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math.OC2026
A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization
Jinlin Liu, Song Chen, Jiaxu Liu +1
This paper studies smoothed matrix-polar spectral gradient flows for unconstrained matrix-valued optimization.The canonical polar-factor map loses smoothness at rank-deficient matr…
math.OC2026
A Backstepping Framework for Unconstrained Accelerated Optimization Algorithms
Song Chen, Jiaxu Liu, Chao Xu
This paper introduces a control-theoretic perspective on unconstrained optimization algorithms using the backstepping methods. We model the optimization process as an augmented str…