Distributed iterative regularization algorithms for monotone Nash games

Aswin Kannan, Uday V. Shanbhag

Research output: Chapter in Book/Report/Conference proceedingConference contribution

15 Citations (Scopus)

Abstract

In this paper, we consider the development of single-timescale schemes for the distributed computation of Nash equilibria. In general, equilibria associated with convex Nash games over continuous strategy sets are wholly captured by the solution set of a variational inequality. Our focus is on Nash games whose equilibrium conditions are given by monotone variational inequalities, a class referred to as monotone Nash games. Unless suitably strong assumptions (such as strong monotonicity) are imposed on the mapping corresponding to the variational inequality, distributed schemes for computing equilibria often require the solution of a sequence of regularized problems, each of which has a unique solution. Such schemes operate on two timescales and are generally harder to implement in online settings. Motivated by this shortcoming, this work focuses on the development of three single timescale iterative regularization schemes that require precisely one projection step at every iteration. The first is an iterative Tikhonov regularization scheme while the second is an analogously constructed iterative proximal-point method. Both schemes are characterized by the property that the regularization/centering parameter are updated after every iteration, rather than when one has an approximate solution to the regularized problem. Finally, a modified form of the proximal-point scheme is also presented where the weight on the proximal term is updated as well.

Original languageEnglish (US)
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
Pages1963-1968
Number of pages6
DOIs
StatePublished - Dec 1 2010
Event2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States
Duration: Dec 15 2010Dec 17 2010

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other2010 49th IEEE Conference on Decision and Control, CDC 2010
CountryUnited States
CityAtlanta, GA
Period12/15/1012/17/10

Fingerprint

Iterative Regularization
Monotone
Game
Time Scales
Variational Inequalities
Proximal Point
Proximal Point Method
Monotone Variational Inequalities
Iteration
Distributed Computation
General Equilibrium
Tikhonov Regularization
Regularization Parameter
Solution Set
Nash Equilibrium
Unique Solution
Monotonicity
Approximate Solution
Projection
Computing

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Kannan, A., & Shanbhag, U. V. (2010). Distributed iterative regularization algorithms for monotone Nash games. In 2010 49th IEEE Conference on Decision and Control, CDC 2010 (pp. 1963-1968). [5717545] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2010.5717545
Kannan, Aswin ; Shanbhag, Uday V. / Distributed iterative regularization algorithms for monotone Nash games. 2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. pp. 1963-1968 (Proceedings of the IEEE Conference on Decision and Control).
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Kannan, A & Shanbhag, UV 2010, Distributed iterative regularization algorithms for monotone Nash games. in 2010 49th IEEE Conference on Decision and Control, CDC 2010., 5717545, Proceedings of the IEEE Conference on Decision and Control, pp. 1963-1968, 2010 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, GA, United States, 12/15/10. https://doi.org/10.1109/CDC.2010.5717545

Distributed iterative regularization algorithms for monotone Nash games. / Kannan, Aswin; Shanbhag, Uday V.

2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. p. 1963-1968 5717545 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Kannan A, Shanbhag UV. Distributed iterative regularization algorithms for monotone Nash games. In 2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. p. 1963-1968. 5717545. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2010.5717545