Pith Number

pith:JNJRFGSW

pith:2026:JNJRFGSWXFBAMSEKCOVJAA4M5D

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The Method of Ellipcenters for strongly convex minimization

Eduarda Ferreira, Ramyro Correa, Roger Behling, Vincent Guigues

The Method of Ellipcenters converges linearly for any differentiable strongly convex objective.

arxiv:2605.12820 v1 · 2026-05-12 · math.OC

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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 derive convergence for any differentiable strongly convex objective

C2weakest assumption

That ellipses can be constructed at each step to capture the ill-conditioning of an arbitrary differentiable strongly convex function while preserving the linear rate.

C3one line summary

ME achieves linear convergence for any differentiable strongly convex objective by centering iterates inside carefully chosen ellipses.

References

18 extracted · 18 resolved · 0 Pith anchors

[1] Introducing the method of ellipcenters, a new first order technique for unconstrained optimization.arXiv, 2025 2025

[2] Two-Point Step Size Gradient Methods.IMA Journal of Numerical Analysis, 8(1):141–148, 1988 1988

[3] IMAGING SCIENCES, 2 (1):183-202, 2009 2009

[4] M´ ethode g´ en´ erale pour la r´ esolution des syst` emes d’´ equations simultan´ ees

[5] Practical Methods of Optimization (2nd ed.)New York: John Wiley & Son, 1987 1987

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:12.228237Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b53129a56b94206488a13aa90038ce8c716dbd5680dc77f95aa4a88d69479e5

Aliases

arxiv: 2605.12820 · arxiv_version: 2605.12820v1 · doi: 10.48550/arxiv.2605.12820 · pith_short_12: JNJRFGSWXFBA · pith_short_16: JNJRFGSWXFBAMSEK · pith_short_8: JNJRFGSW

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JNJRFGSWXFBAMSEKCOVJAA4M5D \
  | 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: 4b53129a56b94206488a13aa90038ce8c716dbd5680dc77f95aa4a88d69479e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e2764d165b152e88d7b2fa912333e5331a63a095c2353c16536870a34b4b63c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-12T23:30:07Z",
    "title_canon_sha256": "e392bc6a42612270b221337824b70e25f1566eb46f9f2b7fe51bbbb739478661"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12820",
    "kind": "arxiv",
    "version": 1
  }
}