Document Type

Conference Proceeding

Original Publication Date


Journal/Book/Conference Title

14th INFORMS Computing Society Conference

First Page


Last Page





Originally published at

Creative Commons Attribution 3.0 Unported License (CC BY 3.0)

Accompanying data files available at

Date of Submission

February 2015


The support vector machine (SVM) is a flexible classification method that accommodates a kernel trick to learn nonlinear decision rules. The traditional formulation as an optimization problem is a quadratic program. In efforts to reduce computational complexity, some have proposed using an L1-norm regularization to create a linear program (LP). In other efforts aimed at increasing the robustness to outliers, investigators have proposed using the ramp loss which results in what may be expressed as a quadratic integer programming problem (QIP). In this paper, we consider combining these ideas for ramp loss SVM with L1-norm regularization. The result is four formulations for SVM that each may be expressed as a mixed integer linear program (MILP). We observe that ramp loss SVM with L1-norm regularization provides robustness to outliers with the linear kernel. We investigate the time required to find good solutions to the various formulations using a branch and bound solver.


Creative Commons Attribution 3.0 Unported (CC BY 3.0)

Is Part Of

VCU Statistical Sciences and Operations Research Publications