Mathematical optimization in classification and regression trees

Abstract Classification and regression trees, as well their variants, are off-the-shelf methods in Machine Learning. In this paper, we review recent contributions within the Continuous Optimization Mixed-Integer Linear paradigms to develop novel formulations research area. We compare those terms of nature decision variables constraints required, optimization algorithms proposed. illustrate how these powerful enhance flexibility tree models, being better suited incorporate desirable properties such cost-sensitivity, explainability, fairness, deal with complex data, functional data.