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Random Function Iterations for Consistent Stochastic Feasibility
We study the convergence of stochastic fixed point iterations in the
consistent case (in the sense of Butnariu and Fl{\aa}m (1995)) in several
different settings, under decreasingly restrictive regularity assumptions of
the fixed point mappings. The iterations are Markov chains and, for the
purposes of this study, convergence is understood in very restrictive terms. We
show that sufficient conditions for geometric (linear) convergence in
expectation of stochastic projection algorithms presented in Nedi\'c (2011),
are in fact necessary for geometric (linear) convergence in expectation more
generally of iterated random functions.Comment: 29 pages, 4 figure