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.

scholarly journals PEMECAHAN MASALAH NONLINEAR PROGRAMMING DENGAN LAGRANGEAN METHOD MENGGUNAKAN SUBSTITUTION METHOD ATAU MICROSOFT EXCEL

2017 ◽  
Vol 4 (2) ◽  
Author(s):  
Rudy Santosa Sudirga
Keyword(s):  
Nonlinear Programming ◽  
Programming Problem ◽  
Lagrange Multipliers ◽  
Optimization Problems ◽  
Stationary Points ◽  
Mathematical Tool ◽  
Nonlinear Programming Problem ◽  
Microsoft Excel ◽  
Substitution Method ◽  
General Technique

<p><em>Lagrange Multipliers are a mathematical tool for constrained optimization of differentiable functions. The given procedure defines the Lagrangean Method for identifying the stationary points of optimization problems with equality constraints; L (ℷ, X) = f(X) – ℷg(X – C). This function is called the Lagrangean function and the parameters ℷ is the Lagrange Multipliers. The partial derivatives of this equation ∂L/∂ℷ = 0 and ∂L/∂X = 0 will give the optimal result for X.</em></p><p><em>However, in some cases, sometimes we have been facing some difficulties to solve nonlinear programming problem with this method, therefore we would like to introduce the <strong>Substitution Method</strong> or <strong>Microsoft Excel Method</strong>, which is simple, easier and faster to solve the nonlinear programming problem. Because of the mathematical nature of nonlinear programming models, and in management science we do not have a single general technique to solve all mathematical models that can arise in practice, therefore simpler approaches should be explored first. In some cases, a “common sense” solution may be reached through simple observations.  </em><em>  </em></p>

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