ForwardDiff example

Consider the function below:

f(x) = (x[1] - 1)^2 + 100 * (x[2] - x[1]^2)^2

f (generic function with 1 method)

We use ForwardDiff for the derivatives.

using ForwardDiff
∇f(x) = ForwardDiff.gradient(f, x)
H(x) = ForwardDiff.hessian(f, x)

H (generic function with 1 method)

Newton's method:

x = [-1.2; 1.0]
for k = 1:10
  println("Iter $k - x = ", x)
  x -= H(x) \ ∇f(x)
end