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math.OC2025
A Generalized Energy-Based Adaptive Gradient Method for Optimization
Lin Feng, Hailiang Liu
Adaptive Gradient Descent with Energy (AEGD) is a variant of Gradient Descent (GD) designed to address step size sensitivity through an energy-based formulation. AEGD is notable fo…
math.OC2025
Variational structure of Fokker-Planck equations with variable mobility
Hailiang Liu, Athanasios E. Tzavaras
We study Fokker--Planck equations with symmetric, positive definite mobility matrices capturing diffusion in heterogeneous environments. A weighted Wasserstein metric is introduced…