Geodesic
Regularized extragradient method for finding a saddle point in an optimal control problem
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 1, pp. 27-37
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We propose a regularized variant of the extragradient method of saddle point search for a convex-concave functional defined on solutions of control systems of linear ordinary differential equations. We assume that the input data of the problem are given inaccurately. Since the problem under consideration is, generally speaking, unstable under a disturbance in the input data, we propose a regularized variant of the extragradient method, investigate its convergence, and construct a regularizing operator. The regularization parameters of the method agree asymptotically with the disturbance level of the input data.
Keywords: extragradient method, optimal control, saddle point, regularization. 
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F. P. Vasil'ev; E. V. Khoroshilova; A. S. Antipin. Regularized extragradient method for finding a saddle point in an optimal control problem. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 1, pp. 27-37. http://geodesic.mathdoc.fr/item/TIMM_2011_17_1_a2/

[1] Oben Zh. P., Ekland I., Prikladnoi nelineinyi analiz, Mir, M., 1988, 510 pp. | MR

[2] Vasilev F. P., Khoroshilova E. V., Antipin A. S., “Ekstragradientnyi metod poiska sedlovoi tochki v zadache optimalnogo upravleniya”, Vestn. Mosk. un-ta. Ser. 15. Vychisl. matematika i kibernetika, 2010, no. 3, 18–22 | MR

[3] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1979, 288 pp. | MR

[4] Bakushinskii A. B., Goncharskii A. V., Iterativnye metody resheniya nekorrektnykh zadach, Nauka, M., 1989, 128 pp. | MR

[5] Vasilev F. P., Metody optimizatsii, Faktorial Press, M., 2002, 524 pp.

[6] Antipin A. S., Vasilev F. P., Shpirko S. V., “Regulyarizovannyi ekstragradientnyi metod resheniya zadach ravnovesnogo programmirovaniya”, Zhurn. vychisl. matematiki i mat. fiziki, 43:10 (2003), 1451–1458 | MR | Zbl