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Book Information

Author(s): Lamberto Cesari
Title: Optimization—Theory and applications, Problems with ordinary differential equations
Additional book information: Applications of Mathematics, vol. 17, Springer-Verlag, New York, 1983, xiv + 542 pp., $68.00. ISBN 0-3879-0676-2

1.: G. A. Bliss, Lectures on the calculus of variations, Univ. of Chicago Press, Chicago, 1946. MR 17881
2.: L. Cesari, Parametric optimization and related topics, Springer-Verlag (to appear). MR 909718
3.: L. Cesari, Optimization with partial differential equations (to appear).
4.: L. Cesari, J. R. LaPalm and D. A. Sanchez, An existence theorem for Lagrange problems with unbounded controls and a slender set of exceptional points, SIAM J. Control Optim. 9 (1971), 590-605; ibid. 11 (1973), 677. MR 308889
5.: F. H. Clarke, Necessary conditions for a general control problem, Calculus of Variations and Control Theory (D. L. Russell, ed.), Academic Press, New York, 1976. MR 638210
6.: F. H. Clarke, The generalized problem of Bolza, SIAM J. Control Optim. 14 (1976), 682-699. MR 412926
7.: A. F. Filippov, On certain questions of optimal control, Vestnik Moskov. Univ. Ser. Mat. Mech. Astronom. Fiz. Him. 1959, no. 2, 25-32; English transl. J. SIAM Control Ser. A 1 (1962), 76-84. MR 122650
8.: A. Ghouila-Houri, Sur la généralisation de la notion de commande d'un système guidable, Rev. Française Informat. Recherche Opérationnelle 1 (1967), No. 4, 7-32. MR 222743
9.: E. Goursat, Cours d'analyse mathématique, Tome III, 5th. ed., Gauthiers-Villars, Paris, 1942.
10.: E. J. McShane, Some existence theorems in the calculus of variations. I-V, Trans. Amer. Math. Soc. 44 (1938), 428-453; ibid. 45 (1939), 151-216.
11.: E. J. McShane, Generalized curves, Duke Math. J. 6 (1940), 513-536. MR 2469
12.: E. J. McShane, Existence theorems for Bolza problems in the calculus of variations, Duke Math. J. 7 (1940), 28-61. MR 3479
13.: L. W. Neustadt, A general theory of minimum-fuel space trajectories, J. SIAM Control Ser. A 3 (1965), 317-356. MR 188840
14.: L. W. Neustadt, An abstract variational theory with applications to a broad class of optimization problems. I, II, SIAM J. Control Optim. 4 (1966), 503-527; ibid. 5 (1967), 90-137. MR 237210
15.: L. W. Neustadt, Optimization--A theory of necessary conditions, Princeton Univ. Press, Princeton, N. J., 1976. MR 440440
16.: L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, The mathematical theory of optimal processes, Fitzmatgiz, Moscow, 1961; English transl., Wiley, New York, 1962. MR 166037
17.: R. W. Rishel, An extended Pontryagin principle for control systems whose control laws contain measures, SIAM J. Control Optim. 3 (1965), 191-205. MR 187980
18.: E. Roxin, The existence of optimal controls, Michigan Math. J. 9 (1962), 109-119. MR 136844
19.: W. W. Schmaedecke, Optimal control theory for nonlinear vector differential equations containing measures, SIAM J. Control Optim. 3 (1965), 231-280. MR 189870
20.: L. Tonelli, Sugli integrali del calcolo delle variazioni in forma ordinaria, Ann. Scuola Norm. Sup. Pisa (2) 3 (1934), 401-405.
21.: F. A. Valentine, The problem of Lagrange with differential inequalities as added side conditions, Contributions to the Calculus of Variations, 1933-1937, Univ. of Chicago Press, Chicago, 1937, pp. 407-448.
22.: J. Warga, Relaxed variational problems, J. Math. Anal. Appl. 4 (1962), 111-128. MR 142020
23.: J. Warga, Minimizing variational curves restricted to a preassigned set, Trans. Amer. Math. Soc. 112 (1964), 432-455. MR 164840
24.: J. Warga, Variational problems with unbounded controls, J. SIAM Control Ser. A 3 (1965), 424-438. MR 194951
25.: J. Warga, Optimal control of differential and functional equations, Academic Press, New York, 1972. MR 372708
26.: J. Warga, Necessary conditions without differentiablility assumptions in optimal control, J. Differential Equations 18 (1975), 41-62. MR 377655
27.: T. Ważewski, Sur la généralisation de la notion des solutions d'une équation au contingent, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 10 (1962), 11-15. MR 153944
28.: T. Ważewski, Sur les systèmes de commande non linéaires dont le contredomaine de commande n'est pas forcément convexe, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 10 (1962), 17-21. MR 153945
29.: L. C. Young, Generalized curves and the existence of an attained absolute minimum in the calculus of variations, C. R. Sci. Lettres Varsovie, C III 30 (1937), 212-234.
30.: L. C. Young, Lectures on the calculus of variations and optimal control theory, Saunders, Philadelphia, 1969. MR 259704

Review Information:
Journal: Bull. Amer. Math. Soc. 9 (1983), 396-401.
DOI: 10.1090/S0273-0979-1983-15227-8
PII: S 0273-0979(1983)15227-8

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