# Big-M method

An alternative to using Phase I, a large number $LaTeX: M$ is used as a linear penalty in the composite objective:
$LaTeX: \min \{ c^T x + M \; e^T v: Ax + v = b, \; x, v \ge 0 \},$
where $LaTeX: v$ is an artificial variable and $LaTeX: e = (1, 1, ..., 1)^T$.