Systems of linear inequalities

[sid_galt]

Hi,
Is there a polynomial time algorithm (polynomial time in terms of the number of input constraints and variables) to solve a system of linear inequalities or or indicate whether a solution for a system of linear inequalities exists or not?
Thanks

 

[Gokul43201]

Polynomial time Simplex?

 

[sid_galt]

Simplex is exponential in the worst-case. Although there's Karmarkar's algorithm, it is for optimization of an objective function. Although it can be used for solving systems of linear inequalities, it takes n^3.5*L^2 time. I was wondering if there was a faster algorithm for giving a solution to the systems of linear inequalities.