Submitted

Transformed Primal-Dual Methods with Variable-Preconditioners

Long Chen, Ruchi Guo and Jingrong Wei

Submitted

arXiv   Bibtex

ABSTRACT:

 This paper introduces a novel Transformed Primal-Dual with
variable-metric/preconditioner (TPDv) algorithm, designed to
efficiently solve affine constrained optimization problems common in
nonlinear partial differential equations (PDEs). Diverging from
traditional methods, TPDv iteratively updates time-evolving
preconditioning operators, enhancing adaptability. The algorithm is
derived and analyzed, demonstrating global linear convergence rates
under mild assumptions. Numerical experiments on challenging nonlinear
PDEs, including the Darcy-Forchheimer model and a nonlinear
electromagnetic problem, showcase the algorithm's superiority over
existing methods in terms of iteration numbers and computational
efficiency. The paper concludes with a comprehensive convergence
analysis.