Solve an optimization problem with Conjugate Gradient Method in Matlab. The range of alpha should be calculated by Matlab as the inequalities provided in hints require.

1. Suppose that we seek to minimize the following function: where is a given parameter. Note that the domain of this function is (a) (Conjugate Gradient Method) Now solve this problem using conjugate gradi 100, using the following ent method. Run your algorithm for starting points: (i) co (8, 90)T () Zo (1,40)T (ii) zo -(15, 68.69)T (iv) = (10.20)T 10 and for (b) What sort of convergence behavior do you observe? Does the optimal solution depend on different initial points? Hint: Note that f(x1, 22) is only defined on the domain X and you have computed a direction d= (d1, d2), then note that a value of the upper bound is effectively given by the largest value of for which the following constraints are satisfied: The largest value of satisfying these conditions can easily be computed by applying appropriate logic