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A Novel Fractional-Order Accelerated Gradient Descent Method for Nonlinear Optimization with Application to Posture Recognition — arXiv:2608.24766

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.24766
License (as archived): CC0-1.0
Archived: 2026-10-18T06:46:32.714Z
SHA-256 of the archived text: 370ce2c6f53289d64814116f5a3348e06ff6704e56329b2a7d69d5fb68a02edb
Stable URL of this page: https://metraipolis.com/documento/dc_da017bf2f07a

How to cite

A Novel Fractional-Order Accelerated Gradient Descent Method for Nonlinear Optimization with Application to Posture Recognition — arXiv:2608.24766 — arXiv (en), https://arxiv.org/abs/2608.24766 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_da017bf2f07a (Metraipolis archive dc_da017bf2f07a, sha256 370ce2c6f53289d64814116f5a3348e06ff6704e56329b2a7d69d5fb68a02edb)

BibTeX

@misc{dcda017bf2f07a,
  title = {A Novel Fractional-Order Accelerated Gradient Descent Method for Nonlinear Optimization with Application to Posture Recognition — arXiv:2608.24766},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.24766},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_da017bf2f07a; sha256 370ce2c6f53289d64814116f5a3348e06ff6704e56329b2a7d69d5fb68a02edb},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.24766. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This article proposes a Caputo fractional accelerated gradient descent (CFAGD) method for unconstrained optimization problems that is applicable to both smooth and a class of non-smooth objective functions. The proposed approach incorporates an adaptive (\b{eta}k)-parameter, which is heuristically updated throughout the iterative process to improve the search direction. Furthermore, the method employs the Caputo fractional derivative together with the adaptive (\b{eta}^k)-parameter, thereby preserving the memory characteristics associated with non-integer-order derivatives. A suitable step-size is selected via an inexact line-search technique based on the Armijo condition. The central idea is to scale the step-size by a positive parameter to improve the behavior of the iterates as they approach an optimal point, thereby generating a descent sequence. Under strong convexity and bounded Hessian assumptions, linear convergence of the proposed method is established. Numerical validations, including neural-network-based examples, further indicate that the CFAGD method can achieve faster and more stable performance than competing approaches.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-26 in math.OC).
Categorie arXiv: Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2608.24766 — 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 2026-10-18T06:39:24.036Z dalla pagina https://arxiv.org/catchup/math.OC/2026-08-26?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).