Metraipolis › archive › dc_ddd62ca191dd

A Local-Linearly Convergent Algorithm for Nonconvex Equality-Constrained Optimization — arXiv:2608.12665

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.12665
License (as archived): CC0-1.0
Archived: 2026-10-19T04:27:49.052Z
SHA-256 of the archived text: f289846f156b4d772d0e3663b0de5c6dd662425a57674b1073df58f6c5d0fb38
Stable URL of this page: https://metraipolis.com/documento/dc_ddd62ca191dd

How to cite

A Local-Linearly Convergent Algorithm for Nonconvex Equality-Constrained Optimization — arXiv:2608.12665 — arXiv (en), https://arxiv.org/abs/2608.12665 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ddd62ca191dd (Metraipolis archive dc_ddd62ca191dd, sha256 f289846f156b4d772d0e3663b0de5c6dd662425a57674b1073df58f6c5d0fb38)

BibTeX

@misc{dcddd62ca191dd,
  title = {A Local-Linearly Convergent Algorithm for Nonconvex Equality-Constrained Optimization — arXiv:2608.12665},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.12665},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ddd62ca191dd; sha256 f289846f156b4d772d0e3663b0de5c6dd662425a57674b1073df58f6c5d0fb38},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.12665. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

For solving nonconvex equality-constrained optimization problems, a recent Gradient-Eigenstep Algorithm by Goyens et al.~is an iteration-efficient approach, based on minimizing Fletcher's augmented Lagrangian function, for finding an approximate second-order stationary point from an arbitrary starting point. In this paper, the analysis of this algorithm is extended, offering a two-fold contribution. First, it is shown that a local-linear rate of convergence can be obtained by this method if it is initiated sufficiently close to a strong second-order stationary point and employs a sufficiently small step-size parameter and sufficiently large penalty parameter. In this case, the algorithm reduces to a gradient descent algorithm applied to minimize Fletcher's augmented Lagrangian. Second, as a particularly useful application of the first result, it is shown that the Gradient-Eigenstep algorithm can be used as an iteration-efficient subproblem solver in the context of a progressive sampling strategy for solving equality-constrained optimization problems when the objective and constraint functions are defined by large sample averages, ultimately offering an algorithm with an improved worst-case sample complexity when compared to an approach that solves a full-sample problem directly.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-08-14 in cs.LG).
Categorie arXiv: Optimization and Control (math.OC) ; Machine Learning (cs.LG); Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2608.12665 — 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 2026-10-19T04:20:35.891Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-08-14?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).