Thread: Confused with the Lagrange method

Ok so I'm doing a project on multivariable optimization, and I am using the lagrange method, and I can use it correctly. However, I cannot explain (which i have to do as part of my project) how the lagrange method works..i am going the route of gradient vectors, and i get confused when i have the gradient vector of f(x,y,z) = the gradient vector of g(x,y,z) * lamda

where lamda is the langrange multiplier.

i dont get why the two gradient vectors are parallel, and thus need a multiplier to determine the magnitude. why arent the gradient vectors the same? why are the parallel?

Originally Posted by stones44

Ok so I'm doing a project on multivariable optimization, and I am using the lagrange method, and I can use it correctly. However, I cannot explain (which i have to do as part of my project) how the lagrange method works..i am going the route of gradient vectors, and i get confused when i have the gradient vector of f(x,y,z) = the gradient vector of g(x,y,z) * lamda

where lamda is the langrange multiplier.

i dont get why the two gradient vectors are parallel, and thus need a multiplier to determine the magnitude. why arent the gradient vectors the same? why are the parallel?

At the largest value of the objective that satisfies the constraint the objective surface (surface where the objective takes the same value as at the maximum) must be kissing the constraint surface (assuming both are sufficiently smooth).

CB