(a) Plot the Rosenbrock function f = (1 - x) 2 + 100(y - x 2 ) 2

(b) Pick a stopping criterion and use the downhill simplex method to search for its minimum starting from x = y = -1, plotting the search path, and comparing the computing time and memory used.

(c) Repeat with the direction set method.

(d) Repeat with the conjugate gradient method.

(e) Repeat with the Levenberg-Marquardt method (using the gradient and Hessian of the function).