Coderivatives of a Karush–Kuhn–Tucker point set map and applications

The problem of minimizing a linear–quadratic function over the Euclidean ball is encountered frequently in the theory of trust-region methods in nonlinear programming. By some tools from Variational Analysis, we investigate the stability of the Karush–Kuhn–Tucker point set map of that problem with respect to total perturbations of its data. Verifiable sufficient conditions for the local Lipschitz-like property of the map are obtained, and the connection of our results with the existing criteria for the lower semicontinuity of this Karush–Kuhn–Tucker point set map is shown.