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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2013_94_1_a2,
     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},
     volume = {94},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_1_a2/}
}
TY  - JOUR
AU  - A. V. Arutyunov
TI  - Properties of the Minimum Function in the Quadratic Problem
JO  - Matematičeskie zametki
PY  - 2013
SP  - 36
EP  - 45
VL  - 94
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_94_1_a2/
LA  - ru
ID  - MZM_2013_94_1_a2
ER  - 
%0 Journal Article
%A A. V. Arutyunov
%T Properties of the Minimum Function in the Quadratic Problem
%J Matematičeskie zametki
%D 2013
%P 36-45
%V 94
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_94_1_a2/
%G ru
%F MZM_2013_94_1_a2
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/

[1] A. V. Arutyunov, “Neotritsatelnost kvadratichnykh form na peresechenii kvadrik i kvadratichnye otobrazheniya”, Matem. zametki, 84:2 (2008), 163–174 | DOI | MR | Zbl

[2] A. V. Arutyunov, A. F. Izmailov, “Teoriya chuvstvitelnosti dlya anormalnykh zadach optimizatsii s ogranicheniyami tipa ravenstv”, Zh. vychisl. matem. i matem. fiz., 43:2 (2003), 186–202 | MR | Zbl

[3] A. V. Arutyunov, A. F. Izmailov, “Abnormal equality-constrained optimization problems: sensitivity theory”, Math. Progam. Ser. A, 100:3 (2004), 485–515 | MR | Zbl

[4] E. R. Avakov, “Teoremy ob otsenkakh v okrestnosti osoboi tochki otobrazheniya”, Matem. zametki, 47:5 (1990), 3–13 | MR | Zbl

[5] A. V. Arutyunov, D. Yu. Karamzin, “Regulyarnye nuli kvadratichnykh otobrazhenii i ikh prilozhenie”, Matem. sb., 202:6 (2011), 3–28 | DOI | MR | Zbl

[6] A. V. Arutyunov, S. E. Zhukovskii, “Suschestvovanie obratnykh otobrazhenii i ikh svoistva”, Differentsialnye uravneniya i topologiya. II, Sb. statei. K 100-letiyu so dnya rozhdeniya akademika Lva Semenovicha Pontryagina, Tr. MIAN, 271, MAIK, M., 2010, 18–28 | MR