{
  "abstract": "Nonlinear Constrained Optimisation (NCO) requires simultaneous satisfaction of the Karush-Kuhn-Tucker (KKT) conditions. Existing methods enforce these conditions through projections, penalties, barriers, or sequential approximations, potentially introducing computational complexity and convergence difficulties. For nonconvex problems, a KKT point need not be a local optimum. This paper reformulates NCO as stabilisation of a unified KKT sliding residual manifold and develops SM-KKT, a projection-free solver. Stationarity, equality feasibility, and regularised Fischer-Burmeister complementarity are integrated into a unified residual system, with complementarity encoding inequality feasibility, dual feasibility, and complementary slackness. The manifold's zero set is shown to be equivalent to the KKT conditions. The required Jacobian saddle-point inertia is characterised and shown, under stated assumptions, to be equivalent to the simultaneous satisfaction of the Linear Independence Constraint Qualification (LICQ) and Second-Order Sufficient Condition (SOSC). This characterisation establishes local stability of the structured correction algorithm under these conditions and distinguishes nondegenerate locally optimal KKT solutions from points failing second-order optimality. SM-KKT computes structured primal--dual corrections and applies a discrete sliding reaching law to drive the KKT residual into a prescribed boundary layer in finite time. Four nonlinear benchmarks show recovery of reference constrained optima with KKT residuals below $10^{-6}$, earlier boundary-layer reaching, and favourable KKT accuracy compared with projected primal-dual, augmented-Lagrangian, quadratic-penalty, and log-barrier baselines.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15545",
  "author_total": 2,
  "authors": [
    {
      "name": "Abdelhafid Zenati"
    },
    {
      "name": "Kamal Youcef-Toumi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8eg7q6485p2yq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15545",
  "fulltext_url": null,
  "id": "8eg7q6485p2yq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15545",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2612|Advanced Optimization Algorithms Research"
    ]
  ],
  "openalex": "W7221811267",
  "pdf_url": "https://arxiv.org/pdf/2610.15545",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8eg7q6485p2yq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15545",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15545"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "KKT Residual Sliding Manifolds: A Projection-Free Structured Finite-Time Solver for Nonlinear Constrained Optimisation",
  "title_text": "KKT Residual Sliding Manifolds: A Projection-Free Structured Finite-Time Solver for Nonlinear Constrained Optimisation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/8eg7q6485p2yq",
  "venue": "arXiv",
  "versions": []
}