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Q(x) = f(x^k) + (x - x^k)^T g^k + \frac{1}{2} (x - x^k)^T \mathbf{B_k} (x - x^k)  \]  A search direction can then be found by computing the vector $x^*$ that minimizes $Q(x)$. Assuming that Hessian is positive-definite, this is $x^* = x^k - \mathbf{H_k} g^k$. The next search point is then found along the ray defined by $ x^k - \alpha \mathbf{H_k} g^k$. The procedure is iterated until the gradient is zero, with some tolerance.  \subsection{The OWL-QN Algorithm}