Final steps

• Update the inverse Hessian approximation using the following formula:

$$s_k = \mathbf{x}_{k+1} - \mathbf{x}_k, \quad y_k = \nabla f(\mathbf{x}_{k+1}) - \nabla f(\mathbf{x}_k)$$ $$H_{k+1} = H_k + \frac{s_k s_k^T}{s_k^T y_k} - \frac{H_k y_k y_k^T H_k}{y_k^T H_k y_k}$$

• Repeat the process until convergence, i.e., $\|\nabla f(\mathbf{x}_k)\|$ is sufficiently small.

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