# Non-trivial feasible solution to unbounded linear programming problem

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?

• 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. – Roman May 26 at 13:57
• Have a look at FindInstance. – Daniel Lichtblau May 26 at 14:55
• 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 – Roman May 26 at 15:00