Pith Number

pith:N56PKYT7

pith:2025:N56PKYT7743JGCVVYLPMU23V3O

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Primal-dual splitting for structured composite monotone inclusions with or without cocoercivity

Hung M. Phan, Matthew K. Tam, Minh N. Dao, Thang D. Truong

A primal-dual splitting algorithm solves structured monotone inclusions without requiring cocoercivity on single-valued operators.

arxiv:2512.10366 v2 · 2025-12-11 · math.OC

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Record completeness

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2 Internet Archive

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4 Citations open

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Claims

C1strongest claim

The proposed algorithm is not only a unification for several contemporary algorithms but also a blueprint to generate new algorithms with graph-based structures using a single transparent convergence analysis. It reduces dimensionality compared with the standard product space technique and yields a larger allowable stepsize range than recent methods.

C2weakest assumption

The set-valued operators are monotone (typically maximally monotone), the linear operators are bounded, and the algorithm parameters (stepsizes and resolvent parameters) can be chosen to satisfy the stated inequalities that guarantee convergence even when single-valued operators lack cocoercivity.

C3one line summary

A new primal-dual splitting algorithm unifies methods for monotone inclusions, handles non-cocoercive operators, reduces dimensionality, and allows larger stepsizes via a single convergence analysis.

References

33 extracted · 33 resolved · 1 Pith anchors

[1] A. Åkerman, E. Chenchene, P. Giselsson, and E. Naldi, Splitting the forward-backward algo- rithm: A full characterization, arXiv:2504.10999

[2] F.J. Aragón-Artacho, R.I. Boţ, and D. Torregrosa-Belén, A primal-dual splitting algorithm for composite monotone inclusions with minimal lifting,Numer. Algorithms93, 103–130 (2023) 2023

[3] F.J. Aragón-Artacho, R. Campoy, and C. López-Pastor, Forward-backward algorithms devised by graphs,SIAM J. Optim.35(4), 2423–2451 (2025) 2025

[4] F.J. Aragón-Artacho, Y. Malitsky, M.K. Tam, and D. Torregrose-Belén, Distributed forward- backward methods for ring networks,Comput Optim Appl.86, 845–870 (2023) 2023

[5] H. Attouch and M. Théra, A general duality principle for the sum of two operators,J. Convex Anal.3, 1–24 (1996) 1996

Receipt and verification

First computed	2026-05-18T03:09:32.712226Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f7cf5627fff36930ab5c2deca6b75dbbbe8bb3996d617477fbffdebb2d8c5fe

Aliases

arxiv: 2512.10366 · arxiv_version: 2512.10366v2 · doi: 10.48550/arxiv.2512.10366 · pith_short_12: N56PKYT7743J · pith_short_16: N56PKYT7743JGCVV · pith_short_8: N56PKYT7

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/N56PKYT7743JGCVVYLPMU23V3O \
  | 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: 6f7cf5627fff36930ab5c2deca6b75dbbbe8bb3996d617477fbffdebb2d8c5fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1dbf514ddd1edeeb0d0ad1608b4a2e86e73a15e7c956a5e47897f5b01b3c0530",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-12-11T07:31:09Z",
    "title_canon_sha256": "2ee6f86678f21abdd1a61d210d1b581b22df302b60ed8042fb2f543f93aa3a1a"
  },
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  "source": {
    "id": "2512.10366",
    "kind": "arxiv",
    "version": 2
  }
}