How do we start this I dont understand it

1. multiple minima (5 pts.). We will explore the behavior of minimization algorithms for a simple univariate case with multiple minima. Let L(a:) = 3:4 149:3 + 60932 7093. (a) Plot the loss function L over the set [1,8]. Is it convex? If yes, why? If no, are there regions where it is (locally) convex? (b) What do you expect the behavior of Nelder-Mead or Newton's method will be? (c) Use the NelderMead algorithm to nd the argument that minimizes L. Initialize your two points randomly in [0, 2]. Plot a vertical bar where the minimizer is, together with the function. Compare to the result of R's optim just for sanity check. (d) Keep track of the \"best\" NealderMead point at each iteration ($1) and make two plots showing this sequence. In the rst plot show the values Man) for di'erent iterations on top of the loss function L. In the second one plot the convergence behavior as in the plot of page 3, w07d1 notes. (e) Repeat the above two problems with initial two points in [6,8]. Explain your result