Problem 3. (30 pts.) Let f(x) 32-1 (a) Calculate the derivative (the gradient) (r) and the second derivative (the Hessian) "() (4pts) (b) Using ro = 10, iterate the gradient descent method (y...
Problem 3. (30 pts.) Let f(x) 32-1 (a) Calculate the derivative (the gradient) (r) and the second derivative (the Hessian) "() (4pts) (b) Using ro = 10, iterate the gradient descent method (you choose your ok) until s(k10-6 (11 pts) (c) Using zo = 10, iterate Newton's method (you choose your 0k ) until Irk-rk-1 < 10-6. (15 pts) Problem 4. (30 pts.) Let D ), (1,2), (3,2), (4,3),(4,4)] be a collection of data points. Your task is to find a line that best "fits" this collection of data (a) Formulate this problem as an optimization problem. Clearly state your objective function, what you are optimizing, and whether it is a minimization problem or a maximization problem. (10pts) (b) Using zo 2, iterate the gradient descent method until k-k-1l< 10-6. (15pts) (c) Plot the points and the line that you found. (5pts) 2 Programming Problems [Bonus 10 pts.] Repeat each step given in Problem 4 using Julia
Problem 3. (30 pts.) Let f(x) 32-1 (a) Calculate the derivative (the gradient) (r) and the second derivative (the Hessian) "() (4pts) (b) Using ro = 10, iterate the gradient descent method (you choose your ok) until s(k10-6 (11 pts) (c) Using zo = 10, iterate Newton's method (you choose your 0k ) until Irk-rk-1