Optimality Measures for Performance Profiles

We examine the importance of optimality measures when benchmarking a set of solvers and show that the scale-invariance requirements we impose lead to a convergence test for nonlinearly constrained optimization solvers that uses a mixture of absolute and relative error measures. We demonstrate that this convergence test is well behaved at any point where the constraints satisfy the Mangasarian--Fromovitz constraint qualification and also avoids the explicit use of a complementarity measure. Computational experiments explore the impact of this convergence test on the benchmarking process with performance profiles.