Necessary and Sufficient Criterion for Convergence to a Variational Inequality Solution
A two-part test characterising exactly which sequences in a Hilbert space converge to the unique solution of an elliptic variational inequality with unilateral constraints: the distance to the constraint set must vanish, and the inequality must hold up to a slack of epsilon_n times one plus the norm gap, with the additive constant inside the slack being what makes the condition necessary as well as sufficient. Subsumes the classical Tykhonov and Levitin-Polyak notions, both of which are shown to miss convergent sequences, and motivates the strictly sharper notion of T-well-posedness.
A Convergence Criterion for Elliptic Variational Inequalities
Claudia Gariboldi (Universidad Nacional de Rio Cuarto), Anna Ochal (Jagiellonian University in Krakow), Mircea Sofonea (University of Perpignan Via Domitia, corresponding author) and Domingo A. Tarzi…