Linear Programs

The following routines attempt to solve primal-dual pairs of linear programs in either “direct” conic form,

\[\begin{split}\min_x & \{\; c^T x \; | \; A x = b \;\wedge\; x \ge 0 \;\}, \\ \max_{y,z} & \{\; - b^T y \; | \; A^T y - z + c = 0 \;\wedge\; z \ge 0 \;\},\end{split}\]

or “affine” conic form

\[\begin{split}\min_{x,s} & \{\; c^T x \; | \; A x = b \;\wedge\; G x + s = h\;\wedge\; s \ge 0 \;\}, \\ \max_{y,z} & \{\; - b^T y - h^T z \; | \; A^T y + G^T z + c = 0 \;\wedge\; z \ge 0 \;\}.\end{split}\]

By default a Mehrotra Predictor-Corrector primal-dual Interior Point Method is used.

• Direct Linear Programs
• Affine Linear Programs