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Convergence Analysis of Newton Methods for Nonlinear Optimal Control Problems — arXiv:2609.30117

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.30117
License (as archived): CC0-1.0
Archived: 2026-10-08T06:07:19.946Z
SHA-256 of the archived text: 297912424788cb096c2c16fc5ccdac79acc7f9c5acc97ce866c9433591bf9968
Stable URL of this page: https://metraipolis.com/documento/dc_87f6c8ff9817

How to cite

Convergence Analysis of Newton Methods for Nonlinear Optimal Control Problems — arXiv:2609.30117 — arXiv (en), https://arxiv.org/abs/2609.30117 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_87f6c8ff9817 (Metraipolis archive dc_87f6c8ff9817, sha256 297912424788cb096c2c16fc5ccdac79acc7f9c5acc97ce866c9433591bf9968)

BibTeX

@misc{dc87f6c8ff9817,
  title = {Convergence Analysis of Newton Methods for Nonlinear Optimal Control Problems — arXiv:2609.30117},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.30117},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_87f6c8ff9817; sha256 297912424788cb096c2c16fc5ccdac79acc7f9c5acc97ce866c9433591bf9968},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.30117. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The main purpose of this paper is to establish the local quadratic convergence of Newton's method for nonlinear optimal control problems. Under suitable smoothness assumptions, the cost functional is first shown to be twice G{â}teaux differentiable with respect to the control. An explicit operator representation of its second derivative is derived, and its continuity in different control spaces is examined. The second-order coercivity condition in $L^2(0,T;\maathbb{R}^m)$ is then shown to be equivalent to the existence of a strongly regular solution to an associated matrix Riccati differential equation, thereby expressing an infinite-dimensional quadratic-form condition in terms of the solvability of a matrix differential equation. On this basis, local quadratic convergence of Newton's method in $L^\infty(0,T;\maathbb{R}^m)$ is established using linear-quadratic optimal control theory. Under suitable structural assumptions, local quadratic convergence in $L^2(0,T;\maathbb{R}^m)$ is also established. Explicit estimates of the corresponding convergence neighborhoods are derived, and the theoretical results are illustrated by numerical examples.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-25 in math.OC).
Categorie arXiv: Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2609.30117 — 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 2026-10-08T05:31:31.176Z dalla pagina https://arxiv.org/catchup/math.OC/2026-09-25?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).