Envelope stepsize control for iterative algorithms based on Fejer processes with attractants

Abstract

Fejer processes are frequently used models for many iterative algorithms in optimization and related areas. They can be combined with different kinds of decomposition schemes and generate various projection-type methods suitable for parallel computations. This paper reviews some recent results on Fejer processes with diminishing disturbances and suggests a new adaptive parameter-free stepsize control rule for such algorithms.

Keywords:

• Fejer processes
• convex optimization
• decomposition
• stepsize control
• subgradient method

AMS Subject Classification :

• 90C25
• 90C52
• 49M27

Acknowledgements

The author wishes to thank G.T. Herman and two anonymous referees for a great amount of meticulous reading of preliminary versions of this paper and many constructive suggestions.

The study was supported by RFBR grant 09-01-90413-Ukr_f_a.