Stochastic Quasi-Fej\'er Block-Coordinate Fixed Point Iterations with Random Sweeping

Understand

This work proposes block-coordinate fixed point algorithms with applications to nonlinear analysis and optimization in Hilbert spaces.

• The asymptotic analysis relies on a notion of stochastic quasi-Fej\'er monotonicity, which is thoroughly investigated.
• The iterative methods under consideration feature random sweeping rules to select arbitrarily the blocks of variables that are activated over the course of the iterations and they allow for stochastic errors in the evaluation of the operators.
• Algorithms using quasinonexpansive operators or compositions of averaged nonexpansive operators are constructed, and weak and strong convergence results are established for the sequences they generate.