A note on using performance and data profiles for training algorithms

This article shows how to use performance and data profile benchmarking tools to improve the performance of algorithms. We propose to achieve this goal by defining and approximately solving suitable optimization problems involving the parameters of the algorithm under consideration. Because these problems do not have derivatives and may involve integer variables, we suggest using a mixed-integer derivative-free optimizer for this task. A numerical illustration is presented (using the BFO package), which indicates that the obtained gains are potentially significant.