# Conjugate directions

Direction vectors chosen in an algorithm that are conjugate with previous directions, with respect to the hessian of the objective. For the unconstrained quadratic, $LaTeX: x^T Qx + c^Tx$ (where $LaTeX: Q$ is symmetric), direction vector $LaTeX: d$ is conjugate if $LaTeX: d^T Q d^k = 0$ for all previous direction vectors, $LaTeX: d^k$.