Removing redundant linear constraints using Gaussian elimination

Question

I have a set of linear constraints in the form of $c_i x \ge d_i$ and I need to identify if an additional constraint is redundant with respect of the previously mentioned set.

Here I found a similar question, however it is not clear to me how to use Gaussian elimination to identify the redundant constraint.

Do you have any hints on this?

Answer 1

See my answer to this MO question.

Answer 2

You might be interested in reading about "pruning constraints" which is discussed in chapter 11 (entitled "Analytic center cutting plane-method") of Vandenberghe's 236c notes. See slide 11-12 ("pruning constraints").