1. Using the gradient descent method to optimize the following functions in the range of x,y ? [-2, 2] with the initial point $x_0$ = [1.5 1.5].
f(x, y) = x$^2$ + xy + 2y$^2$
a. Choose the stop criteria as
$|f_{i} - f_{i-1}| < 10^{-1}$
where $f_{i-1}$ and $f_i$ represent the values at $t$ + 1 and $t$ steps.
b. Choose learning rate: 0.1, get the final solution ($x$) which is the coordinate [x,y] when the algorithm stop. Plot the trajectory of x (all x from $x_0$ to x) together with the f(x,y) in the same figure which is similar as follows
