Consider the function J(x1, x2) = 1+ (2x1 – 2)2 – 10x1e-(x2-1)2. = > = = > (a) By hand, show that (x1, x2) = (7,1) is a

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Consider The Function J X1 X2 1 2x1 2 2 10x1e X2 1 2 A By Hand Show That X1 X2 7 1 Is A 1 (94.36 KiB) Viewed 19 times

Consider the function J(x1, x2) = 1+ (2x1 – 2)2 – 10x1e-(x2-1)2. = > = = > (a) By hand, show that (x1, x2) = (7,1) is a stationary point of the function J (i.e. show that both partial derivatives of J are zero at this point). (b) Calculate the Hessian of J, and verify that (x1, x2) = (7,1) is a minimum of J. (c) Write code to apply gradient descent to find the minimum of J. Start with an initial guess of (x1, x2) = (0,0), and take 500 steps with 8 =0.01. Check that you obtain a solution that is close to the true solution. = -