3 papers
math.OC2026
Adam-SHANG: A Convergent Adam-Type Method for Stochastic Smooth Convex Optimization
Yaxin Yu, Long Chen, Minfu Feng
We propose Adam-SHANG, a Lyapunov-guided Adam-type method that couples momentum, adaptive preconditioning, and a curvature-aware correction through a more stable lagged-preconditio…
math.OC2026
Deterministic Adam-Inspired Methods with Accelerated Convergence Rate
Yaxin Yu, Long Chen, Zeyi Xu
Adam is widely used, but its convergence theory remains incomplete even in the deterministic full-batch setting because momentum and adaptive preconditioning are tightly coupled. F…
math.OC2026
SHANG++: Robust Stochastic Acceleration under Multiplicative Noise
Yaxin Yu, Long Chen, Minfu Feng
Under the multiplicative noise scaling (MNS) condition, original Nesterov acceleration is provably sensitive to noise and may diverge when gradient noise overwhelms the signal. In…