Pith. sign in

REVIEW 3 cited by

Splitting the Forward-Backward Algorithm: A Full Characterization

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 2504.10999 v1 pith:R6KOJO22 submitted 2025-04-15 math.OC

Anton {AA}kerman , Enis Chenchene , Pontus Giselsson , Emanuele Naldi This is my paper · ORCID
classification math.OC
keywords methodscocoerciveevaluationsminimalmonotoneoperatorssplittingachieve
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We study frugal splitting algorithms with minimal lifting for solving monotone inclusion problems involving sums of maximal monotone and cocoercive operators. Building on a foundational result by Ryu, we fully characterize all methods that use only individual resolvent evaluations, direct evaluations of cocoercive operators, and minimal memory resources while ensuring convergence via averaged fixed-point iterations. We show that all such methods are captured by a unified framework, which includes known schemes and enables new ones with promising features. Systematic numerical experiments lead us to propose three design heuristics to achieve excellent performances in practice, yielding significant gains over existing methods.

Discussion (0). Continue with ORCID 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. A frugal primal-dual splitting with minimal lifting over arbitrary rooted trees

    math.OC 2026-07 conditional novelty 7.0 of 10

    A new tree-structured primal-dual splitting algorithm solves a broad class of monotone inclusions with minimal lifting, recovering Douglas–Rachford and Chambolle–Pock as special cases.

  2. Relocated Fixed-Point Iterations with Applications to Variable Stepsize Resolvent Splitting

    math.OC 2025-07 accept novelty 7.0 of 10

    The relocated fixed-point iteration framework proves weak convergence of variable-stepsize Douglas-Rachford and resolvent splitting methods without requiring a common fixed point.

  3. A primal-dual splitting algorithm for monotone inclusions with applications

    math.OC 2026-06 unverdicted novelty 6.0 of 10

    A new primal-dual splitting method for structured monotone inclusions that generalizes prior algorithms, requires one resolvent evaluation per step, and proves weak convergence under monotonicity plus strong convergen...

Pith tools