Q1. Let f(x, x) = (x - 1) + (x - 3) - 1.8(x - 1)(x-3);...

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Q1. Let f(x₁, x₂) = (x₁ - 1)² + (x₂ - 3)² - 1.8(x₁ - 1)(x₂-3); xº = [0,0]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 Hº = 1 e) Do one iteration of Quasi-Newton (DFP) method toward finding a minimum; let Fº=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(x₁, x₂) = 0.01(x₁ - 1) + 0.01 (x₂-3)* + (x₁ - 1)² + (x₂ - 3)² - 1.8(x₁ - 1)(x₂ - 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 Hº = I d) Do two iterations of Quasi-Newton (DFP) method toward finding a minimum; let Fº= 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 (x₁, x₂) = 100 (x₂-x2)² + (1-x₂)²; 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(x₁, x₂) = (x₁ - 1)² + (x₂ - 3)2 - 1.8(x₁ - 1)(x₂-3); xº = [0,0], Ao = 1 Do two iterations of trust region method toward finding the minimum Q1. Let f(x₁, x₂) = (x₁ - 1)² + (x₂ - 3)² - 1.8(x₁ - 1)(x₂-3); xº = [0,0]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 Hº = 1 e) Do one iteration of Quasi-Newton (DFP) method toward finding a minimum; let Fº=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(x₁, x₂) = 0.01(x₁ - 1) + 0.01 (x₂-3)* + (x₁ - 1)² + (x₂ - 3)² - 1.8(x₁ - 1)(x₂ - 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 Hº = I d) Do two iterations of Quasi-Newton (DFP) method toward finding a minimum; let Fº= 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 (x₁, x₂) = 100 (x₂-x2)² + (1-x₂)²; 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(x₁, x₂) = (x₁ - 1)² + (x₂ - 3)2 - 1.8(x₁ - 1)(x₂-3); xº = [0,0], Ao = 1 Do two iterations of trust region method toward finding the minimum

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Q1 Let fx1 x2 x1 1 x2 3 18x1 1x2 3 x0 0 0 a Steepest Descent Method Calculate the gradient fx fx1 fx2 Initialize x x0 Compute the search direction d f... View the full answer