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( 1 2 scores ) Given an optimization problem min f ( x ) = x 1 2 + 2 x 2 2 - 2

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Given an optimization problem min

f (x) = x_{1}^{2} + 2 x_{2}^{2} - 2 x_{1} x_{2} .

Let the initial iterate

x^{(1)} = (- 1, 2)^{T} .

Use the Newton's method to solve this problem and find the next iterate

x^{(2)} .

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