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arXiv · 2312.12355

Transformed Primal-Dual Methods with Variable-Preconditioners

Long Chen·Ruchi Guo·Jingrong Wei
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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.

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Long Chen, Ruchi Guo, Jingrong Wei. 2023-12-19. Transformed Primal-Dual Methods with Variable-Preconditioners. https://arxiv.org/abs/2312.12355

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