Bulletin of the American Mathematical Society

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Book Information:

Author: Vladimir M. Tikhomirov
Title: Fundamental principles of the theory of extremal problems
Additional book information: translated by Bernd Luderer. John Wiley and Sons, Chichester, New York, Brisbane, Toronto and Singapore, 1986, 136 pp., $27.00. ISBN 0-471-905631.

V. M. Alekseev, V. M. Tihomirov, and S. V. Fomin, Optimal′noe upravlenie, “Nauka”, Moscow, 1979 (Russian). MR 566022

V. Barbu and Th. Precupanu, Convexity and optimization in Banach spaces, Revised edition, Editura Academiei, Bucharest; Sijthoff & Noordhoff International Publishers, Alphen aan den Rijn, 1978. Translated from the Romanian. MR 0513634

Lamberto Cesari, Optimization—theory and applications, Applications of Mathematics (New York), vol. 17, Springer-Verlag, New York, 1983. Problems with ordinary differential equations. MR 688142, DOI 10.1007/978-1-4613-8165-5

Frank H. Clarke, Optimization and nonsmooth analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, Inc., New York, 1983. A Wiley-Interscience Publication. MR 709590

George M. Ewing, Calculus of variations with applications, W. W. Norton & Co. Inc., New York, 1969. MR 0242032

[ET] Ivar Ekeland and Roger Ternam, Convex analysis and variational problems, North-Holland, Amsterdam, 1976.

A. D. Ioffe and V. M. Tikhomirov, Teoriya èkstremal′nykh zadach, Seriya “Nelineĭnyĭ Analiz i ego Prilozheniya”. [Series in Nonlinear Analysis and its Applications], Izdat. “Nauka”, Moscow, 1974 (Russian). MR 0410502

R. Tyrrell Rockafellar, Convex analysis, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Reprint of the 1970 original; Princeton Paperbacks. MR 1451876

Peter Smith, Convexity methods in variational calculus, Electronic & Electrical Engineering Research Studies: Applied and Engineering Mathematics Series, vol. 1, Research Studies Press, Ltd., Chichester; John Wiley & Sons, Inc., New York, 1985. MR 782676

John L. Troutman, Variational calculus with elementary convexity, Undergraduate Texts in Mathematics, Springer-Verlag, New York-Berlin, 1983. With the assistance of W. Hrusa. MR 697723

[Ze] Eberhard Zeidler, Nonlinear functional analysis with applications. III, Springer-Verlag, New York, 1983.

L. Cesari, A tribute to Leonida Tonelli: Leonida Tonelli (1885–1946) and his 20th century legacy, Contributions to modern calculus of variations (Bologna, 1985) Pitman Res. Notes Math. Ser., vol. 148, Longman Sci. Tech., Harlow, 1987, pp. 1–12. MR 894068

Frank H. Clarke and R. B. Vinter, Existence and regularity in the small in the calculus of variations, J. Differential Equations 59 (1985), no. 3, 336–354. MR 807852, DOI 10.1016/0022-0396(85)90145-7

3. F. H. Clarke and P. D. Löwen, An intermediate existence theory in the calculus of variations (to appear).

Vera Zeidan, Sufficient conditions for the generalized problem of Bolza, Trans. Amer. Math. Soc. 275 (1983), no. 2, 561–586. MR 682718, DOI 10.1090/S0002-9947-1983-0682718-3

1.

Lamberto Cesari (ed.), Contributions to modern calculus of variations, Longman Scientific & Technical (copublished by John Wiley & Sons, New York, 1987). MR 894068

2.

F. H. Clarke and R. B. Vinter, Existence and regularity in the small in the calculus of variations, J. Differential Equations 59 (1985), 336-354. MR 807852

3.

F. H. Clarke and P. D. Löwen, An intermediate existence theory in the calculus of variations (to appear).

4.

V. M. Zeidan, Sufficient conditions for the generalized problem of Bolza, Trans. Amer. Math. Soc. 275 (1983), 561-586. MR 682718

[Ew] George M. Ewing, Calculus of variations with applications, W. W. Norton & Co., New York, 1969; reprinted by Dover Publications, New York, 1985. [ET] Ivar Ekeland and Roger Ternam, Convex analysis and variational problems, North-Holland, Amsterdam, 1976. [IT] A. D. Ioffe and V. M. Tikhomirov, Theory of extremal problems, "Nauka", Moscow, 1974 (Russian); English transl.: North-Holland, Amsterdam, 1979. [Ro] R. Tyrall Rockafellar, Convex analysis, Princeton Univ. Press, Princeton, N. J., 1969. [Sm] Peter Smith, Convexity methods in variational calculus, Research Studies Press Ltd., 1985 (marketed by John Wiley & Sons, New York). [Tr] John L. Troutman, Variational calculus with elementary convexity, Springer-Verlag, New York, 1983. (Supplement: Optimal control with elementary convexity (1986) available by request through publisher.) [Ze] Eberhard Zeidler, Nonlinear functional analysis with applications. III, Springer-Verlag, New York, 1983. 1. Lamberto Cesari (ed.), Contributions to modern calculus of variations, Longman Scientific & Technical (copublished by John Wiley & Sons, New York, 1987). 2. F. H. Clarke and R. B. Vinter, Existence and regularity in the small in the calculus of variations, J. Differential Equations 59 (1985), 336-354. 3. F. H. Clarke and P. D. Löwen, An intermediate existence theory in the calculus of variations (to appear). 4. V. M. Zeidan, Sufficient conditions for the generalized problem of Bolza, Trans. Amer. Math. Soc. 275 (1983), 561-586.