Constraint classification in mathematical programming

Consider a set of algebraic inequality constraints defining either an empty or a nonempty feasible region. It is known that each constraint can be classified as either absolutely strongly redundant, relatively strongly redundant, absolutely weakly redundant, relatively weakly redundant, or necessary. The authors show that it is worth making a distinction between weakly necessary constraints and strongly necessary constraints. They also present a feasible set cover method which can detect both weakly and strongly necessary constraints. The main interest in constraint classification is due to the advantages gained by the removal of redundant constraints. Since classification errors are likely to occur, the authors examine how the removal of a single constraint can affect the classification of the remaining constraints.