Test if a system of linear inequalities has a solution.system of linear inequalities A x...

Ayanna Trujillo

Ayanna Trujillo



Test if a system of linear inequalities has a solution.
system of linear inequalities A x > 0 where A is a m × n matrix with m n. Is there a simple way to check whether it has a solution?
What if one of the columns of A is parametrized? In a more general case, I have one of the columns of A ( t ) as a ( t ) = t v + w, where t [ 0 , 1 ]. Is there a way to check whether all of the systems
A ( t ) x > 0 , t [ 0 , 1 ]
have a solution?

Answer & Explanation




2022-06-27Added 21 answers

Numerically solving the following linear program
minimize 0 subject to A x ε 1 m
should produce a solution or tell you that none exists. Pick a small ε > 0. If m and n are small enough, you could even use quantifier elimination.

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