110 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
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
Distributed Generalized Nash Equilibrium Seeking for Energy Sharing Games
With the proliferation of distributed generators and energy storage systems,
traditional passive consumers in power systems have been gradually evolving
into the so-called "prosumers", i.e., proactive consumers, which can both
produce and consume power. To encourage energy exchange among prosumers, energy
sharing is increasingly adopted, which is usually formulated as a generalized
Nash game (GNG). In this paper, a distributed approach is proposed to seek the
Generalized Nash equilibrium (GNE) of the energy sharing game. To this end, we
convert the GNG into an equivalent optimization problem. A
Krasnosel'ski{\v{i}}-Mann iteration type algorithm is thereby devised to solve
the problem and consequently find the GNE in a distributed manner. The
convergence of the proposed algorithm is proved rigorously based on the
nonexpansive operator theory. The performance of the algorithm is validated by
experiments with three prosumers, and the scalability is tested by simulations
using 123 prosumers
Tracking-based distributed equilibrium seeking for aggregative games
We propose fully-distributed algorithms for Nash equilibrium seeking in
aggregative games over networks. We first consider the case where local
constraints are present and we design an algorithm combining, for each agent,
(i) the projected pseudo-gradient descent and (ii) a tracking mechanism to
locally reconstruct the aggregative variable. To handle coupling constraints
arising in generalized settings, we propose another distributed algorithm based
on (i) a recently emerged augmented primal-dual scheme and (ii) two tracking
mechanisms to reconstruct, for each agent, both the aggregative variable and
the coupling constraint satisfaction. Leveraging tools from singular
perturbations analysis, we prove linear convergence to the Nash equilibrium for
both schemes. Finally, we run extensive numerical simulations to confirm the
effectiveness of our methods and compare them with state-of-the-art distributed
equilibrium-seeking algorithms
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
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