
Journal of Convex Analysis 30 (2023), No. 4, 13791390 Copyright Heldermann Verlag 2023 A Lower Bound for a Condition Number Theorem of Variational Inequalities Tullio Zolezzi DIMA, University of Genova, Italy zolezzi@dima.unige.it Nonlinear variational inequalities in Banach spaces are considered. A suitable notion of condition number with respect to the righthand side is introduced. A distance among variational inequalities is defined. Based on a new criterion about the Lipschitz property of setvalued mappings, it is shown that the distance to suitably restricted illconditioned variational inequalities is bounded from below by the reciprocal of the condition number. By using a similar upper bound of the companion paper "An upper bound for a condition number theorem of variational inequalities", we obtain a full condition number theorem for variational inequalities. The particular case of convex minimization problems is considered. Known results dealing with optimization problems are thereby generalized. Keywords: Variational inequalities, Lipschitz setvalued mappings, condition number theorems. MSC: 49J40, 49K40, 49J53, 90C31. [ Fulltextpdf (104 KB)] for subscribers only. 