Iterative processes based on Fejer mappings with diminishing problem-specific shifts in the arguments are considered. Such structure allows fine-tuning of Fejer processes by directing them toward selected subsets of attracting sets. Use of various Fejer operators provides ample opportunities for decomposition and parallel computations. Subgradient projection algorithms with sequential and simultaneous projections on segmented constraints are considered as an example. To speed up convergence of this type of algorithms the novel step-size rule is proposed.
IACP FEAB RAS, Vladivostok, Russia, December 2008