Using matlab or java:

1. Write a program to implement steepest descent using line search. Terminate the line search when the length of the interval is less than 10-6. Apply the program to Rosen brock's function 2 f(x) 100(12-21)2 + (1-x1) Analytically determine the minimizer for Rosenbrock's function and show that it satis- fies the FONC and SOSC. Consider the rate at which f(xk) approaches the minimunm value. Determine if this is consistent with the convergence theory for steepest descent . Do all of the above for the qundratic Use the theory to explain any differences in the performance of the algorithm on these two problems