5 papers
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…
A Novel Preconditioning Framework for Solving Nonlinear PDEs based on Fenchel-Rockafellar Duality and Transformed Primal-Dual Techniques
Long Chen, Ruchi Guo, Jingrong Wei +1
A DualTPD method is proposed for solving nonlinear partial differential equations. The method is characterized by three main features. First, decoupling via Fenchel--Rockafellar du…
Accelerated Gradient Methods Through Variable and Operator Splitting
Long Chen, Luo Hao, Jingrong Wei
This paper introduces a unified framework for accelerated gradient methods through the variable and operator splitting (VOS). The operator splitting decouples the optimization proc…
Accelerated Over-Relaxation Heavy-Ball Method: Achieving Global Accelerated Convergence with Broad Generalization
Jingrong Wei, Long Chen
The heavy-ball momentum method accelerates gradient descent with a momentum term but lacks accelerated convergence for general smooth strongly convex problems. This work introduces…
Transformed Primal-Dual Methods with Variable-Preconditioners
Long Chen, Ruchi Guo, Jingrong Wei
This paper introduces a novel Transformed Primal-Dual with variable-metric/preconditioner (TPDv) algorithm, designed to efficiently solve affine constrained optimization problems c…