{
  "abstract": "Motivated by networked systems in which equilibrium conditions apply to a regulated state rather than directly to the decision variable, we study transformed-state general variational inequalities. Using a projection-residual reformulation, we develop residual feedback methods that operate in the decision space without inverting the state mapping $H$. For a one-step method, we establish an $\\mathcal{O}(T^{-1/2})$ best-iterate residual rate under solution-restricted cocoercivity and linear convergence under solution-restricted strong monotonicity and residual Lipschitz continuity. We also obtain an $\\mathcal{O}(T^{-1/2})$ best-iterate residual rate for a predictor-corrector method applied to the induced GVI residual under monotonicity and Lipschitz continuity. The assumptions are imposed directly on the computable residual and are illustrated by affine network and rank-deficient examples. Finally, we extend the residual framework to generalized quasi-variational inequalities with decision-dependent feasible sets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36286",
  "author_total": 2,
  "authors": [
    {
      "name": "Griffin Smith"
    },
    {
      "name": "Afrooz Jalilzadeh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dzx65jr5a53ks.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36286",
  "fulltext_url": null,
  "id": "dzx65jr5a53ks",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36286",
  "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": "W7214934159",
  "pdf_url": "https://arxiv.org/pdf/2609.36286",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dzx65jr5a53ks.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36286",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36286"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Residual Feedback for Transformed-State Equilibrium Seeking via General Variational Inequalities",
  "title_text": "Residual Feedback for Transformed-State Equilibrium Seeking via General Variational Inequalities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/dzx65jr5a53ks",
  "venue": "arXiv",
  "versions": []
}