Lagrange Multiplier method

The basic Lagrange multiplier method is to find the function f (x1,x2,...) In G (x1,x2,...) The method of =0 the extremum under constrained conditions .

Main idea: The introduction of a new parameter λ (Lagrange multiplier), the constraints of the function and the original function together, so that can be matched with the number of variables equal to the equation, so as to obtain the original function Extremum of the various variables of the solution.

Assume that the objective function of the extremum needs to be f (x, y) and the limit is φ (x, y) =m

Solution: Set g (x, Y) =m-φ (x, y)

define a new function: F (x,y,λ) =f (x, y) +λg (x, y )

the equations are listed using partial derivative methods: ? F/?x=0,huh? F/?y=0,huh? F/?λ=0

The value of the x,y,λ is obtained, and the extremum of the objective function can be achieved by substituting

Lagrange Multiplier method