Infeasibility, Unboundedness and Instability

All users will, generally, encounter occasions in which an instance of the model they are developing is solved and found to be infeasible or unbounded. An infeasible problem is a problem that has no solution while an unbounded problem is one where the constraints do not restrict the objective function and the objective goes to infinity. Both situations often arise due to errors or shortcomings in the formulation or in the data defining the problem. When such a result is found it is typically not clear what it is about the formulation or the data that has caused the problem.

Problem instability arises when the coefficient values of the problem are such that the optimization algorithms find it difficult to converge to a solution. This is typically because of large ratios between the largest and smallest coefficients in the rows or columns and the handling of the range of numerical values in the algorithm is causing floating point accuracy issues. Problem instability generally manifests in either long run times or spurious infeasibilities.

It is often difficult to deal with these issues since it is often difficult to diagnose the cause of the problems. In this chapter we discuss the various approaches and tools provided by the Optimizer for handling these issues.