Q1. Let f(x, x) = (x - 1) + (x - 3) - 1.8(x - 1)(x-3); x = [0,0] a) Do two iterations of Steepest descent method toward finding a minimum b) Do two iterations of Conjugate gradient method toward finding a minimum c) Do one iteration of Newton's method toward finding a minimum d) Do one iteration of Quasi-Newton (BFGS) method toward finding a minimum; let H = 1 e) Do one iteration of Quasi-Newton (DFP) method toward finding a minimum; let F=1 f) Apply Armijo's rule in the steepest descent direction followed by quadratic fit to estimate the minimum g) Use Matlab 'fminunc' command to find the minimum Q2. Let f(x, x) = 0.01(x - 1) + 0.01 (x-3)* + (x - 1) + (x - 3) - 1.8(x - 1)(x - 3); x = [0,0] a) Do two iterations of Steepest descent method toward finding a minimum b) Do two iterations of Conjugate gradient method toward finding a minimum c) Do two iterations of Quasi-Newton (BFGS) method toward finding a minimum; let H = I d) Do two iterations of Quasi-Newton (DFP) method toward finding a minimum; let F= I e) Apply Armijo's rule in the steepest descent direction followed by quadratic fit to estimate the minimum f) Use Matlab 'fminunc' command to find the minimum Q3. Let f (x, x) = 100 (x-x2) + (1-x); x = [1,1]" a) Do two iterations of Steepest descent method toward finding a minimum b) Do two iterations of Conjugate gradient method toward finding a minimum c) Do two iterations of Quasi-Newton (BFGS) method toward finding a minimum; let H = 1 d) Do two iterations of Quasi-Newton (DFP) method toward finding a minimum; let F" = I e) Apply Armijo's rule in the steepest descent direction followed by quadratic fit to estimate the minimum f) Use Matlab 'fminunc' command to find the minimum Q4. Let f(x, x) = (x - 1) + (x - 3)2 - 1.8(x - 1)(x-3); x = [0,0], Ao = 1 Do two iterations of trust region method toward finding the minimum