Stability of Linear-Quadratic Minimization over Euclidean Balls

Stability properties of the problem of minimizing a (nonconvex) linear-quadratic function over an Euclidean ball, known as the trust-region subproblem, are studied in this paper. We investigate in detail the case where the linear part of the objective function is perturbed and obtain necessary and sufficient conditions for the upper/lower semicontinuity of the Karush-Kuhn-Tucker point set map and the global solution map, explicit formulas for computing the directional derivative and the Fréchet derivative of the optimal value function. Stability of the Karush-Kuhn-Tucker point set under the perturbation of the quadratic form is also studied.