Use python please and show the optimization path on each contour plot. Write a numerical code to minimize the Rosenbrock function defined below using a slew of gradient

based optimization algorithmsWrite a numerical code to minimize the Rosenbrock function defined below using a slew of gradient

based optimization algorithms. The function is a non$-$convex function and has a global minimum at

$(1,1).$ The minimum is at the bottom of a narrow parabolic valley that is curved on the $x-y$ plane.

The function is often used to test the performance of optimization algorithms.

$f(x,y)=(1-x{)}^2+100(y-x^2{)}^2$

$($a$)$ Write four codes using the steepest descent method, nonlinear conjugate gradient, quasi$-$Newton, and Newton method to

solve for the minimum of the function. Use a simple backtracking line search method to compute

the step length. You may choose one particular algorithm for the conjugate gradient $($either the

Hestenes$-$Stiefel, Polak$-$Ribiere, or Fletcher$-$Reeves$)$ and quasi$-$Newton $($DFP or BFGS$)$ method.

$($b$)$ Provide the following in a written report:

$($a$)$ Convergence of the gradient $(y-$axis: $log$ of the gradient, $x-$axis: iteration$)$ and a comparison

of the convergence.

$($b$)$ Contour plot of the path of the optimization algorithm.use python U