Write a program that implements the dogleg method. Choose Bk to be the exact Hessian. Apply it to solve Rosenbrock’s function. Experiment with the update rule for the trust-region by changing the constants in Algorithm 4.1, or by designing your own rules.

Given  > 0, A, E (0, Â), and n € [0, u):
for k = 0, 1, 2, ..
Obtain pk by (approximately) solving (4.3);
Evaluate Pk from (4.4);
if rhoₖ < 5
Δₖ₊₁= 1/4 Δₖ
else
if rhoₖ > 3/4 and || rhox || = Δₖ
Δₖ₊₁ = min(2Δₖ, Â)
else
Δₖ₊₁ = Δₖ;
if rhoₖ > n
Xₖ₊₁ = Xₖ + rhoₖ
else
Xₖ₊₁ = Xₖ;
end (for).