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Relaxed variational problems. (English) Zbl 0102.31801


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[1] Young, L. C., Generalized curves and the existence of an attained absolute minimum in the calculus of variations, Compt. rend. soc. sci. et lettres Varsovie, Cl. III, 30, 212-234 (1937) · Zbl 0019.21901
[2] Young, L. C., Necessary conditions in the calculus of variations, Acta Math., 69, 239-258 (1938) · Zbl 0019.26702
[3] McShane, E. J., Generalized curves, Duke Math. J., 6, 513-536 (1940) · Zbl 0023.39801
[4] McShane, E. J., Necessary conditions in generalized-curve problems of the calculus of variations, Duke Math. J., 7, 1-27 (1940) · Zbl 0024.32503
[5] McShane, E. J., Existence theorems for Bolza problems in the calculus of variations, Duke Math., 7, 28-61 (1940) · Zbl 0024.32504
[6] Pontryagin, L. S., Optimum control processes, Uspekhi Mat. Nauk., 14, No. 1 (85) (1959), (Associated Technical Services, Inc. Translation RJ-2192) · Zbl 0090.30803
[7] Boltyanskii, V. G.; Gamkrelidze, R. V.; Pontryagin, L. S., The theory of optimum processes, Doklady Akad. Nauk SSSR, 110, No. 1, 7-10 (1956) · Zbl 0071.18203
[8] Gamkrelidze, R. V., The theory of optimum processes in linear systems, Doklady Akad. Nauk., 116, No. 1, 9-11 (1957) · Zbl 0080.07001
[9] Gamkrelidze, R. V., Optimum-rate processes with bounded phase coordinates, Doklady Akad. Nauk SSSR, 125, No. 3, 475-478 (1959) · Zbl 0090.30801
[10] Boltyanskii, V. G., The maximum principle in the theory of optimum processes, Doklady Akad. Nauk SSSR, 119, No. 6 (1958) · Zbl 0082.16603
[11] Bellman, R., Dynamic Programming (1957), Princeton Univ. Press: Princeton Univ. Press Princeton, New Jersey, Chap. IX · Zbl 0077.13605
[12] Bushaw, D. W., Optimal discontinuous forcing terms, (Contributions to the Theory of Nonlinear Oscillations, IV (1958), Princeton Univ. Press: Princeton Univ. Press Princeton, New Jersey) · Zbl 0083.08401
[13] LaSalle, J. P., Time optimal control systems, (Proc. Natl. Acad. Sci. U.S., 45 (1959)), 573-577 · Zbl 0085.34403
[14] Bellman, R.; Glicksberg, I.; Gross, O., On the “bang-bang” control problem, Quart. Appl. Math., 14, 11-18 (1956) · Zbl 0073.11501
[15] Krasovskii, N., Concerning the theory of optimal control, Avtomat i Telemekh., 18, 960-970 (1957)
[16] Eggleston, H. G., Convexity, (Cambridge Tracts in Mathematics and Mathematical Physics. No. 47 (1958), Cambridge Univ. Press), 34-38 · Zbl 0086.15302
[17] McShane, E. J., Integration, ((1944), Princeton Univ. Press: Princeton Univ. Press Princeton, New Jersey), 344-345 · Zbl 0551.28001
[18] Warga, J., Necessary conditions for minimum in relaxed variational problems, J. Math. Anal. and Appl., 4, 129-145 (1962) · Zbl 0102.31802
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