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Lagrange’s Method

What is meant by Lagrange's method?
a procedure for finding maximum and minimum values of a function of several variables when the variables are restricted by additional conditions.
What's the steps of Lagrange's method?
Lagrange multiplier technique, quick recap
Step 1: Introduce a new variable ‍ , and define a new function ‍ as follows: L ( x , y , … Step 2: Set the gradient of ‍ equal to the zero vector. ∇ L ( x , y , … Step 3: Consider each solution, which will look something like ( x 0 , y 0 , … , λ 0 ) ‍ .
Plug each one into ‍ .
What is the Lagrange factor method?
Lagrange multiplier method is a technique for finding a maximum or minimum of a function F(x,y,z) subject to a constraint (also called side condition) of the form G(x,y,z) = 0.
Figure 1: The four possible cases of varying end points in the direction of y.
Lagrange's equations provides an analytic method to analyze dynamical systems by a scalar procedure starting from the scalar quantities of kinetic energy, potential energy and (virtual) work, expressed in terms of generalized coordinates.

The method of Lagrange multipliers relies on the intuition that at a maximum, f(x, y) cannot be increasing in the direction of any such neighboring point that also has g = 0. If it were, we could walk along g = 0 to get higher, meaning that the starting point wasn't actually the maximum.

Method of Lagrange Multipliers

Lagrange’s Method

What is meant by Lagrange's method?

What's the steps of Lagrange's method?

Lagrange multiplier technique, quick recap

What is the Lagrange factor method?