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I. QUESTION 1: ABOUT GRADIENT DESCENT [30 POINTS] Consider the following function: : RR, f(x) = 5xx+3x. (1) We want to find its optimum
I. QUESTION 1: ABOUT GRADIENT DESCENT [30 POINTS] Consider the following function: : RR, f(x) = 5xx+3x. (1) We want to find its optimum variable x* and its minimum function value f* = f(x*). A. Simple gradient descent [20 points] With a fixed learning rate n = 0.01, solve two iterations of the gradient descent algorithm and find x* and f* after these two iterations. Start with the initial point x = 1. Hint: Use the chain rule and derivative of multiplication for calculation of the derivative. B. Momentum [10 points] Solve the second iteration of gradient descent in Section I-A with momentum term (with a = = 0.1 and n = 0.01), and find x* and * after this second iteration. Start with the initial point x = 1.
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