Question: Consider the following convex quadratic optimization problem given by where minimizexR fo(x) = xPx+q7x, 5 4 6 5 P = 4 9 15 ,q=

Consider the following convex quadratic optimization problem given by where minimizexR fo(x) = xPx+q7x, 5 4 6 5 P = 4 9 15 ,q= 6 15 35 6 Plot the sequence fo(xk), k = 0,1,... for each of the methods below, with the initial point x0 = [246]T. (a) Solve the problem using the gradient descent method with Armijo backtracking line search with parameters Y 0.5 and 3 = 0.8 = (b) Solve the problem using the Newton's method. How many iterations does it take to find the optimal point? (c) Solve the problem using the Davidon-Fletcher-Powell (DFP) method. (d) Solve the problem using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method.

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