Fields of extremals and sufficient conditions for the simplest problem of the calculus of variations

Journal of Global Optimization

Volumn 40, Issue 1-3, 2008, Pages 41-50

  Carlson, Dean A ^a   Leitmann, George ^b  

^a American Mathematical Society   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Direct method; Field of extremals; Sufficient conditions

Indexed keywords

GLOBAL OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

DIRECT METHODS; ELEMENTARY PROOF; FIELD OF EXTREMALS; SUFFICIENT CONDITIONS;

VARIATIONAL TECHNIQUES;

EID: 38849188007     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-007-9171-z     Document Type: Conference Paper

References (12)

1. Bolza O. (1973). Calculus of Variations. Chelsea Publishing Company, New York, NY
2. Carathéodory C. (1982). Calculus of Variations and Partial Differential Equations. Chelsea, New York, NY
3. Carlson D.A. (2002). An observation on two methods of obtaining solutions to variational problems. J. Optim. Theory Appl. 114: 345-362
4. Carlson D.A. and Leitmann G. (2004). An extension of the coordinate transformation method for open-loop Nash equilibria. J. Optim. Theory Appl. 123: 27-47
5. Carlson D.A. and Leitmann G. (2005). A coordinate transformation method for the extremization of multiple integrals. J. Optim. Theory Appl. 127: 523-533
6. Carlson, D.A., Leitmann, G.: The direct method for a class of infinite Horizon Dynamic games. Adv. Comput. Manage. Sci. 7(19), 319-334. Springer, New York, NY (2005)
7. Carlson, D.A., Leitmann, G.: A direct method for open-loop Dynamic games for affine control systems. GERAD 25th Anniv. Ser. 10(2), 37-55. Springer, New York, NY (2005)
8. Ewing, G.M.: Calculus of Variations with Applications. Dover Publications, Inc., 31 East 2nd Street, Mineola, NY, P 11501 (1985). Reprint of work published by W. W. Norton & Co., New York (1969)
9. Leitmann G. (1967). A note on absolute extrema of certain integrals. Int. J. NonLin. Mech. 2: 55-59
10. Leitmann G. (2001). On a class of direct optimization problems. J. Optim. Theory Appl. 108: 467-481
11. Leitmann G. (2004). A direct method of optimization and its applications to a class of differential games. Dyn. Contin. Discrete Impulsive Syst. Ser. A 11: 191-204
12. Todhunter, I.: A history of the calculus of variations during the nineteenth century. Chelsea Publishing Company, New York, NY Reprint of original 1861 edition