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 Rosenbrock's function

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Analytically determine the minimizer for Rosenbrocks's function and show that it satisfies the FONC (First Order Necessary Conditions) and SOSC (). Consider the rate at which approaches the minimum value. Determine if this is consistent with the convergence theory for steepest descent.

Do all of the above for the quadratic

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Use the theory to explain any differences in the performance of the algorithm on these two problems.

Write a program to implement steepest descent using line search. Terminate the line search when the length of the interval is less than 106. Apply the program to Rosen brock's function f(x)-100(2-2- 2 + (1-r.)2. 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 minimum value. Determine if this is consistent with the convergence theory for steepest descent Do all of the above for the quadratic Use the theory to explain any differences in the performance of the algorithm on these two problems