Calculus Optimization Methods/Lagrange Multipliers
The method of Lagrange multipliers solves the constrained optimization problem by transforming it into a non-constrained optimization problem of the form:
Then finding the gradient and hessian as was done above will determine any optimum values of .
Suppose we now want to find optimum values for subject to from .
Then the Lagrangian method will result in a non-constrained function.
The gradient for this new function is
Finding the stationary points of the above equations can be obtained from their matrix from.
This results in .
Next we can use the hessian as before to determine the type of this stationary point.
Since then the solution minimizes subject to with .Last modified on 15 February 2011, at 16:38