Consider the minimization problem on slide 1 with fixed step size. The objective function is f(x1,x2)=(10x12+x22)/2 a. write r code for the gradient decent algorithm. Show that the algorithm converges to the global minimum. python

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Consider the minimization problem on slide 1 with fixed step size. The objective function is f(x1,x2)=(10x12+x22)/2

a. write r code for the gradient decent algorithm. Show that the algorithm converges to the global minimum.

python

Fixed step size
Simply take t = t for all k = 1, 2, 3, ..., can diverge if t is too big.
Consider f(x) = (10x² + x3)/2, gradient descent after 8 steps:
20
10
0
-10
-20
-20
-10
O
10
8
Transcribed Image Text:Fixed step size Simply take t = t for all k = 1, 2, 3, ..., can diverge if t is too big. Consider f(x) = (10x² + x3)/2, gradient descent after 8 steps: 20 10 0 -10 -20 -20 -10 O 10 8
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