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In this paper, a new optimization framework is defined that includes theoptimization framework recently proposed in [1]-[2] as a special case. Theconvex optimization in [1]-[2] includes centralized optimization anddistributed optimization over random networks, so does the optimization definedhere. It is shown that the proposed algorithm in [2] converges almost surelyand in mean square to a solution of the optimization problem here undersuitable assumptions.

Convex Optimization over Fixed Value Point Set of Quasi-Nonexpansive Random Operators on Hilbert Spaces