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A Passivity-Based Analysis of First-Order Momentum-Based Methods — arXiv:2608.05492

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.05492
License (as archived): CC0-1.0
Archived: 2026-10-31T11:09:20.390Z
SHA-256 of the archived text: 5b137023e8a515f182d81ba955fd6def6bd374819b6c67f7a0df48779183d9e7
Stable URL of this page: https://metraipolis.com/documento/dc_366a738e55e4

How to cite

A Passivity-Based Analysis of First-Order Momentum-Based Methods — arXiv:2608.05492 — arXiv (en), https://arxiv.org/abs/2608.05492 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_366a738e55e4 (Metraipolis archive dc_366a738e55e4, sha256 5b137023e8a515f182d81ba955fd6def6bd374819b6c67f7a0df48779183d9e7)

BibTeX

@misc{dc366a738e55e4,
  title = {A Passivity-Based Analysis of First-Order Momentum-Based Methods — arXiv:2608.05492},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.05492},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_366a738e55e4; sha256 5b137023e8a515f182d81ba955fd6def6bd374819b6c67f7a0df48779183d9e7},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.05492. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This paper presents a discrete-time passivity-based analysis of first-order momentum-based methods for a class of functions whose gradient has lower and upper sector bounds of $0$ and $L$, respectively. Through a loop transformation, it is shown that momentum-based methods can be represented as a passive controller in negative feedback with an output strictly passive (OSP) system. The weak passivity theorem is then used to derive explicit hyperparameter conditions under which the shifted gradient asymptotically vanishes. Under an additional assumption that requires the existence of a unique stationary point and excludes arbitrarily small gradients far from that point, convergence of the iterates to the global minimizer is established.

Tema degli esploratori: calcolo e infrastrutture (retro-catalogo arXiv: annunci del 2026-08-07 in eess.SY).
Categorie arXiv: Systems and Control (eess.SY) ; Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2608.05492 — 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 2026-10-31T10:59:37.440Z dalla pagina https://arxiv.org/catchup/eess.SY/2026-08-07?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).