(Solved): QUESTION 4.[8 pts] Use the method of gradient descent to find the minimum of a function: f(x,y)= ...

QUESTION $$4.[8$$ pts] Use the method of gradient descent to find the minimum of a function: $$f(x,y)?=\frac{5}{9}{x}^2?\frac{8}{9}xy??\frac{56}{9}{x}^{?}+\frac{5}{9}{y}^2+\frac{52}{9}y+\frac{164}{9}$$ Use the method of gradient descent to find the $$(x,y)$$ value that produces the minimum $$z=f(x,y)$$ when we start gradient descent from $$(0,0)$$ and use a learning rate of $$?=0.1$$. Stop the gradient descent when either: i. Difference in consecutive $$x_i$$ values is less than $$0.000001\left(?x_{n+1}?x_n?<0.000001\right)$$ or ii. The number of gradient descent iterations exceeds 1024 .