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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.NA2025
Variable-preconditioned transformed primal-dual method for generalized Wasserstein Gradient Flows
Jin Zeng, Dawei Zhan, Ruchi Guo +1
We propose a Variable-Preconditioned Transformed Primal-Dual (VPTPD) method for solving generalized Wasserstein gradient flows based on the structure-preserving JKO scheme. This is…
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…