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math.OC2026
Stochastic Saddle Avoidance Beyond Unit Excitation and Smoothness: A Pathwise Lyapunov-Perron Framework
Junwen Qiu, Bohao Ma, Andre Milzarek +1
Unit excitation (UE) is a common assumption in stochastic saddle avoidance: the stochastic error must have a uniformly positive component along every direction, in expectation. Thi…
math.OC2026
Shuffling the Stochastic Mirror Descent via Dual Lipschitz Continuity and Kernel Conditioning
Junwen Qiu, Leilei Mei, Junyu Zhang
The global Lipschitz smoothness condition underlies most convergence and complexity analyses via two key consequences: the descent lemma and the gradient Lipschitz continuity. How…
math.OC2026
A New Kernel Regularity Condition for Distributed Mirror Descent: Broader Coverage and Simpler Analysis
Junwen Qiu, Ziyang Zeng, Leilei Mei +1
Existing convergence analyses of distributed optimization methods in non-Euclidean geometries typically rely on kernel assumptions: (i) global Lipschitz smoothness and (ii) bi-conv…