arXiv subjects

Giuseppe Belgioioso

Publications and source records attributed to Giuseppe Belgioioso.

39 records · Page 3Linked to original sources

arXiv2018

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.

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arXiv2018

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.

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arXiv2018

On the convergence of discrete-time linear systems: A linear time-varying Mann iteration converges iff the operator is strictly pseudocontractive

We adopt an operator-theoretic perspective to study convergence of linear fixed-point iterations and discrete- time linear systems. We mainly focus on the so-called Krasnoselskij-Mann iteration x(k+1) = ( 1 - α(k) ) x(k) + α(k) A x(k), which is relevant for distributed computation in optimization and game theory, when A is not available in a centralized way. We show that convergence to a vector in the kernel of (I-A) is equivalent to strict pseudocontractiveness of the linear operator x -> Ax. We also characterize some relevant operator-theoretic properties of linear operators via eigenvalue location and linear matrix inequalities. We apply the convergence conditions to multi-agent linear systems with vanishing step sizes, in particular, to linear consensus dynamics and equilibrium seeking in monotone linear-quadratic games.

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