{
  "abstract": "We develop an adaptive acceleration of generalized conditional gradient methods for convex objectives with a strongly convex regularizer. A computable primal--dual residual certifies Lyapunov decrease without evaluating the regularizer or any Hessian. Each iteration accepts a balanced accelerated trial when the residual is nonpositive; otherwise it takes a mirror-descent step with doubling backtracking and sets the auxiliary parameter explicitly from the dual decrease and the stopping gap. Under uniform strong-convexity and smoothness bounds on the relevant sublevel set, the method converges globally at a linear rate. Near a nondegenerate minimizer, balanced trials pass above a fixed curvature threshold. The adaptive curvature updates then guarantee a positive fraction of accelerated steps and a local accelerated rate. The method applies directly to entropically regularized Jordan--Kinderlehrer--Otto (JKO) steps whose energies contain nonlocal interaction terms with nondiagonal Hessians. Experiments on JKO steps for granular media and for Poisson--Nernst--Planck systems, in one and three dimensions, show that the method reduces both oracle calls and computing time by a large fraction compared with generalized conditional gradient methods with fixed or adaptive step sizes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25473",
  "author_total": 2,
  "authors": [
    {
      "name": "Long Chen"
    },
    {
      "name": "Zeyi Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1qy4cc5m84jpv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25473",
  "fulltext_url": null,
  "id": "1qy4cc5m84jpv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25473",
  "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": "W7223048123",
  "pdf_url": "https://arxiv.org/pdf/2610.25473",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1qy4cc5m84jpv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25473",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25473"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Acceleration of Generalized Conditional Gradient Methods",
  "title_text": "Acceleration of Generalized Conditional Gradient Methods",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/1qy4cc5m84jpv",
  "venue": "arXiv",
  "versions": []
}