Let f Rn R be a continuous differentiable function that has an achievable finite global minimum f (x) f with an L Lipschitz continuous gradient Given some starting point x0 Rn such that f (x0) is finite, suppose that we optimization the function f using gradient descent (GD) with iterates xk 1 xk f (xk), (1) where (0, 1 L (a) (5 points) Show that j 0 f (xj )2 2

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Let f   Rn R be a continuous differentiable function that has an achievable finite global minimum f (x)   f with an L Lipschitz continuous gradient  Given some starting point x0 Rn such that f (x0) is finite, suppose that we optimization the function f using gradient descent (GD) with iterates xk 1   xk f (xk), (1) where (0, 1 L    (a) (5 points) Show that j 0 f (xj )2 2

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Question: Let f : Rn R be a continuous differentiable function that has an achievable finite global minimum f (x) = f with an L-Lipschitz continuous

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