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On Stability of Monotone Variational Inequalities in Hilbert Space Via Hausdorff Convergence

Author

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  • Joachim Gwinner

    (Institute of Applied Mathematics, Universität der Bundeswehr München, Department of Aerospace Engineering)

Abstract

This note is concerned with stability of monotone variational inequalities (VIs) in Hilbert spaces. Here we prove a convergence result under appropriate conditions for perturbations not only in the right hand side, but also in the convex functional and in the constraint set. We present a novel approach based on Hausdorff set convergence to handle perturbations in arbitrary closed convex constraint sets. To provide an illustrative application of our abstract stability theory we study a nonlinear nonsmooth unilateral variational problem and derive a new stability result.

Suggested Citation

  • Joachim Gwinner, 2026. "On Stability of Monotone Variational Inequalities in Hilbert Space Via Hausdorff Convergence," Springer Optimization and Its Applications,, Springer.
    • Handle: RePEc:spr:spochp:978-3-032-07860-5_13
    DOI: 10.1007/978-3-032-07860-5_13
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