Transformation matrices <i>T</i>_<i>v</i>, and constraint vectors <i>c</i>_<i>v</i> and <i>d</i>_<i>v</i>, that define the truncation <i>c</i>_<i>v</i> < <i>T</i>_<i>v</i><i>x</i> < <i>d</i>_<i>v</i> for six relevant regions shown in Fig 2.

Dummy inequalities −∞ < xi < ∞ were introduced into the transformation matrices T1, T2 and T3 to ensure that these matrices have rank equal to their dimension. The order of rows in T23, c23 and d23 has been switched so that this matrix and these vectors possess the form that would be obtained from a generalised two-step algorithm for ST-MNDs of any dimension described later in the “Materials and methods” section.