| \begin{array}{rl}{\left[\begin{array}{lll}{A}&{0}&{0}\\{0}&{A^{\top}}&{I}\\{S^{k}}&{0}&{X^{k}}\end{array}\right]\left[\begin{array}{l}{\dot{x}}\\{\dot{\lambda}}\\{\dot{s}}\end{array}\right]}&{=\left[\begin{array}{c}{r_{b}(x^{k})}\\{r_{c}(\lambda^{k},s^{k})}\\{x^{k}\circ s^{k}}\end{array}\right]}\\{\left[\begin{array}{lll}{A}&{0}&{0}\\{0}&{A^{\top}}&{I}\\{S^{k}}&{0}&{X^{k}}\end{array}\right]\left[\begin{array}{l}{\ddot{x}}\\{\ddot{\lambda}}\\{\ddot{s}}\end{array}\right]}&{=\left[\begin{array}{c}{0}\\{0}\\{-2\dot{x}\circ\dot{s}}\end{array}\right].}\end{array} |
