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@article{TM_2010_268_a5, author = {F. Clarke}, title = {The {Pontryagin} maximum principle and a~unified theory of dynamic optimization}, journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova}, pages = {64--75}, publisher = {mathdoc}, volume = {268}, year = {2010}, language = {en}, url = {http://geodesic.mathdoc.fr/item/TM_2010_268_a5/} }
F. Clarke. The Pontryagin maximum principle and a~unified theory of dynamic optimization. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and topology. I, Tome 268 (2010), pp. 64-75. http://geodesic.mathdoc.fr/item/TM_2010_268_a5/
[1] Arutyunov A. V., Optimality conditions. Abnormal and degenerate problems, Kluwer, Dordrecht, 2000 | MR | Zbl
[2] Bliss G. A., Lectures on the calculus of variations, Univ. Chicago Press, Chicago, 1946 | MR | Zbl
[3] Clarke F. H., Necessary conditions for nonsmooth problems in optimal control and the calculus of variations, Doct. Thes., Univ. Washington, 1973
[4] Clarke F. H., “Necessary conditions for nonsmooth variational problems”, Optimal control theory and its applications, Lect. Notes Econ. and Math. Syst., 106, Springer, New York, 1974, 70–91 | DOI
[5] Clarke F. H., “Le principe du maximum avec un minimum d'hypothèses”, C. r. Acad. sci. Paris, 281 (1975), 281–283 | MR | Zbl
[6] Clarke F. H., “Maximum principles without differentiability”, Bull. Amer. Math. Soc., 81 (1975), 219–222 | DOI | MR | Zbl
[7] Clarke F. H., “The generalized problem of Bolza”, SIAM J. Control and Optim., 14 (1976), 682–699 | DOI | MR | Zbl
[8] Clarke F. H., “The maximum principle under minimal hypotheses”, SIAM J. Control and Optim., 14 (1976), 1078–1091 | DOI | MR | Zbl
[9] Clarke F., “The maximum principle in optimal control, then and now”, Control and Cybern., 34 (2005), 709–722 | MR | Zbl
[10] Clarke F., Necessary conditions in dynamic optimization, Mem. AMS, 173, no. 816, Amer. Math. Soc., Providence, RI, 2005 | MR
[11] Clarke F. H., de Pinho M. R., “The nonsmooth maximum principle”, Control and Cybern. (to appear)
[12] Clarke F. H., de Pinho M. R., “Optimal control problems with mixed constraints”, SIAM J. Control and Optim. (to appear)
[13] Clarke F. H., Ledyaev Yu. S., Stern R. J., Wolenski P. R., Nonsmooth analysis and control theory, Grad. Texts Math., 178, Springer, New York, 1998 | MR | Zbl
[14] de Pinho M. R., Ferreira M. M., Fontes F., “Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems”, ESAIM Control Optim. and Calc. Var., 11 (2005), 614–632 | DOI | MR | Zbl
[15] de Pinho M. R., Vinter R. B., “An Euler–Lagrange inclusion for optimal control problems”, IEEE Trans. Autom. Control, 40 (1995), 1191–1198 | DOI | MR | Zbl
[16] de Pinho M. R., Vinter R. B., “Necessary conditions for optimal control problems involving nonlinear differential algebraic equations”, J. Math. Anal. and Appl., 212 (1997), 493–516 | DOI | MR | Zbl
[17] de Pinho M. R., Vinter R. B., Zheng H., “A maximum principle for optimal control problems with mixed constraints”, IMA J. Math. Control and Inf., 18 (2001), 189–205 | DOI | MR | Zbl
[18] Devdariani E. N., Ledyaev Yu. S., “Maximum principle for implicit control systems”, Appl. Math. and Optim., 40 (1999), 79–103 | DOI | MR | Zbl
[19] Dmitruk A. V., “Maximum principle for the general optimal control problem with phase and regular mixed constraints”, Comput. Math. and Modeling, 4 (1993), 364–377 | DOI | MR
[20] Dubovitskii A. Ya., Milyutin A. A., “Teoriya printsipa maksimuma”, Metody teorii ekstremalnykh zadach v ekonomike, Nauka, M., 1981, 6–47 | MR
[21] Hestenes M. R., Calculus of variations and optimal control theory, J. Wiley and Sons, New York, 1966 | MR | Zbl
[22] Ioffe A. D., Rockafellar R. T., “The Euler and Weierstrass conditions for nonsmooth variational problems”, Calc. Var. and Partial Diff. Equat., 4 (1996), 59–87 | DOI | MR | Zbl
[23] Ioffe A. D., Tikhomirov V. M., Teoriya ekstremalnykh zadach, Nauka, M., 1974 | MR | Zbl
[24] Milyutin A. A., Osmolovskii N. P., Calculus of variations and optimal control, Amer. Math. Soc., Providence, RI, 1998 | MR | Zbl
[25] Neustadt L. W., Optimization: A theory of necessary conditions, Princeton Univ. Press, Princeton, 1976 | MR | Zbl
[26] Páles Z., Zeidan V., “Optimal control problems with set-valued control and state constraints”, SIAM J. Optim., 14 (2003), 334–358 | DOI | MR | Zbl
[27] Stefani G., Zezza P., “Optimality conditions for a constrained control problem”, SIAM J. Control and Optim., 34 (1996), 635–659 | DOI | MR | Zbl
[28] Vinter R., Optimal control, Birkhäuser, Boston, 2000 | MR | Zbl
[29] Warga J., Optimal control of differential and functional equations, Acad. Press, New York, 1972 | MR | Zbl