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\section*{Home work 3}

Minimize $ f(x)= x_1^2+ x_2^4 + x_1\,x_2$ using Trust Region method. The starting  point is $ (1, 1)$, radius $\Delta_0$ of the trust region in the first step is $\Delta_0=0.7$. Use quadratic approximation of $f$. Perform three steps. Use contour plot to visualize the optimization process.
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