Pith Number

pith:IJQDH27X

pith:2026:IJQDH27XNZJP3INKHD4ORZ3QAS

not attested not anchored not stored refs pending

Curvature-Dependent Lower Bounds for Frank-Wolfe

Christophe Roux, Jannis Halbey, Sebastian Pokutta

Frank-Wolfe cannot converge faster than order T to the minus p over p minus one on p-uniformly convex sets for p at least 3.

arxiv:2605.10595 v2 · 2026-05-11 · math.OC

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\usepackage{pith}
\pithnumber{IJQDH27XNZJP3INKHD4ORZ3QAS}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

we establish a matching Ω(T^{-p/(p-1)}) lower bound for every p≥3 under exact line search or short steps, and extend the lower bound to objectives satisfying a Hölderian error bound.

C2weakest assumption

The analysis relies on the dynamics of Frank-Wolfe iterates on simple instances under the assumption that the feasible set is p-uniformly convex for p≥3 and the objective satisfies standard smoothness and convexity.

C3one line summary

Matching Ω(T^{-p/(p-1)}) lower bounds are proven for Frank-Wolfe convergence on p-uniformly convex domains for p ≥ 3.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:04:35.776014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

426033ebf76e52fda1aa38f8e8e7700499dcd6f9566c2e281822d6173cd471ba

Aliases

arxiv: 2605.10595 · arxiv_version: 2605.10595v2 · doi: 10.48550/arxiv.2605.10595 · pith_short_12: IJQDH27XNZJP · pith_short_16: IJQDH27XNZJP3INK · pith_short_8: IJQDH27X

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/IJQDH27XNZJP3INKHD4ORZ3QAS \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 426033ebf76e52fda1aa38f8e8e7700499dcd6f9566c2e281822d6173cd471ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdb693a76827e3b9247dc5bc562d90ee4282e1a47600b2b6285dc5859e51befa",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-11T14:01:13Z",
    "title_canon_sha256": "c7afa1e1a16956f47773ee55483abf8a5346611273bd2edfe54fdd50a5bffd73"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.10595",
    "kind": "arxiv",
    "version": 2
  }
}