Linear Convergence in Time-Varying Generalized Nash Equilibrium Problems

Conference paper (2023)

Authors

M. Bianchi Team Sergio Grammatico - Mechanical, Maritime and Materials Engineering
E. Benenati Team Sergio Grammatico - Mechanical, Maritime and Materials Engineering , ETH Zürich
S. Grammatico Team Sergio Grammatico - Mechanical, Maritime and Materials Engineering ,
Research Group
Team Sergio Grammatico (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2023 M. Bianchi, E. Benenati, S. Grammatico
DOI: https://doi.org/10.1109/CDC49753.2023.10383331
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Published Date

2023

Language

English

Reuse Rights

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Sergio Grammatico

Abstract

We study generalized games with full row rank equality coupling constraints and we provide a strikingly simple proof of strong monotonicity of the associated KKT operator. This allows us to show linear convergence to a variational equilibrium of the resulting primal-dual pseudo-gradient dynamics. Then, we propose a fully-distributed algorithm with linear convergence guarantee for aggregative games under partial-decision information. Based on these results, we establish stability properties for online GNE seeking in games with time-varying cost functions and constraints. Finally, we illustrate our findings numerically on an economic dispatch problem for peer-to-peer energy markets.

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