Optimality Measures for Performance Profiles

We examine the influence of optimality measures on the benchmarking process, and show that scaling requirements lead to a convergence test for nonlinearly constrained solvers that uses a mixture of absolute and relative error measures. We show 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. Our computational experiments explore the impact of this convergence test on the benchmarking process with performance profiles.