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Minimizing variational curves restricted to a preassigned set. (English) Zbl 0129.07403


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[1] J. Warga, Relaxed variational problems, J. Math. Anal. Appl. 4 (1962), 111 – 128. , https://doi.org/10.1016/0022-247X(62)90033-1 J. Warga, Necessary conditions for minimum in relaxed variational problems, J. Math. Anal. Appl. 4 (1962), 129 – 145. · Zbl 0102.31802 · doi:10.1016/0022-247X(62)90034-3
[2] J. Warga, Relaxed variational problems, J. Math. Anal. Appl. 4 (1962), 111 – 128. , https://doi.org/10.1016/0022-247X(62)90033-1 J. Warga, Necessary conditions for minimum in relaxed variational problems, J. Math. Anal. Appl. 4 (1962), 129 – 145. · Zbl 0102.31802 · doi:10.1016/0022-247X(62)90034-3
[3] L. C. Young, Generalized curves and the existence of an attained absolute minimum in the calculus of variations, C. R. Soc. Sci. Lettres Varsovie Cl. III 30 (1937), 212-234. · Zbl 0019.21901
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[5] A. F. Filippov, On certain questions in the theory of optimal control, J. SIAM Control Ser. A 1 (1962), 76 – 84. · Zbl 0139.05102
[6] R. V. Gamkrelidze, Optimum-rate processes with bounded phase coordinates, Dokl. Akad. Nauk SSSR 125 (1959), 475 – 478 (Russian). · Zbl 0090.30801
[7] Математическая теория оптимал\(^{\приме}\)ных процессов, Государств. Издат. Физ.-Мат. Лит., Мосцощ, 1961 (Руссиан). Л. С. Понтрягин, В. Г. Болтянскии, Р. В. Гамкрелидзе, анд Е. Ф. Мищенко, Тхе матхематицал тхеоры оф оптимал процессес, Транслатед фром тхе Руссиан бы К. Н. Трирогофф; едитед бы Л. Щ. Неустадт, Интерсциенце Публишерс Јохн Щилеы & Сонс, Инц. Нещ Ыорк-Лондон, 1962. Л. С. Понтрјагин, В. Г. Болтјанскиј, Р. В. Гамкрелидзе, анд Е. Ф. Мисčенко, Матхематисче Тхеорие оптималер Прозессе, Р. Олденбоург, Мунич-Виенна, 1964 (Герман).
[8] L. C. Young, Necessary conditions in the calculus of variations, Acta Math. 69 (1938), no. 1, 229 – 258. · Zbl 0019.26702 · doi:10.1007/BF02547714
[9] E. J. McShane, Necessary conditions in generalized-curve problems of the calculus of variations, Duke Math. J. 7 (1940), 1 – 27. · Zbl 0024.32503
[10] V. G. Boltyanskiĭ, R. V. Gamkrelidze, and L. S. Pontryagin, On the theory of optimal processes, Dokl. Akad. Nauk SSSR (N.S.) 110 (1956), 7 – 10 (Russian). · Zbl 0071.18203
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