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Accelerated Prox-Level Methods for Unknown Piecewise-Smooth Optimization II: Function-constrained Optimization — arXiv:2609.03251

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.03251
License (as archived): CC0-1.0
Archived: 2026-10-17T02:26:43.181Z
SHA-256 of the archived text: 55ba6539643d32d4c30380e07a92b0465b977f6d9d771d11e35acfb125f0cbff
Stable URL of this page: https://metraipolis.com/documento/dc_fbdb428d451e

How to cite

Accelerated Prox-Level Methods for Unknown Piecewise-Smooth Optimization II: Function-constrained Optimization — arXiv:2609.03251 — arXiv (en), https://arxiv.org/abs/2609.03251 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_fbdb428d451e (Metraipolis archive dc_fbdb428d451e, sha256 55ba6539643d32d4c30380e07a92b0465b977f6d9d771d11e35acfb125f0cbff)

BibTeX

@misc{dcfbdb428d451e,
  title = {Accelerated Prox-Level Methods for Unknown Piecewise-Smooth Optimization II: Function-constrained Optimization — arXiv:2609.03251},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.03251},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_fbdb428d451e; sha256 55ba6539643d32d4c30380e07a92b0465b977f6d9d771d11e35acfb125f0cbff},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.03251. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We introduce an anytime, almost parameter-free algorithm for convex function-constrained optimization, in which the objective and constraint functions are unknown piecewise-smooth. Our algorithm, Restarted Penalty APEX (Penalty Accelerated Prox-level method for Exploring Piecewise Smoothness), is an accelerated bundle-level method based on the penalty approach. For problems satisfying quadratic growth, the proposed method is the first to achieve optimal oracle complexity without knowing the growth modulus or the exact penalty coefficient. Furthermore, Restarted Penalty APEX generates a verifiable certificate that bounds both the optimality gap and the constraint violation. This certificate also appears to be new to the literature.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-04 in math.OC).
Categorie arXiv: Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2609.03251 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T02:07:43.327Z dalla pagina https://arxiv.org/catchup/math.OC/2026-09-04?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).