On Finding a Relative Interior Point of a Polyhedral Set

This paper proposes a new linear program for finding a relative interior point of a polyhedral set. Based on characterizing the relative interior of a polyhedral set through its polyhedral representing sets, two main contribu- tions are made. First, we complete the existing results in the literature that require the non-negativity of the given polyhedral set. Then, we deal with the general case where this requirement may not be met.