On distributed generalized nash equilibrium seeking

Sergio Grammatico

doi:10.1007/978-3-030-35032-1_4

On distributed generalized nash equilibrium seeking

Sergio Grammatico^*

^*Corresponding author for this work

Team Bart De Schutter

Research output: Chapter in Book/Conference proceedings/Edited volume › Chapter › Scientific › peer-review

Abstract

Generalized Nash equilibrium problems describe multi-agent systems where each decision maker, or agent, aims at minimizing its individual cost function, yet all are subject to shared, coupling constraints. Distributed algorithms represent viable solution methods for solving generalized Nash equilibrium problems, since they require the agents to optimize and communicate locally, besides agree on the shared resources with selected other agents. The design of efficient solution algorithms is however extremely challenging from a theoretical perspective. In this chapter, we show that operator theory offers the appropriate mathematical tools to design distributed solution methods for generalized Nash equilibrium problems.

Original language	English
Title of host publication	Analytics for the Sharing Economy
Subtitle of host publication	Mathematics, Engineering and Business Perspectives
Editors	Emanuele Crisostom, Bissan Ghaddar, Florian Häusler, Joe Naoum-Sawaya, Giovanni Russo
Place of Publication	Cham, Switzerland
Publisher	Springer
Pages	39-49
ISBN (Electronic)	978-3-030-35032-1
ISBN (Print)	978-3-030-35031-4
DOIs	https://doi.org/10.1007/978-3-030-35032-1_4
Publication status	Published - 2020

Keywords

Control Theory
Generalized nash equilibrium problem
Monotone operator theory
Operator splitting

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10.1007/978-3-030-35032-1_4

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On distributed generalized nash equilibrium seeking. / Grammatico, Sergio.
Analytics for the Sharing Economy: Mathematics, Engineering and Business Perspectives. ed. / Emanuele Crisostom; Bissan Ghaddar; Florian Häusler; Joe Naoum-Sawaya; Giovanni Russo. Cham, Switzerland: Springer, 2020. p. 39-49.

Research output: Chapter in Book/Conference proceedings/Edited volume › Chapter › Scientific › peer-review

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AB - Generalized Nash equilibrium problems describe multi-agent systems where each decision maker, or agent, aims at minimizing its individual cost function, yet all are subject to shared, coupling constraints. Distributed algorithms represent viable solution methods for solving generalized Nash equilibrium problems, since they require the agents to optimize and communicate locally, besides agree on the shared resources with selected other agents. The design of efficient solution algorithms is however extremely challenging from a theoretical perspective. In this chapter, we show that operator theory offers the appropriate mathematical tools to design distributed solution methods for generalized Nash equilibrium problems.

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KW - Monotone operator theory

KW - Operator splitting

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On distributed generalized nash equilibrium seeking

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