Computing Fixed Points by Averaging

  • Thomas L. Magnanti
  • Georgia Perakis
Part of the Applied Optimization book series (APOP, volume 63)

Abstract

Averaging methods for solving fixed point problems combine the underlying fixed point map T with some “well-behaved” map g. The map g might, for example, be contractive or might be a nonexpansive map whose fixed points include those of the original map T. One class of averaging methods (inside averaging) averages any current iterate with its image under the map g, and then applies the map T. Another averaging method (outside averaging) first applies the maps T and g and then takes averages. When g is the identity map, outside averaging averages a given point with its image under the map T. In this paper we summarize a number of known results concerning these averaging methods, including (i) a general averaging framework that approximates the original fixed point problem with a trajectory of averaged (parametrized) fixed point subproblems, and (ii) a procedure for following these trajectories approximately to ease the computations.

Keywords

Variational Inequality Average Method Variational Inequality Problem Point Solution Function Iteration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Thomas L. Magnanti
  • Georgia Perakis

There are no affiliations available

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