Pith. sign in

REVIEW 3 cited by

An Affine Invariant Linear Convergence Analysis for Frank-Wolfe Algorithms

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 1312.7864 v2 pith:UHKU75Q7 submitted 2013-12-30 math.OC

Simon Lacoste-Julien , Martin Jaggi This is my paper · ORCID
classification math.OC
keywords convergencefrank-wolfelinearalgorithmsaffinealgorithmconstantsdomain
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

We study the linear convergence of variants of the Frank-Wolfe algorithms for some classes of strongly convex problems, using only affine-invariant quantities. As in Guelat & Marcotte (1986), we show the linear convergence of the standard Frank-Wolfe algorithm when the solution is in the interior of the domain, but with affine invariant constants. We also show the linear convergence of the away-steps variant of the Frank-Wolfe algorithm, but with constants which only depend on the geometry of the domain, and not any property of the location of the optimal solution. Running these algorithms does not require knowing any problem specific parameters.

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. Linear Convergence of the Frank-Wolfe Algorithm over Product Polytopes

    math.OC 2025-05 conditional novelty 7.0 of 10

    For product polytopes, the pyramidal width composes as sqrt(δ1²δ2²/(δ1²+δ2²)) and the vertex-facet distance as the componentwise minimum, which yields linear convergence of Away Frank-Wolfe for PL objectives.

  2. Variable Smoothing for Weakly Convex Problems with Non-Euclidean Directions

    math.OC 2026-08 conditional novelty 6.0 of 10

    MELMO provably matches the best known convergence rates for weakly convex composite optimization while allowing non-Euclidean update directions.

  3. An Absolute-Error Proximal Bundle Method through the Lens of Frank-Wolf

    math.OC 2024-11 conditional novelty 6.0 of 10

    A modified proximal bundle method with a fixed absolute accuracy null-step test is shown via Frank-Wolfe duality to have O(ε^{-4/5} log^{2/5}(1/ε)) iteration complexity.

Pith tools