  This paper surveys the machine learning literature and presents in an
optimization framework several commonly used machine learning approaches.
Particularly, mathematical optimization models are presented for regression,
classification, clustering, deep learning, and adversarial learning, as well as
new emerging applications in machine teaching, empirical model learning, and
Bayesian network structure learning. Such models can benefit from the
advancement of numerical optimization techniques which have already played a
distinctive role in several machine learning settings. The strengths and the
shortcomings of these models are discussed and potential research directions
and open problems are highlighted.
