given a system of inequalities expressed in the following way:

$Ax>\underset{\_}{k}$

where $A\in {\mathbb{M}}_{n,m(\mathbb{R})}$, with n>m, and $\underset{\_}{k}=(k,k,\dots ,k)\in {\mathbb{R}}^{n}$

In general, the system might or might not admit solutions. I would like to find a solution $x\in {\mathbb{R}}^{m}$ that minimizes the number of violated inequalities.

$Ax>\underset{\_}{k}$

where $A\in {\mathbb{M}}_{n,m(\mathbb{R})}$, with n>m, and $\underset{\_}{k}=(k,k,\dots ,k)\in {\mathbb{R}}^{n}$

In general, the system might or might not admit solutions. I would like to find a solution $x\in {\mathbb{R}}^{m}$ that minimizes the number of violated inequalities.