Revised simplex method: Difference between revisions

Content deleted Content added
Line 19:
:<math>
\begin{align}
\boldsymbol{Ax} & = \boldsymbol{b}\text{,} \\
\boldsymbol{A}^{\mathrm{T}} \boldsymbol{\lambda} + \boldsymbol{s} & = \boldsymbol{c}\text{,} \\
\boldsymbol{x} & \ge \boldsymbol{0}\text{,} \\
\boldsymbol{s} & \ge \boldsymbol{0}\text{,} \\
\boldsymbol{s}^{\mathrm{T}} \boldsymbol{x} & = 0
\end{align}
Line 51:
\boldsymbol{c_B} \\
\boldsymbol{c_N}
\end{bmatrix}\text{,} \\
\boldsymbol{s} & =
\begin{bmatrix}
\boldsymbol{s_B} \\
\boldsymbol{s_N}
\end{bmatrix}\text{.}
\end{align}
</math>
Line 65:
\begin{align}
\boldsymbol{B}^{\mathrm{T}} \boldsymbol{\lambda} & = \boldsymbol{c_B}\text{,} \\
\boldsymbol{N}^{\mathrm{T}} \boldsymbol{\lambda} + \boldsymbol{s_N} & = \boldsymbol{c_N}\text{,}
\end{align}
</math>
Line 73:
:<math>
\begin{align}
\boldsymbol{\lambda} & = \boldsymbol{B}^{-\mathrm{T}} \boldsymbol{c_B}\text{,} \\
\boldsymbol{s_N} & = \boldsymbol{c_N} - \boldsymbol{N}^{\mathrm{T}} \boldsymbol{\lambda}\text{.}
\end{align}
</math>