173 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
Nash and Wardrop equilibria in aggregative games with coupling constraints
We consider the framework of aggregative games, in which the cost function of
each agent depends on his own strategy and on the average population strategy.
As first contribution, we investigate the relations between the concepts of
Nash and Wardrop equilibrium. By exploiting a characterization of the two
equilibria as solutions of variational inequalities, we bound their distance
with a decreasing function of the population size. As second contribution, we
propose two decentralized algorithms that converge to such equilibria and are
capable of coping with constraints coupling the strategies of different agents.
Finally, we study the applications of charging of electric vehicles and of
route choice on a road network.Comment: IEEE Trans. on Automatic Control (Accepted without changes). The
first three authors contributed equall
Projected-gradient algorithms for generalized equilibrium seeking in Aggregative Games are preconditioned Forward-Backward methods
We show that projected-gradient methods for the distributed computation of
generalized Nash equilibria in aggregative games are preconditioned
forward-backward splitting methods applied to the KKT operator of the game.
Specifically, we adopt the preconditioned forward-backward design, recently
conceived by Yi and Pavel in the manuscript "A distributed primal-dual
algorithm for computation of generalized Nash equilibria via operator splitting
methods" for generalized Nash equilibrium seeking in aggregative games.
Consequently, we notice that two projected-gradient methods recently proposed
in the literature are preconditioned forward-backward methods. More generally,
we provide a unifying operator-theoretic ground to design projected-gradient
methods for generalized equilibrium seeking in aggregative games
A relaxed-inertial forward-backward-forward algorithm for Stochastic Generalized Nash equilibrium seeking
In this paper we propose a new operator splitting algorithm for distributed
Nash equilibrium seeking under stochastic uncertainty, featuring relaxation and
inertial effects. Our work is inspired by recent deterministic operator
splitting methods, designed for solving structured monotone inclusion problems.
The algorithm is derived from a forward-backward-forward scheme for solving
structured monotone inclusion problems featuring a Lipschitz continuous and
monotone game operator. To the best of our knowledge, this is the first
distributed (generalized) Nash equilibrium seeking algorithm featuring
acceleration techniques in stochastic Nash games without assuming cocoercivity.
Numerical examples illustrate the effect of inertia and relaxation on the
performance of our proposed algorithm
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