optimization - How to show that the method of steepest descent does not converge in a finite number of steps? - Mathematics Stack Exchange

I have a function, $$f(\mathbf{x})=x_1^2+4x_2^2-4x_1-8x_2,$$ which can also be expressed as $$f(\mathbf{x})=(x_1-2)^2+4(x_2-1)^2-8.$$ I've deduced the minimizer $\mathbf{x^*}$ as $(2,1)$ with $f^*

Solved Suppose that xk and xk+1 are two consecutive points

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Solved 2. In this problem we study the convergence property

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Solved 1. Implement the steepest descent and fixed-step size

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