Isolating Infeasibility

A number of the basic methods for isolating IISs do not depend on any properties of the optimization model itself. Instead they are purely logical, requiring nothing more than the ability to evaluate constraints or to determine whether a set or subset of constraints is feasible or infeasible. It is quite difficult to accurately determine the feasibility status of an arbitrary set of constraints in some model forms. In practice, we can rely on this ability only for sets of linear constraints. Numerical difficulties, usually related to the feasibility tolerances, can arise even for linear constraints, but this is fortunately relatively rare. Accurate assessment of the feasibility status for nonlinear programs can be quite difficult, and can even be problematic for mixed-integer programs.

For this reason, many of the general logical algorithms described in this Section are currently applicable only to linear systems. However there is hope that they will eventually be applicable to other classes of optimization models as better algorithms for accurately determining feasibility status in those other classes appear.