Consider the unconstrained optimization problem min f(x)=+++122 +223-321-22-23 +3. 1.1 (5 marks) Write down the first order necessary condition and the second order necessary condition for the optimality. 1.2 (5 marks) Perform two iterations of the steepest descent method with -1.5 the initial point o 0.5 to find the minimum. Write down the -0.5 iterates 2 and 22. 1.3 (5 marks) Perform two iterations of the conjugate gradient method -1.5 0.5 to find the minimum. Write down -0.5 with the initial point zo == the iterates II and 12. 1.4 (5 marks) Find the smallest positive number a such that ha(x) = ax++++-32-2-2+3 is a convex function. 1.5 (5 marks) Does h, (z) have a global minimizer for any a > 0? Give the reason for your answer. Find all minimizers of h,(r) by using the sufficient condition for optimality when he(r) has a global minimizer.