Inequality Constraints in the Calculus of Variations
Canadian journal of mathematics, Tome 29 (1977) no. 3, pp. 528-540

Voir la notice de l'article provenant de la source Cambridge University Press

The classical multiplier rule. The purpose of this section is to review the multiplier rule in order to place the results of this report in perspective. Let us begin by considering the following problem of Mayer in the calculus of variations: we seek to minimize
Clarke, Frank H. Inequality Constraints in the Calculus of Variations. Canadian journal of mathematics, Tome 29 (1977) no. 3, pp. 528-540. doi: 10.4153/CJM-1977-055-6
@article{10_4153_CJM_1977_055_6,
     author = {Clarke, Frank H.},
     title = {Inequality {Constraints} in the {Calculus} of {Variations}},
     journal = {Canadian journal of mathematics},
     pages = {528--540},
     year = {1977},
     volume = {29},
     number = {3},
     doi = {10.4153/CJM-1977-055-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-055-6/}
}
TY  - JOUR
AU  - Clarke, Frank H.
TI  - Inequality Constraints in the Calculus of Variations
JO  - Canadian journal of mathematics
PY  - 1977
SP  - 528
EP  - 540
VL  - 29
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-055-6/
DO  - 10.4153/CJM-1977-055-6
ID  - 10_4153_CJM_1977_055_6
ER  - 
%0 Journal Article
%A Clarke, Frank H.
%T Inequality Constraints in the Calculus of Variations
%J Canadian journal of mathematics
%D 1977
%P 528-540
%V 29
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1977-055-6/
%R 10.4153/CJM-1977-055-6
%F 10_4153_CJM_1977_055_6

[1] 1. Berkovitz, L. D., Variational methods in problems of control and programming, J. Math. Anal. Appl. 3 (1961), 145–169. Google Scholar

[2] 2. Bliss, G. A., The problem of Lagrange in the calculus of variations, Amer. J. Math. 52 (1930), 673–744. Google Scholar

[3] 3. Clarke, F. H., Generalized gradients and applications, Trans. Amer. Math. Soc. 205 (1975), 247–262. Google Scholar

[4] 4. Clarke, F. H. The maximum principle under minimal hypotheses, SI AM J. Control and Optimization 14 (1976) 1078–1091. Google Scholar

[5] 5. Clarke, F. H. Necessary conditions for a general control problem, in Proceedings of the Symposium on the Calculus of Variations and Optimal Control, Russell, D. L., Editor (Mathematics Research Center, University of Wisconsin-Madison), Academic Press, N.Y. (1976). Google Scholar

[6] 6. Clarke, F. H. Necessary conditions for a general control problem, in Proceedings of the Symposium on the Calculus of Variations and Optimal Control, Russell, D. L. Necessary conditions for a general control problem, in Proceedings of the Symposium on the Calculus of Variations and Optimal Control, Russell, D. L. A new approach to Lagrange multipliers, Math, of Operations Res. 1 (1976) 165–174. Google Scholar

[7] 7. Hestenes, M. R., Calculus of variations and optimal control theory (Wiley, N.Y., 1966). Google Scholar

[8] 8. Pennisi, L. L., An indirect sufficiency proof for the problem of Lagrange with differential inequalities as added side conditions, Trans. Amer. Math. Soc. 74 (1953), 177–198. Google Scholar

[9] 9. Rockafellar, R. T., Convex analysis (Princeton Press, Princeton, N.J., 1970). Google Scholar

[10] 10. Rockafellar, R. T. Measurable dependence of convex sets, J. Math. Anal. Appl. 28 (1969), 4–25. Google Scholar

[11] 11. Sagan, H., Introduction to the calculus of variations (McGraw-Hill, N.Y., 1969). Google Scholar

[12] 12. Valentine, F. A., The problem of Lagrange with differential inequalities as added side conditions, in Contributions to the Calculus of Variations 1933–37, Department of Mathematics, University of Chicago (University of Chicago Press, Chicago). Google Scholar

Cité par Sources :