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I have a linear programming problem that I know is either unbounded or the only feasible solution is the 0 vector (depending on input). In fact, it isn't strictly a linear programming problem since I don't have an objective function, just a list of linear inequalities that need to be solved. I'm using trick to determine whether a solution exists. For each variable $x_i$, I run Mathematica's built in LinearProgramming function twice, once with objective $-x_i$ and once with objective $x_i$. If there exists non-trivial solutions then for at least one of these objective functions Mathematica reports that the linear program is unbounded.

Here's the problem, however, I would like an example feasible solution. I don't care which one. Just give me any feasible solution that isn't the 0 vector. How can I get Mathematica to do this?

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  • $\begingroup$ I think you will get much better answers if you provide a working example. Right now you're expecting people to speculate and run code in their head. $\endgroup$ – Roman May 26 at 13:57
  • $\begingroup$ Have a look at FindInstance. $\endgroup$ – Daniel Lichtblau May 26 at 14:55
  • $\begingroup$ It sounds like your problem has nothing to do with linear programming. To find an instance that satisfies a set of inequalities, you can try to use FindInstance. Oops, duplicate, thanks @DanielLichtblau $\endgroup$ – Roman May 26 at 15:00

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