In machine learning and applied fields of statistics, receiver operating characterization (ROC) analysis is commonly used to select optimal algorithms/models. However, at a lecture I once attended on mathematical optimization, I remember the lecturer saying that ROC analysis just wasn't considered a useful approach to optimization. No justification was offered. As a non-mathematician, I want to know (1) is this true that ROC analysis is not used in optimization problems and (2) if so, why?
The lecturer was wrong. It is now an active area of research (though outside my speciality). For instance, in a paper at NIPS in 2003, they discuss using ROC AUC instead of error as an objective function in training neural networks.