Pith. sign in

REVIEW 3 cited by

Transformed Primal-Dual Methods with Variable-Preconditioners

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2312.12355 v1 pith:JVRTTIP5 submitted 2023-12-19 math.NA cs.NA

Long Chen , Ruchi Guo , Jingrong Wei This is my paper
classification math.NAcs.NA
keywords algorithmmethodsnonlinearconvergencepdesprimal-dualtpdvtransformed
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original 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.

Discussion (0). Sign in to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Inexact projected preconditioned gradient methods with variable metrics: a Lyapunov convergence theory (extended version)

    math.OC 2025-06 conditional novelty 7.0 of 10

    Inexact projected preconditioned gradient methods with variable metrics are shown to converge exponentially in continuous time and linearly in discrete time via a new Lyapunov analysis.

  2. Variable-preconditioned transformed primal-dual method for generalized Wasserstein Gradient Flows

    math.NA 2025-09 conditional novelty 6.0 of 10

    VPTPD is a variable-preconditioned transformed primal-dual algorithm for dynamic JKO schemes that reports large speedups over prior primal-dual methods in 1D to 3D numerical tests.

  3. Parallel multilevel methods for solving the Darcy--Forchheimer model based on a nearly semicoercive formulation

    math.NA 2025-07 conditional novelty 5.0 of 10

    Darcy-Forchheimer mixed finite element problems are recast as nearly semicoercive convex programs and solved by a multilevel additive Schwarz method with epsilon-robust convergence.

Pith tools