Linear Convergence in Time-Varying Generalized Nash Equilibrium Problems
Mattia Bianchi (TU Delft - Mechanical Engineering)
Emilio Benenati (TU Delft - Mechanical Engineering, ETH Zürich)
Sergio Grammatico (TU Delft - Mechanical Engineering, TU Delft - Mechanical Engineering)
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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.