Pith Number

pith:HKF5WRBM

pith:2024:HKF5WRBM53GPA7QX2KFCNYK355

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A Riemannian gradient descent method for optimization on the indefinite Stiefel manifold

Dinh Van Tiep, Nguyen Thanh Son

A Riemannian gradient descent method on the indefinite Stiefel manifold X^T A X = J converges globally to critical points.

arxiv:2410.22068 v3 · 2024-10-29 · math.OC

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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 ... suggest a Riemannian gradient descent method using the attained materials, whose global convergence is guaranteed. Our results not only cover the known cases, the orthogonal and generalized Stiefel manifolds, but also provide a Riemannian optimization solution for other constrained problems which has not been investigated.

C2weakest assumption

The feasible set X^T A X = J constitutes a differentiable manifold (the indefinite Stiefel manifold) that admits a Riemannian metric allowing construction of the associated geometric structure and a well-defined Cayley retraction.

C3one line summary

Develops Riemannian gradient descent with Cayley retraction on the indefinite Stiefel manifold X^T A X = J, proves global convergence, generalizes orthogonal cases, and applies to eigenvalue problems and Procrustes-type matrix equations.

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

A generalized canonical metric for optimization on the indefinite Stiefel manifold

Receipt and verification

First computed	2026-05-26T01:03:09.536728Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a8bdb442ceeccf07e17d28a26e15bef4662b5875dece7b12a0444faabede767

Aliases

arxiv: 2410.22068 · arxiv_version: 2410.22068v3 · doi: 10.48550/arxiv.2410.22068 · pith_short_12: HKF5WRBM53GP · pith_short_16: HKF5WRBM53GPA7QX · pith_short_8: HKF5WRBM

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HKF5WRBM53GPA7QX2KFCNYK355 \
  | 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: 3a8bdb442ceeccf07e17d28a26e15bef4662b5875dece7b12a0444faabede767

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48d2ce38b6bdcd7238a36e27dfe1c61e8840d44f9b44b0bf67278dbf90f6ad98",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2024-10-29T14:27:52Z",
    "title_canon_sha256": "f69e1e2cc76c4e7715e2a6efefaf7633599c9dce86c4866e6de0609cdaea1a57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2410.22068",
    "kind": "arxiv",
    "version": 3
  }
}