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Mini-Batch Stochastic Krasnosel'ski\uı-Mann Algorithm for Nonexpansive Fixed Point Problems
Hideaki Iiduka
The Krasnosel'ski\uı-Mann algorithm is a well-known method for finding fixed points of a nonexpansive mapping with strong theoretical guarantees. However, there are practical large…
Mini-Batch Stochastic Halpern Algorithm for Nonexpansive Fixed Point Problems
Hideaki Iiduka
The Halpern algorithm is a powerful fixed point approximation method for finding the closest point in the fixed point set of a nonexpansive mapping to the initial point. However, i…
A general framework of Riemannian adaptive optimization methods with a convergence analysis
Hiroyuki Sakai, Hideaki Iiduka
This paper proposes a general framework of Riemannian adaptive optimization methods. The framework encapsulates several stochastic optimization algorithms on Riemannian manifolds a…
Convergence of Riemannian Stochastic Gradient Descent on Hadamard Manifold
Hiroyuki Sakai, Hideaki Iiduka
Novel convergence analyses are presented of Riemannian stochastic gradient descent (RSGD) on a Hadamard manifold. RSGD is the most basic Riemannian stochastic optimization algorith…