Bulletin of the American Mathematical Society

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Book Information:

Author: 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.

Gilbert A. Bliss, Lectures on the Calculus of Variations, University of Chicago Press, Chicago, Ill., 1946. MR 0017881

Jürgen Guddat, Hubertus Th. Jongen, Bernd Kummer, and František Nožička (eds.), Parametric optimization and related topics, Mathematical Research, vol. 35, Akademie-Verlag, Berlin, 1987. Papers from the international conference held in Plaue, October 7–12, 1985. MR 909718

3.

L. Cesari, Optimization with partial differential equations (to appear).

L. Cesari, J. R. La Palm, and D. A. Sánchez, An existence theorem for Lagrange problems with unbounded controls and a slender set of exceptional points, SIAM J. Control 9 (1971), 590–605. MR 0308889

Frank H. Clarke, Necessary conditions for a general control problem, Calculus of variations and control theory (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975; dedicated to Laurence Chisholm Young on the occasion of his 70th birthday), Publ. Math. Res. Center Univ. Wisconsin, No. 36, Academic Press, New York, 1976, pp. 257–278. MR 0638210

Frank H. Clarke, The generalized problem of Bolza, SIAM J. Control Optim. 14 (1976), no. 4, 682–699. MR 412926, DOI 10.1137/0314044

A. F. Filippov, On some questions in the theory of optimal regulation: existence of a solution of the problem of optimal regulation in the class of bounded measurable functions, Vestnik Moskov. Univ. Ser. Mat. Meh. Astr. Fiz. Him. 1959 (1959), no. 2, 25–32 (Russian). MR 0122650

Alain Ghouila-Houri, Sur la ǵnéralisation de la notion de commande d’un système guidable, Rev. Française Informat. Recherche Opérationnelle 1 (1967), no. 4, 7–32 (French). MR 0222743

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.

E. J. McShane, Generalized curves, Duke Math. J. 6 (1940), 513–536. MR 2469

E. J. McShane, Existence theorems for Bolza problems in the calculus of variations, Duke Math. J. 7 (1940), 28–61. MR 3479

Lucien W. Neustadt, A general theory of minimum-fuel space trajectories, J. SIAM Control Ser. A 3 (1965), 317–356. MR 188840

Lucien W. Neustadt, An abstract variational theory with applications to a broad class of optimization problems. II. Applications, SIAM J. Control 5 (1967), 90–137. MR 0237210

Lucien W. Neustadt, Optimization, Princeton University Press, Princeton, N. J., 1976. A theory of necessary conditions; With a chapter by H. T. Banks. MR 0440440

L. S. Pontrjagin, V. G. Boltjanskiĭ, R. V. Gamkrelidze, and E. F. Miščenko, Matematicheskaya teoriya optimal′nykh protsessov, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1961 (Russian). MR 0166036

Raymond W. Rishel, An extended Pontryagin principle for control systems whose control laws contain measures, J. SIAM Control Ser. A 3 (1965), 191–205. MR 187980

Emilio Roxin, The existence of optimal controls, Michigan Math. J. 9 (1962), 109–119. MR 136844

W. W. Schmaedeke, Optimal control theory for nonlinear vector differential equations containing measures, J. SIAM Control Ser. A 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.

J. Warga, Relaxed variational problems, J. Math. Anal. Appl. 4 (1962), 111–128. MR 142020, DOI 10.1016/0022-247X(62)90033-1

J. Warga, Minimizing variational curves restricted to a preassigned set, Trans. Amer. Math. Soc. 112 (1964), 432–455. MR 164840, DOI 10.1090/S0002-9947-1964-0164840-1

J. Warga, Variational problems with unbounded controls, J. SIAM Control Ser. A 3 (1965), 424–438. MR 194951

J. Warga, Optimal control of differential and functional equations, Academic Press, New York-London, 1972. MR 0372708

J. Warga, Necessary conditions without differentiability assumptions in optimal control, J. Differential Equations 18 (1975), 41–62. MR 377655, DOI 10.1016/0022-0396(75)90080-7

T. Ważewski, Sur une généralisation de la notion des solutions d’une équation au contingent, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 10 (1962), 11–15 (French). MR 153944

T. Ważewski, Sur les systèmes de commande non linéaires dont le contredomaine de commande n’est pas forcément convexe, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 10 (1962), 17–21 (French). 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.

L. C. Young, Lectures on the calculus of variations and optimal control theory, W. B. Saunders Co., Philadelphia-London-Toronto, Ont., 1969. Foreword by Wendell H. Fleming. MR 0259704

1.

G. A. Bliss, Lectures on the calculus of variations, Univ. of Chicago Press, Chicago, 1946. MR 0017881

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