Geodesic
Properties of the Minimum Function in the Quadratic Problem
Matematičeskie zametki, Tome 94 (2013) no. 1, pp. 36-45

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Perturbations of the quadratic form minimization problem under quadratic constraints of the type of equalities are considered. The minimum function $\omega$ 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 $\omega$ 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. 
A. V. Arutyunov. Properties of the Minimum Function in the Quadratic Problem. Matematičeskie zametki, Tome 94 (2013) no. 1, pp. 36-45. http://geodesic.mathdoc.fr/item/MZM_2013_94_1_a2/
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