Pith Number

pith:CO7X4HHQ

pith:2026:CO7X4HHQBAFAONA2P3TTBSCJL5

not attested not anchored not stored refs pending

Optimal Acceleration for Proximal Minimization of the Sum of Convex and Strongly Convex Functions

Beh\c{c}et A\c{c}{\i}kme\c{s}e, Ernest K. Ryu, Govind M. Chari, Uijeong Jang

Fast Douglas-Rachford Splitting achieves optimal O(1/N²) convergence for sums of convex and strongly convex functions.

arxiv:2605.08593 v2 · 2026-05-09 · math.OC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CO7X4HHQBAFAONA2P3TTBSCJL5}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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 present Fast Douglas--Rachford Splitting (FDR), an accelerated method that improves the constants established in the prior works, and provide a complexity lower bound establishing that both the O(1/N^2) convergence rate and the leading-order constant of FDR's rate are optimal.

C2weakest assumption

The lower bound holds for the general class of convex-plus-strongly-convex problems (or monotone-plus-strongly-monotone operators) without extra structure or restrictions on the proximal operators.

C3one line summary

FDR achieves the optimal O(1/N²) convergence rate with the best leading constant for proximal minimization of convex plus strongly convex functions.

Receipt and verification

First computed	2026-05-21T01:04:27.232352Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13bf7e1cf0080a07341a7ee730c8495f474e54e26ab260c4c0c8fd7b5c5e7c5a

Aliases

arxiv: 2605.08593 · arxiv_version: 2605.08593v2 · doi: 10.48550/arxiv.2605.08593 · pith_short_12: CO7X4HHQBAFA · pith_short_16: CO7X4HHQBAFAONA2 · pith_short_8: CO7X4HHQ

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/CO7X4HHQBAFAONA2P3TTBSCJL5 \
  | 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: 13bf7e1cf0080a07341a7ee730c8495f474e54e26ab260c4c0c8fd7b5c5e7c5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58ff501d4b7e62d45e5cd1bf65ab2f98942855a45ea649f9494f5f78ee3425f5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-09T01:17:24Z",
    "title_canon_sha256": "b764907f518978ab8e27fde567bb48d5269ec51ff018fd48a8aa7ef5ceaf4a1d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.08593",
    "kind": "arxiv",
    "version": 2
  }
}