## Mathematical Programming in Machine Learning (1996)

Venue: | Nonlinear Optimization and Applications |

Citations: | 13 - 2 self |

### BibTeX

@INPROCEEDINGS{Mangasarian96mathematicalprogramming,

author = {O. L. Mangasarian},

title = {Mathematical Programming in Machine Learning},

booktitle = {Nonlinear Optimization and Applications},

year = {1996},

pages = {283--295},

publisher = {Plenum Publishing}

}

### OpenURL

### Abstract

We describe in this work a number of central problems of machine learning and show how they can be modeled and solved as mathematical programs of various complexity. 1 Introduction Machine learning can be thought of as generalizing information gleaned from given data to new unseen data. As such it can be considered as determining a mapping between an input set and an output set in a robust manner that is amenable to generalization. In this work we shall concentrate on a number of fundamental problems of machine learning, and show how mathematical programming plays a significant role in their formulation and solution. In Section 2 we consider the classical problem of discriminating between two point sets in the n-dimensional real space R n , and show that its complexity ranges from polynomial-time to NP-complete, depending on the measure of error employed. When the traditional distance of a misclassified point to a separating plane is used as an error, a single linear program [6, 15,...