Using MATLAB please plot the history of iterations the step length by semilogy.

3.1 Program the steepest descent and Newton algorithms using the backtracking line search, Algorithm 3.1. Use them to minimize the Rosenbrock function (2.22). Set the initial step length a1 and print the step length used by each method at each iteration. First try the initial point xo = ( 1.2, 1 .2)" and then the more difficult starting point xo = (-12, 1)T. Algorithm 3.1 (Backtracking Line Search). Choose > 0, e (0, 1), c e (0, 1); Set -u; repeat until f (xk + pk) f(m) + coN fin ; end (repeat) Terminate with ak-a. rjx) -y -jx)j-1,2,.... m, (2.2)