Transformed Primal-Dual Methods with Variable-Preconditioners
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.
Cite
@article{arxiv.2312.12355,
title = {Transformed Primal-Dual Methods with Variable-Preconditioners},
author = {Long Chen and Ruchi Guo and Jingrong Wei},
journal= {arXiv preprint arXiv:2312.12355},
year = {2023}
}