{
  "abstract": "We study continuous-time primal-dual dynamics for tracking solutions of time-dependent constrained optimization problems. First, for uniformly strongly convex-strongly concave saddle functions, we establish explicit finite-time tracking and additive-disturbance bounds. For convex problems, we then introduce a directional primal regularization, combined with dual Tikhonov regularization, and quantify the resulting optimization bias and constraint violation. For smooth nonconvex problems, we couple a proximal local convexification with a two-time-scale primal-dual flow and obtain a local tracking result under constraint qualification, second-order sufficiency, and temporal regularity. Numerical traffic-signal experiments at a single intersection evaluate the proposed method under vehicle-throughput and pedestrian-aware objectives, comparing it with standard signal-control schemes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19916",
  "author_total": 2,
  "authors": [
    {
      "name": "Miguel Vaquero"
    },
    {
      "name": "Jorge Cortés"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dmzs3356mg38j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19916",
  "fulltext_url": null,
  "id": "dmzs3356mg38j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19916",
  "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",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7221958836",
  "pdf_url": "https://arxiv.org/pdf/2610.19916",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dmzs3356mg38j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19916",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19916"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "On the Regularization of Primal-Dual Dynamics in Time-Dependent Nonconvex Optimization",
  "title_text": "On the Regularization of Primal-Dual Dynamics in Time-Dependent Nonconvex Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/dmzs3356mg38j",
  "venue": "arXiv",
  "versions": []
}