The Quadratic Programming Solver

For a quadratic programming problem, an irreducible infeasible set (IIS) is an infeasible subset of constraints and variable bounds that becomes feasible if any single constraint or variable bound is removed. It is possible to have more than one IIS in an infeasible QP. Identifying an IIS can help isolate the structural infeasibility in a QP. The IIS= ON option directs the QP solver to search for an IIS in a specified QP.

Whether a quadratic programming problem is feasible or infeasible is determined by its constraints and variable bounds, which have nothing to do with its objective function. When you specify the IIS=ON option, the QP solver treats this problem as a linear programming problem by ignoring its objective function. Then finding IIS is the same as what the LP solver does with the IIS=ON option. See the section Irreducible Infeasible Set in Chapter 7: The Linear Programming Solver, for more information about the irreducible infeasible set.