{
  "abstract": "We study accelerated proximal gradient methods with general stepsizes for convex composite multiobjective optimization, in which every objective is the sum of a smooth convex term and a proper closed convex extended-valued term, and the proximal subproblem retains a separate offset for each objective. The momentum coefficient may depend on the computed trajectory. For a two-parameter root momentum rule we prove boundedness, weighted square summability of the displacements, a merit-function rate of $o(k^{-2})$, and displacement decay of $o(k^{-1})$ whenever the first parameter converges to a value in $(0,1)$; the second parameter need not converge or have bounded total variation. The analysis is organized as a chain of basic estimates, an energy identity, coefficient asymptotics, and auxiliary lemmas that are reused in every regime. For the critical parameter $α=3$ we establish the finite bound $u_0(x^N)\\le 2\\ell R/[N(N+3)]$, square summability of the displacements, displacement decay $O(1/N)$, and convergence of the full sequence to a weak Pareto point. The remaining little-o question at $α=3$ is shown to be exactly the vanishing of a nonnegative critical energy, so it is separated from the large-$O$ estimate rather than left as a missing step. For $1<α<3$ we give the rate $O(N^{-(α-1)})$ and for every $α>0$ the qualitative conclusion $u_0(x^k)\\to0$, $F_i(x^k)\\to c_i$, and $\\sum_k D_k/k<\\infty$. A table summarizes the rate picture over the whole positive range of $α$, and a JOS1 experiment illustrates the predicted little-$o$ separation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06125",
  "author_total": 1,
  "authors": [
    {
      "name": "Chengzhi Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0d6vc0894c4zc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06125",
  "fulltext_url": null,
  "id": "0d6vc0894c4zc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06125",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06125",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0d6vc0894c4zc.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06125",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06125"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "The Convergence Rate of Accelerated Proximal Gradient Methods with General Inertia Term for Convex Composite Multiobjective Optimization",
  "title_text": "The Convergence Rate of Accelerated Proximal Gradient Methods with General Inertia Term for Convex Composite Multiobjective Optimization",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:08Z",
  "url": "https://research.draconitic.com/paper/0d6vc0894c4zc",
  "venue": "arXiv",
  "versions": []
}