{
  "annotation_id": "034cbf0d-4b3a-4e69-8c8f-df10153d4aff",
  "date_created": "2026-02-17T05:53:15.698000Z",
  "date_modified": "2026-02-17T05:53:15.698000Z",
  "file_hash": "28566b9414fc3e0abfa82a71acd20b47e796f325052f65c3b50a633fbe96a220",
  "private": false,
  "record": {
    "abstract": "This paper investigates a class of generalized inverse mixed variational inequality problems (GIMVIPs), which consist in finding a vector $\\overline{w}\\in \\R^d$ such that \\[ F(\\bar w)\\in \\Omega \\quad \\text{and} \\quad \\langle h(\\bar w), v-F(\\bar w) \\rangle + g(v)-g(F(\\bar w)) \\ge 0, \\quad \\forall v\\in \\Omega, \\] where \\(h,F:\\R^d\\to\\R^d\\) are single-valued operators, \\(g:\\Omega\\to\\R\\cup\\{+\\infty\\}\\) is a proper function, and \\(\\Omega\\) is a closed convex set.\n  Two novel continuous-time dynamical systems are proposed to study the finite-time and predefined-time stability of solutions to GIMVIPs in finite-dimensional Hilbert spaces. Under suitable assumptions on the involved operators and model parameters, Lyapunov-based techniques are employed to establish finite-time and predefined-time convergence of the generated trajectories.\n  Although both dynamical systems exhibit accelerated convergence, the settling time of the finite-time stable system depends on the initial condition, whereas the predefined-time stable system admits a uniform upper bound on the convergence time that is independent of the initial state and can be explicitly prescribed through user-selected parameters. Moreover, by applying a forward Euler discretization to the continuous-time dynamics, a proximal point-type iterative algorithm is derived, and its fixed-time convergence property is rigorously analyzed. Numerical experiments are provided to illustrate the effectiveness and advantages of the proposed methods.",
    "arxiv_id": "2601.08700",
    "authors": [
      "Nam Van Tran"
    ],
    "categories": [
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Novel Dynamical Systems with Finite-Time and Predefined-Time Stability for Generalized Inverse Mixed Variational Inequality Problems",
    "url": "https://arxiv.org/abs/2601.08700",
    "version": "v2"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e0c89c24-28de-4d09-813d-5ad31fc8cc41",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}