Pith Number

pith:6TWU7XGD

pith:2026:6TWU7XGDA3B7PVEKVTDIXD6F6S

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A Proximal Gradient Framework for Composite Multiobjective Optimization on Riemannian Manifolds

Kangming Chen

A proximal gradient method converges composite multiobjective optimization problems on Riemannian manifolds to Pareto stationary points at an O(1/k) rate.

arxiv:2605.16731 v1 · 2026-05-16 · math.OC

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Claims

C1strongest claim

establishes global convergence to Pareto stationary points, together with an O(1/k) convergence rate

C2weakest assumption

The composite structure of the vector-valued objective functions and the Riemannian manifold admit well-defined proximal mappings and retraction operations that preserve the necessary descent properties (implicit in the framework description for composite optimization problems on manifolds).

C3one line summary

The Riemannian Multiobjective Proximal Gradient Method (RMPGM) directly optimizes vector-valued composite objectives on Riemannian manifolds and converges globally to Pareto stationary points with an O(1/k) rate.

References

31 extracted · 31 resolved · 0 Pith anchors

[1] Absil, P.-A., Mahony, R., Sepulchre, R.: Optimization Algorithms on Matrix Manifolds, p. 224. Princeton University Press, Princeton, NJ (2008) 2008

[2] Cambridge University Press 2023 · doi:10.1017/9781009166164

[3] Foundations of Computational Mathematics7, 303–330 (2007) 2007

[4] Computational and Applied Mathematics45(4), 151 (2026) 2026

[5] SIAM Journal on Optimization32(4), 2690–2717 (2022) 2022

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:02:38.830668Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f4ed4fdcc306c3f7d48aacc68b8fc5f4a8f0d8dd88f10f0036275485f639c362

Aliases

arxiv: 2605.16731 · arxiv_version: 2605.16731v1 · doi: 10.48550/arxiv.2605.16731 · pith_short_12: 6TWU7XGDA3B7 · pith_short_16: 6TWU7XGDA3B7PVEK · pith_short_8: 6TWU7XGD

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6TWU7XGDA3B7PVEKVTDIXD6F6S \
  | 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: f4ed4fdcc306c3f7d48aacc68b8fc5f4a8f0d8dd88f10f0036275485f639c362

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf7d1a6be0e76f18244fd6de915ede10ff8d2bc167a0aeb58d45e0e492279425",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-16T00:47:45Z",
    "title_canon_sha256": "e1209c6b9dd5c09013587d47e1aa968b29be1456161fbd584cdc80bcbe90fb68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16731",
    "kind": "arxiv",
    "version": 1
  }
}