Lagrange multiplier problem

1. How do you solve a Lagrange multiplier problem?
2. How do you explain the Lagrange multiplier?
3. Why does the Lagrange multiplier fail?
4. What is the drawback of Lagrange multiplier?

How do you solve a Lagrange multiplier problem?

A good approach to solving a Lagrange multiplier problem is to first elimi$ nate the Lagrange multiplier # using the two equations fx / #gx and fy / #gy. Then solve for x and y by combining the result with the constraint g ! x, y" / k, thus producing the critical points.

How do you explain the Lagrange multiplier?

So the bottom line is that Lagrange multipliers is really just an algorithm that finds where the gradient of a function points in the same direction as the gradients of its constraints, while also satisfying those constraints.

Why does the Lagrange multiplier fail?

The Lagrange-multiplier method fails because ∇g = 0 at the point (x, y) = (0, 1) where f attains its minimum on g = 0. As a result, the curve g(x, y) = 0 is not smooth with a well-defined normal vector at that point (see figure).

What is the drawback of Lagrange multiplier?

If the function is discontinuous the calculation with lagrange becomes complex. In addition, if the function is not monotonic or nonconvex, optimization might be difficult as there might be multiple solutions or folds on the functional surface. These are some areas that using Lagrange multipliers will be tricky.