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

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

Chapter 13 in Convex and Variational Analysis with Applications, 2026, pp 255-265 from Springer

Abstract: 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.

Keywords: Monotone variational inequality; Projection to closed convex set; Coercivity; Hausdorff set convergence; Unilateral constraint; Nonsmooth convex functional; 49J40; 49K40; 35J87 (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-032-07860-5_13

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DOI: 10.1007/978-3-032-07860-5_13

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