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A generalization of Lagrange multipliers

Published online by Cambridge University Press:  17 April 2009

B. D. Craven
B. D. Craven
Affiliation:
University of Melbourne, Parkville, Victoria.
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Abstract

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The method of Lagrange multipliers for solving a constrained stationary-value problem is generalized to allow the functions to take values in arbitrary Banach spaces (over the real field). The set of Lagrange multipliers in a finite-dimensional problem is shown to be replaced by a continuous linear mapping between the relevant Banach spaces. This theorem is applied to a calculus of variations problem, where the functional whose stationary value is sought and the constraint functional each take values in Banach spaces. Several generalizations of the Euler-Lagrange equation are obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 3 , Issue 3 , December 1970 , pp. 353 - 362
Copyright
Copyright © Australian Mathematical Society 1970

References

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