Abstract
We show that projected-gradient methods for the distributed computation of generalized Nash equilibria in ag- gregative games are preconditioned forward-backward splitting methods appliedto 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 meth- ods. More generally, we provide a unifying operator-theoretic ground to design projected-gradient methods for generalized equilibrium seeking in aggregative games.
| Original language | English |
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| Title of host publication | 2018 European Control Conference, ECC 2018 |
| Place of Publication | Piscataway |
| Publisher | Institute of Electrical and Electronics Engineers |
| Pages | 2188-2193 |
| Number of pages | 6 |
| ISBN (Electronic) | 978-3-9524-2698-2 |
| DOIs | |
| Publication status | Published - 27 Nov 2018 |
| Event | 16th European Control Conference, ECC 2018 - Limassol, Cyprus, Limassol, Cyprus Duration: 12 Jun 2018 → 15 Jun 2018 Conference number: 16 |
Conference
| Conference | 16th European Control Conference, ECC 2018 |
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| Abbreviated title | ECC 2018 |
| Country/Territory | Cyprus |
| City | Limassol |
| Period | 12/06/18 → 15/06/18 |
Funding
G. Belgioioso is with the Control Systems group, TU Eindhoven, The Netherlands. S. Grammatico is with the Delft Center for Systems and Control (DCSC), TU Delft, The Netherlands. E-mail addresses: [email protected], [email protected]. This work was partially supported by the Netherlands Organisation for Scientific Research (NWO) under research projects OMEGA (grant n. 613.001.702) and P2P-TALES (grant n. 647.003.003).