On the existence of Lagrange multipliers in nonlinear programming in Banach spaces

2005 ◽  
pp. 89-104 ◽  
Author(s):  
Jean-Paul Penot
Keyword(s):  
Nonlinear Programming ◽  
Banach Spaces ◽  
Lagrange Multipliers

scholarly journals A generalization of Lagrange multipliers

1970 ◽  
Vol 3 (3) ◽  
pp. 353-362 ◽  
Author(s):  
B. D. Craven
Keyword(s):  
Banach Spaces ◽  
Lagrange Multipliers ◽  
Lagrange Equation ◽  
Linear Mapping ◽  
Real Field ◽  
Dimensional Problem ◽  
Continuous Linear ◽  
Continuous Linear Mapping ◽  
Finite Dimensional ◽  
Method Of Lagrange Multipliers

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.

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