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. 
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     author = {A. V. Arutyunov},
     title = {Properties of the {Minimum} {Function} in the {Quadratic} {Problem}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {36--45},
     publisher = {mathdoc},
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     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_1_a2/}
}
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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/