{
  "abstract": "This paper focuses on a class of nonconvex nonsmooth multicomposite optimization problems for training RNNs (Recurrent Neural Networks). We first establish easily verifiable conditions under which an approximate first-order d-stationary point of the problem is guaranteed to be an approximate second-order d-stationary point. Subsequently, we propose a sequential regularized piecewise affine algorithm, SRPA, that minimizes a regularized piecewise affine function at each iteration, where the idea of active-set strategy is incorporated to reduce the computational cost per iteration. Leveraging the aforementioned conditions for second-order d-stationarity, we establish the global convergence of SRPA to second-order d-stationary points and the complexity bound of $ \\mathcal{O}(ε^{-2}) $ for obtaining an $ ε$-approximate second-order d-stationary point. Finally, numerical experiments for training RNNs on synthetic and real-world datasets demonstrate the promising performance of SRPA compared with state-of-the-art algorithms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18325",
  "author_total": 3,
  "authors": [
    {
      "name": "Lingzi Jin"
    },
    {
      "name": "Xiao Wang"
    },
    {
      "name": "Xiaojun Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/746y9gxxnej0r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18325",
  "fulltext_url": null,
  "id": "746y9gxxnej0r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18325",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7213515614",
  "pdf_url": "https://arxiv.org/pdf/2609.18325",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/746y9gxxnej0r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18325",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18325"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A sequential regularized piecewise affine algorithm for nonconvex nonsmooth multicomposite optimization in RNN training",
  "title_text": "A sequential regularized piecewise affine algorithm for nonconvex nonsmooth multicomposite optimization in RNN training",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/746y9gxxnej0r",
  "venue": "arXiv",
  "versions": []
}