Identifying relatively irreducible infeasible subsystems of linear inequalities

A classical problem in the study of an infeasible system linear inequalities is to determine irreducible subsystems (IISs), i.e., subsets whose proper are feasible. In this article, we examine a particular situation where only given subsystem interest for analysis infeasibility. For this, define relatively (RIISs) as that with respect subsystem. It generalization definition IIS, since IIS full system. We provide practical characterization RIISs, making link alternative polyhedron commonly used detection IISs. then turn RIISs can be obtained from Phase I simplex algorithm. answer open question regarding covering clusters IISs and show result cannot generalized RIISs. thus develop algorithm find Our findings numerically illustrated on Netlib programs.