3 papers
math.NA2026
Average block nonlinear Kaczmarz methods with adaptive momentum for nonlinear systems of equations
Renjie Ding, Dongling Wang, Jun Zou
The Kaczmarz method is widely recognized as an efficient iterative algorithm for solving large-scale linear systems, owing to its simplicity and low memory requirements. However, t…
math.NA2025
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…
math.OC2025
Inexact projected preconditioned gradient methods with variable metrics: a Lyapunov convergence theory (extended version)
Ruchi Guo, Jun Zou
Projected gradient methods are widely used for constrained optimization. A key application is for partial differential equations (PDEs), where the objective functional represents p…