Four methods for global numerical black box optimization with origins in the mathematical programming community are described and experimentally compared with the state of the art evolutionary method, BIPOP-CMA-ES. The methods chosen for the comparison exhibit various features that are potentially interesting for the evolutionary computation community: systematic sampling of the search space (DIRECT, MCS) possibly combined with a local search method (MCS), or a multi-start approach (NEWUOA, GLOBAL) possibly equipped with a careful selection of points to run a local optimizer from (GLOBAL). The recently proposed “comparing continuous optimizers” (COCO) methodology was adopted as the basis for the comparison. Based on the results, we draw suggestions about which algorithm should be used depending on the available budget of function evaluations, and we propose several possibilities for hybridizing evolutionary algorithms (EAs) with features of the other compared algorithms.