1. Write a program to implement steepest descent using line search. Terminate th

Question

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

Explanation / Answer

import numphy

import minhelper

def rosenbrock(x):

X=x[0]

Y=x[1]

a=1.-x

b=y-x*x

return a*a+b*b*100

def main():

target=[1,1]

easy_init=[2,2]

hard_init=[-1.2,1]

minhelper.show_minimisation_results(rosenbrock,target,easi_init,hard_init)

if_name_=='___main_____':

main()

THE ABOVE EQUATION IS GUASS NEWTON METHOD.THERE IS A VAST DIFFERENCE BETWEEN THESE TWO

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