Please help me with coding the Matlab script for this question. Thanks a lot.

Numerical optimization An important problem in numerical computing is finding the minimum z of a function f(z). This is very much related to the root-finding problem. Indeed, if f is differentiable, then a minimum r -r" of f(r) is a zero of the derivative f'(r) Unfortunately, an approach based applying the bisection method f (r) work, since the derivative values may not be available in practice. Fortunately, there is an algorithm similar to the bisection method can be used to find the minimum r using values of f(ar) only Recall that the bisection method produces pairs of numbers an, bn]. For finding minima, we will instead produce a sequence of triples Can, bra, cn] that have the following bracketing property (0.1) f (an) f(bn) and f (bn) f(cm) Hence bm can be used as an approximation to the minimum at step n. To compute such triples the algorithm proceeds in the following way: 1. Choose a new point r using the formula: bn (cn bn) if (cn bn) (bn -an) bm r (an bn) if (cn bn) (bn -an) 2. Update the triple using the formula: Dan, z, b if ac bm and f(z) f(bn) [bn, z, cnl if ac bn and f(z) f(bn) (0.2) n+1, Cn-+ n +1 Dar, bn, cnl if ac bn and f(z) f(bn) Dan, bn, if ac bn and f(z) f(bn) You may wish to verify that the update formula in (0.2) guarantees the bracketing property (0.1) holds at each step of the algorithm. Note that the choice of Y in (0.1) will affect the convergence 3-y 6. rate. It is possible to prove that the optimal choice is You should use this value Y throughout. Your task in this assignment is to examine this algorithm. First, write a script to implement the algorithm. Once you have done this, run it for N 100 iterations on the function cos