Abstract:
Perturbations of the quadratic form minimization problem under quadratic constraints of the type of equalities are considered. The minimum function ω in this problem which, to each perturbation of the original problem, assigns a sharp lower bound in the perturbed problem is studied. Sufficient conditions for the upper and lower semicontinuity of the minimum function ω both at zero and in its neighborhood are obtained. Examples showing the importance of these conditions are given.
Keywords:
quadratic mapping, quadratic form minimization, minimum function, upper and lower semicontinuity.
Citation:
A. V. Arutyunov, “Properties of the Minimum Function in the Quadratic Problem”, Mat. Zametki, 94:1 (2013), 36–45; Math. Notes, 94:1 (2013), 32–40