#second-order-optimization

Question 1: Single choice

Near the current point $\mathbf{w}_0$ , a function $J$ is approximated by $f(\mathbf{w}) = J(\mathbf{w}_0) + \mathbf{g}^\top(\mathbf{w} - \mathbf{w}_0) + \tfrac12(\mathbf{w} - \mathbf{w}_0)^\top H(\mathbf{w} - \mathbf{w}_0)$ , where $\mathbf{g}$ is the gradient and $H$ a symmetric positive definite Hessian. Which point minimises $f$ , i.e. what is the Newton update?

$\mathbf{w}^* = \mathbf{w}_0 - H\mathbf{g}$ 1
$\mathbf{w}^* = \mathbf{w}_0 + H^{-1}\mathbf{g}$ 2
$\mathbf{w}^* = \mathbf{w}_0 - \mathbf{g}$ 3
$\mathbf{w}^* = \mathbf{w}_0 - H^{-1}\mathbf{g}$ 4

#second-order-optimization

Timed test