Please ANSWER (B) only

1. Consider an iterative search method to find the minimiser of a unimodal function f: R R over interval (a, b). Let In, n = 1,2,..., be the length of the uncertainty interval obtained after (n+1) f-calculations, and to be the length of the initial interval. Define the reduction rate of iteration k > 1 to be = L. We assume that the iterative search method i compares the function values at two intermediate points in each iteration in order to reduce the uncertainty interval; ii reuses the left/right immediate point in the previous iteration as the right/left immediate point; iii chooses the intermediate points in a symmetric way. (a) Show that the problem of minimising the length of the uncertainty interval In, n > 2, can be formulated as min 71.72..., s.t. 172...un 7+1 = 1-7, k = 1,...,n-1 1 to be = L. We assume that the iterative search method i compares the function values at two intermediate points in each iteration in order to reduce the uncertainty interval; ii reuses the left/right immediate point in the previous iteration as the right/left immediate point; iii chooses the intermediate points in a symmetric way. (a) Show that the problem of minimising the length of the uncertainty interval In, n > 2, can be formulated as min 71.72..., s.t. 172...un 7+1 = 1-7, k = 1,...,n-1