What question did this study set out to answer?

The aim is to generalize Mirror Descent to Riemannian manifolds for improved optimization processes.

June 6, 2026Analysis and Applications

Mirror Descent on Riemannian Manifolds

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Authors

JJJiaxin JiangHunan University LSLei ShiTongji University JTJiyuan Tan

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Implication

Randomized trial demonstrates optimized techniques for large-scale problems in Riemannian manifolds, suggesting broad applicability in diverse fields.

Key Points

The aim is to generalize Mirror Descent to Riemannian manifolds for improved optimization processes.
Developed a Riemannian Mirror Descent (RMD) framework via reparameterization.
Introduced a stochastic variant of RMD with convergence guarantees.
Applied RMD to the Stiefel manifold and reduced it to Curvilinear Gradient Descent.
Established non-asymptotic convergence guarantees for both RMD and stochastic RMD.
The RMD framework effectively addresses large-scale manifold optimization problems.
Specialization of stochastic RMD resulted in a stochastic version of Curvilinear Gradient Descent.

Cite This Study

Jiang et al. (2026) studied this question.

synapsesocial.com/papers/6a23b9ca71a5da9775e75a56 https://doi.org/10.1142/s0219530526500521

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Implication

Randomized trial demonstrates optimized techniques for large-scale problems in Riemannian manifolds, suggesting broad applicability in diverse fields.

Mirror Descent on Riemannian Manifolds

Discussion

Member takes

Implication

Key Points

Cite This Study

Mirror Descent on Riemannian Manifolds

Discussion

Member takes

Implication

Key Points

Cite This Study

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