title: Linear programming feasibility: Non connexe solution ensemble
body: <p>I would like to solve a feasibility problem subject to linear constraint. My constraint look like:</p>
  <ul>
  <li>abs(x_i - x_j) &lt; d_ij_1</li>
  <li>abs(x_i - x_j - a) &lt; d_ij_2</li>
  <li>abs(x_i - x_j) &gt; d_ij_3</li>
  <li>etc...</li>
  </ul>
  <p>I am adding a picture of an example for just 3 variables domain (I am fixing the first variable to 0). I know that the white region are valid solution, and for instance I can choose the red dot.
  <a href="https://i.stack.imgur.com/y7hm4.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/y7hm4.png" alt="enter image description here" /></a></p>
  <p>My issue is as I increase the number of unknown x_j, I cannot represent the problem anymore in a way that make it easy to find a solution. I was wondering how can I try to solve such a problem ? Would linear programming help, even though the solution space is not really connexe here ? For scale, I am looking at solving it for ~6-10 variables. Also, I posted here as I don't know what stack would be the most fitted for this kind of problem</p>