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Multi-Trajectory Parallel-in-Iteration Optimization — arXiv:2611.03621

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.03621
License (as archived): CC0-1.0
Archived: 2026-11-03T18:46:28.768Z
SHA-256 of the archived text: fa283f2ac225231bc7f31a2469f67e8cd66c441378a7e1965fc9daeec6cad828
Stable URL of this page: https://metraipolis.com/documento/dc_3f85dedecb3e

How to cite

Multi-Trajectory Parallel-in-Iteration Optimization — arXiv:2611.03621 — arXiv (en), https://arxiv.org/abs/2611.03621 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_3f85dedecb3e (Metraipolis archive dc_3f85dedecb3e, sha256 fa283f2ac225231bc7f31a2469f67e8cd66c441378a7e1965fc9daeec6cad828)

BibTeX

@misc{dc3f85dedecb3e,
  title = {Multi-Trajectory Parallel-in-Iteration Optimization — arXiv:2611.03621},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.03621},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_3f85dedecb3e; sha256 fa283f2ac225231bc7f31a2469f67e8cd66c441378a7e1965fc9daeec6cad828},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.03621. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Previously, we developed a ``parallel-in-iteration'' optimization framework that uses multigrid reduction-in-time (MGRIT) to parallelize slowly converging optimization methods, such as gradient descent. Unlike time-dependent evolution problems, optimization requires only a final point with a sufficiently small gradient, rather than an accurate approximation of the entire trajectory of iterates. This motivates a different use of MGRIT: instead of repeatedly improving the approximation of a single long trajectory, we introduce restarted MGRIT (R-MGRIT), which performs one MGRIT iteration on a trajectory, takes the approximate final point as a new initial guess, and repeats the process on a new trajectory. Each restart thus defines a new all-at-once system, allowing progress toward the solution without accurately approximating the preceding trajectory. Moreover, we find that these trajectories can be shortened without increasing the number of restarts needed for convergence. We provide theoretical results comparing MGRIT and R-MGRIT for linear problems and demonstrate the convergence behavior of the shortened trajectories numerically for both linear and nonlinear problems. Shortening the trajectories increases the estimated parallel speedup while reducing the number of processors required.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.OC, nuovi lavori del giorno).
Categorie arXiv: Numerical Analysis (math.NA) ; Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2611.03621 — 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 2026-11-03T18:14:37.824Z dalla pagina https://arxiv.org/list/math.OC/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).