Pith Number

pith:HKUGEYQO

pith:2025:HKUGEYQOA6XDW5SRXMOOSDSOP4

not attested not anchored not stored refs pending

The Golden Ratio Proximal ADMM with Norm Independent Step-Sizes for Separable Convex Optimization

Santanu Soe, V. Vetrivel

Two new step-size rules let golden-ratio proximal ADMM solve separable convex problems without operator norm estimates.

arxiv:2510.05779 v3 · 2025-10-07 · math.OC

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\pithnumber{HKUGEYQOA6XDW5SRXMOOSDSOP4}

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4 Citations 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 propose two step-size strategies for the Golden ratio proximal ADMM (GrpADMM) to solve linearly constrained separable convex optimization problems. Both strategies eliminate explicit operator norm estimates by relying on inexpensive local information computed at the current iterate and requiring no backtracking.

C2weakest assumption

Under standard assumptions, we establish global convergence of the generated iterates and derive sublinear convergence rates for both algorithms.

C3one line summary

Two norm-independent step-size strategies for golden-ratio proximal ADMM are proposed, with global convergence and sublinear rates proved under standard assumptions for separable convex problems.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-19T16:09:51.486879Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3aa862620e07ae3b7651bb1ce90e4e7f32a19169e82636ba2d102b1fd4b0cd51

Aliases

arxiv: 2510.05779 · arxiv_version: 2510.05779v3 · doi: 10.48550/arxiv.2510.05779 · pith_short_12: HKUGEYQOA6XD · pith_short_16: HKUGEYQOA6XDW5SR · pith_short_8: HKUGEYQO

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HKUGEYQOA6XDW5SRXMOOSDSOP4 \
  | 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: 3aa862620e07ae3b7651bb1ce90e4e7f32a19169e82636ba2d102b1fd4b0cd51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48914145e8e5d18d8afd9821e201b827ea4edd363b39ab24f7a1b6690d80333a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-10-07T10:48:53Z",
    "title_canon_sha256": "24975db7a15374c01fc7433f1afa0b6330cd5584e46b7064d6d1951712e3bbcc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.05779",
    "kind": "arxiv",
    "version": 3
  }
}