Riemannian stochastic fixed point optimization algorithm

This paper considers a stochastic optimization problem over the fixed point sets of quasinonexpansive mappings on Riemannian manifolds. The enables us to consider hierarchical problems complicated sets, such as intersection many closed convex set all minimizers nonsmooth function, and sublevel functions. We focus adaptive learning rate algorithms, which adapt step-sizes (referred rates in machine field) find optimal solutions quickly. then propose algorithm, combines approximation methods manifolds with algorithms. also give convergence analyses proposed algorithm for smooth nonconvex optimization. analysis results indicate that, small constant step-sizes, approximates solution problem. Consideration case step-size sequences are diminishing demonstrates that solves guaranteed rate. provides numerical comparisons demonstrate effectiveness algorithms formulas based Adam AMSGrad.