Abstract
In this note we present stability results for semicoercive variational inequalities. These include in the symmetric case convex quadratic variational problems that are not necessarily strictly or uniformly convex. Here we investigate only perturbations in the right-hand side of the inequality constraint, which defines the underlying convex set of the variational inequality. Based on a recent abstract discretization theorem we derive sufficient conditions for the norm convergence of the solutions of the perturbed variational inequalities to the solution of the unperturbed one. In detail we consider a finite dimensional variational inequality that describes constrained market equilibria in economics. Further we discuss both a domain integral and a boundary integral variational inequality for Neumann-Signorini problems involving the Laplacian. These nonlinear elliptic boundary value problems model more general unilateral problems in mathematical physics.
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© 1992 Springer-Verlag Berlin Heidelberg
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Gwinner, J. (1992). On Stability for Semicoercive Variational Inequalities Applied to Constrained Market Equilibria and Neumann-Signorini Problems. In: Oettli, W., Pallaschke, D. (eds) Advances in Optimization. Lecture Notes in Economics and Mathematical Systems, vol 382. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51682-5_30
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DOI: https://doi.org/10.1007/978-3-642-51682-5_30
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