48 research outputs found
A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games
We address the generalized aggregative equilibrium seeking problem for
noncooperative agents playing average aggregative games with affine coupling
constraints. First, we use operator theory to characterize the generalized
aggregative equilibria of the game as the zeros of a monotone set-valued
operator. Then, we massage the Douglas-Rachford splitting to solve the monotone
inclusion problem and derive a single layer, semi-decentralized algorithm whose
global convergence is guaranteed under mild assumptions. The potential of the
proposed Douglas-Rachford algorithm is shown on a simplified resource
allocation game, where we observe faster convergence with respect to
forward-backward algorithms.Comment: arXiv admin note: text overlap with arXiv:1803.1044
Distributed generalized Nash equilibrium seeking in aggregative games on time-varying networks
We design the first fully-distributed algorithm for generalized Nash
equilibrium seeking in aggregative games on a time-varying communication
network, under partial-decision information, i.e., the agents have no direct
access to the aggregate decision. The algorithm is derived by integrating
dynamic tracking into a projected pseudo-gradient algorithm. The convergence
analysis relies on the framework of monotone operator splitting and the
Krasnosel'skii-Mann fixed-point iteration with errors.Comment: 14 pages, 4 figure
Tutorial on Congestion Control in Multi-Area Transmission Grids via Online Feedback Equilibrium Seeking
Online feedback optimization (OFO) is an emerging control methodology for
real-time optimal steady-state control of complex dynamical systems. This
tutorial focuses on the application of OFO for the autonomous operation of
large-scale transmission grids, with a specific goal of minimizing renewable
generation curtailment and losses while satisfying voltage and current limits.
When this control methodology is applied to multi-area transmission grids,
where each area independently manages its congestion while being dynamically
interconnected with the rest of the grid, a non-cooperative game arises. In
this context, OFO must be interpreted as an online feedback equilibrium seeking
(FES) scheme. Our analysis incorporates technical tools from game theory and
monotone operator theory to evaluate the stability and performance of
multi-area grid operation. Through numerical simulations, we illustrate the key
challenge of this non-cooperative setting: on the one hand, independent
multi-area decisions are suboptimal compared to a centralized control scheme;
on the other hand, some areas are heavily penalized by the centralized
decision, which may discourage participation in the coordination mechanism
Semi-decentralized generalized Nash equilibrium seeking in monotone aggregative games
We address the generalized Nash equilibrium seeking problem for a population
of agents playing aggregative games with affine coupling constraints. We focus
on semi-decentralized communication architectures, where there is a central
coordinator able to gather and broadcast signals of aggregative nature to the
agents. By exploiting the framework of monotone operator theory and operator
splitting, we first critically review the most relevant available algorithms
and then design two novel schemes: (i) a single-layer, fixed-step algorithm
with convergence guarantee for general (non cocoercive, non-strictly) monotone
aggregative games and (ii) a single-layer proximal-type algorithm for a class
of monotone aggregative games with linearly coupled cost functions. We also
design novel accelerated variants of the algorithms via (alternating) inertial
and over-relaxation steps. Finally, we show via numerical simulations that the
proposed algorithms outperform those in the literature in terms of convergence
speed
An asynchronous distributed and scalable generalized Nash equilibrium seeking algorithm for strongly monotone games
In this paper, we present three distributed algorithms to solve a class of Generalized Nash Equilibrium (GNE) seeking problems in strongly monotone games. The first one (SD-GENO) is based on synchronous updates of the agents, while the second and the third (AD-GEED and AD-GENO) represent asynchronous solutions that are robust to communication delays. AD-GENO can be seen as a refinement of AD-GEED, since it only requires node auxiliary variables, enhancing the scalability of the algorithm. Our main contribution is to prove convergence to a v-GNE variational-GNE (vGNE) of the game via an operator-theoretic approach. Finally, we apply the algorithms to network Cournot games and show how different activation sequences and delays affect convergence. We also compare the proposed algorithms to a state-of-the-art algorithm solving a similar problem, and observe that AD-GENO outperforms it.</p