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Fix another equation in ipm.tex
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amontoison committed Apr 22, 2024
1 parent 072f1aa commit e6fd8bc
Showing 1 changed file with 3 additions and 3 deletions.
6 changes: 3 additions & 3 deletions tex/sections/ipm.tex
Original file line number Diff line number Diff line change
Expand Up @@ -248,8 +248,8 @@ \subsection{Solving the KKT conditions with the interior-point method}
\tag{$K_1$}
\setlength\arraycolsep{3pt}
\begin{bmatrix}
K & G^\top \\
G & -\delta_c I \phantom{^\top}
K & \phantom{-} G^\top \\
G & -\delta_c I
\end{bmatrix}
\begin{bmatrix}
d_x \\ d_y
Expand All @@ -273,7 +273,7 @@ \subsection{Solving the KKT conditions with the interior-point method}
\end{equation}
Using the solution of the system~\eqref{eq:kkt:condensed},
we recover the updates on the slacks and inequality multipliers with
$d_z = -C r_2 + D_H(H d_x + r_4)$ and $d_s = -(D_s + \delta_w I)^{-1}(r_2 - d_z)$.
$d_z = -C r_2 + D_H(H d_x + r_4)$ and $d_s = -(D_s + \delta_w I)^{-1}(r_2 + d_z)$.
Using Sylvester's law of inertia, we can prove that
\begin{equation}
\label{eq:ipm:inertia}
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