Linear Lyapunov--Krotov functions and sufficient conditions for optimality in the form of the maximum principle
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2002), pp. 11-22.

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N. V. Antipina; V. A. Dykhta. Linear Lyapunov--Krotov functions and sufficient conditions for optimality in the form of the maximum principle. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2002), pp. 11-22. http://geodesic.mathdoc.fr/item/IVM_2002_12_a1/

[1] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Fizmatgiz, M., 1961, 388 pp.

[2] Mangasarian O. L., “Control problems with kinks”, IEEE Trans., AC-15, 1970, 570–575 | MR

[3] Arrow K. J., “Application of control theory to economic growth”, Math. of the decision sci., II, Lect. in Appl. Math., 12, 1968, 85–119 | MR | Zbl

[4] Errou K., “Primenenie teorii upravleniya k ekonomicheskomu rostu”, Matematicheskaya ekonomika, ed. B. S. Mityagin, Mir, M., 1974, 7–45

[5] Blagodatskikh V. I., “Dostatochnoe uslovie optimalnosti”, Differents. uravneniya, 9:3 (1973), 416–422

[6] Blagodatskikh V. I., Filippov A. F., “Differentsialnye vklyucheniya i optimalnoe upravlenie”, Tr. MIAN SSSR, 169, 1985, 194–252 | MR | Zbl

[7] Krotov V. F., Gurman V. I., Metody i zadachi optimalnogo upravleniya, Nauka, M., 1973, 446 pp. | MR | Zbl

[8] Krotov V. F., Global methods in optimal control theory, Marcel Dekker, New York, 1996, 408 pp. | MR | Zbl

[9] Velichenko V. V., “O metode polya ekstremalei i dostatochnykh usloviyakh optimalnosti”, Zhurn. vychisl. matem. i matem. fiziki, 14:1 (1974), 45–67

[10] Dykhta V. A., “Printsip rasshireniya v kachestvennoi teorii upravleniya”, Metody resheniya zadach teorii upravleniya na osnove printsipa rasshireniya, eds. V. A. Baturin, V. A. Dykhta, A. I. Moskalenko i dr., Nauka, Novosibirsk, 1990, 5–48

[11] Dykhta V. A., Antipina N. V., “Sufficient optimality conditions for classical and impulsive optimal control problems”, Proc. of 10th IEEE Mediterranean Conf. on Control and Automation, MED2002 (July 9–July 12, 2002), Lisbon, Portugal, 10

[12] Afanasev A. P., Dikusar V. V., Milyutin A. A., Chukanov S. A., Neobkhodimoe uslovie v optimalnom upravlenii, Nauka, M., 1990, 319 pp. | MR

[13] Milyutin A. A., Osmolovskii N. P., Calculus of variations and optimal control, Amer. Math. Soc., Providence, Rhode Island, 1998, 372 pp. | MR | Zbl

[14] Levitin E. S., Milyutin A. A., Osmolovskii N. P., “Usloviya vysshikh poryadkov lokalnogo minimuma v zadachakh s ogranicheniyami”, UMN, 33:6 (1978), 85–148 | MR | Zbl

[15] Rush N., Abets P., Lalua M., Pryamoi metod Lyapunova v teorii ustoichivosti, Mir, M., 1980, 300 pp. | MR

[16] Klark F., Optimizatsiya i negladkii analiz, Nauka, M., 1988, 280 pp. | MR | Zbl

[17] Alekseev V. M., Tikhomirov V. M., Fomin S. V., Optimalnoe upravlenie, Nauka, M., 1979, 429 pp. | MR

[18] Vinter R. B., “Dynamic programming for optimal control problems with terminal constraints”, Lect. Notes Math., 1985, 190–202 | MR | Zbl

[19] Vinter R. B., Optimal control, Burkhäuser, Boston–Basel–Berlin, 2000, 504 pp. | MR

[20] Dubovitskii A. Ya., Milyutin A. A., “Zadachi na ekstremum pri nalichii ogranichenii”, Zhurn. vychisl. matem. i matem. fiz., 5:3 (1965), 395–453 | Zbl

[21] Pshenichnyi B. N., Neobkhodimye usloviya ekstremuma, Nauka, M., 1982, 143 pp. | MR