Geodesic
On the stable sequential Lagrange principle in convex programming and its application for solving unstable problems
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 4, pp. 231-240
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The convex programming problem in a Hilbert space with an operator equality constraint and a finite number of functional inequality constraints is considered. The Lagrange principle stable with respect to errors in the initial data is proved for this problem in a sequential nondifferential form. The possibility of its application for solving unstable optimization problems and inverse problems is discussed.
Keywords: convex programming, sequential optimization, parametric problem, Lagrange principle in non-differential form, Kuhn–Tucker theorem, duality, regularization, optimal control, inverse problem.
Mots-clés : perturbation method 
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M. I. Sumin. On the stable sequential Lagrange principle in convex programming and its application for solving unstable problems. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 4, pp. 231-240. http://geodesic.mathdoc.fr/item/TIMM_2013_19_4_a23/

[1] Vasilev F. P., Metody optimizatsii, v 2 kn., MTsNMO, M., 2011, 1056 pp.

[2] Sumin M. I., “Regulyarizatsiya v lineino vypukloi zadache matematicheskogo programmirovaniya na osnove teorii dvoistvennosti”, Zhurn. vychisl. matematiki i mat. fiziki, 47:4 (2007), 602–625 | MR | Zbl

[3] Sumin M. I., Nekorrektnye zadachi i metody ikh resheniya. Materialy k lektsiyam dlya studentov starshikh kursov, Izd-vo Nizhegorod. gos. un-ta, N. Novgorod, 2009, 289 pp.

[4] Sumin M. I., “Regulyarizovannaya parametricheskaya teorema Kuna–Takkera v gilbertovom prostranstve”, Zhurn. vychisl. matematiki i mat. fiziki, 51:9 (2011), 1594–1615 | MR | Zbl

[5] Sumin M. I., “On the stable sequential Kuhn-Tucker theorem and its applications”, Appl. Math., 3:10A, Special iss. “Optimization” (2012), 1334–1350 | DOI

[6] Varga Dzh., Optimalnoe upravlenie differentsialnymi i funktsionalnymi uravneniyami, Nauka, M., 1977, 624 pp.

[7] Alekseev V. M., Tikhomirov V. M., Fomin S. V., Optimalnoe upravlenie, Nauka, M., 1979, 432 pp.

[8] Sumin M. I., “Regulyarizovannyi gradientnyi dvoistvennyi metod resheniya obratnoi zadachi finalnogo nablyudeniya dlya parabolicheskogo uravneniya”, Zhurn. vychisl. matematiki i mat. fiziki, 44:11 (2004), 2001–2019 | MR | Zbl

[9] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967, 736 pp.

[10] Plotnikov V. I., “Teoremy edinstvennosti, suschestvovaniya i apriornye svoistva obobschennykh reshenii”, Dokl. AN SSSR, 165:1 (1965), 33–35 | Zbl