Lagrange Multipliers Optimization - Complex Functions

1. What is Lagrange multiplier optimization?
2. How do you use the Lagrange multiplier to maximize a function?
3. What is meant by the Lagrangian function of a constrained Optimisation problem?

What is Lagrange multiplier optimization?

In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables).

How do you use the Lagrange multiplier to maximize a function?

Maximize (or minimize) : f(x,y)given : g(x,y)=c, find the points (x,y) that solve the equation ∇f(x,y)=λ∇g(x,y) for some constant λ (the number λ is called the Lagrange multiplier). If there is a constrained maximum or minimum, then it must be such a point.

What is meant by the Lagrangian function of a constrained Optimisation problem?

The Lagrange multiplier technique is how we take advantage of the observation made in the last video, that the solution to a constrained optimization problem occurs when the contour lines of the function being maximized are tangent to the constraint curve. Created by Grant Sanderson.