2/14/22 , 10:50 AM Optimization Optimization D35020 Problem 1 Interval Bisection Search and Golden Section Search - 1-D Optimization We have learned from lecture that the Interval Bisection Search (IBS) is a derivativebased Search Method for a global minimum xop, in a box constraint. Additionally, both R and Python implement 1D direct searches (no gradient) using Golden Section Search (G88). G88 chooses an interior point xGSS such that the larger subinterval is the same fraction of U L as the smaller subinterval is to the larger subinterval. Wiki summarizes the further details of GSS in the following figure. i i Diagram of a golden-section search. The initial triplet of '5' xvalues is {x1 ,x2,x3}. If f(x4)=f4a, the triplet {x1,x2,x4} is chosen for the next iteration. If f(x4)=f4b, the triplet (x2,x4,x3} is chosen. In this exercise, you will compare the number of iterations for IBS and GSS to reach a certain tolerance condition. Does GSS reach the tolerance condition with fewer iterations, on average? We will consider minimizing the convex functionf(x) = x2 in this problem. Of course, the minimum occurs at x = 0, but we focus here on the smallest number of iterations T until $ U_T - L_T l