Linear programming feasibility: Non connexe solution ensemble

Question

I would like to solve a feasibility problem subject to linear constraint. My constraint look like:

• abs(x_i - x_j) < d_ij_1
• abs(x_i - x_j - a) < d_ij_2
• abs(x_i - x_j) > d_ij_3
• etc...

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.

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

question from:https://stackoverflow.com/questions/65649318/linear-programming-feasibility-non-connexe-solution-ensemble

Answer 1

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