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

Ayanna Trujillo

Ayanna Trujillo

Answered

2022-06-26

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

humbast2

humbast2

Expert

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.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?