Distributed generalized Nash equilibrium seeking: A singular perturbation-based approach

In this paper, a distributed optimization algorithm is proposed for aggregative game with coupled constraints. Based on the singular perturbation system, the generalized Nash equilibrium is sought by a group of agents. By employing the average consensus method in the fast manifold, the aggregates in the object function can be estimated via simple information exchanges, as well as the aggregate of dual variables, which provides necessary information for the fully distributed algorithm design. Moreover, the exponential convergence of the proposed algorithm is explored based on the Lyapunov method, the properties of the variational inequality and the characteristic of the singular perturbation system. Application to the resource competition problem in smart grid verifies the effectiveness of the proposed algorithm. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper proposes a distributed optimization algorithm for aggregative game with coupled constraints. The algorithm seeks the generalized Nash equilibrium based on the singular perturbation system by using the average consensus method in the fast manifold. The estimation of aggregates and dual variable aggregates is achieved through simple information exchanges, providing necessary information for the fully distributed algorithm design. The exponential convergence of the algorithm is explored based on the Lyapunov method, the properties of the variational inequality, and the characteristic of the singular perturbation system. The effectiveness of the proposed algorithm is verified through its application to the resource competition problem in smart grid.