A p-norm Discrimination Model for Two Linearly Inseparable Sets

We propose a new p-norm linear discrimination model that generalizes the model of Bennett and Mangasarian (Optim. Methods Softw. 1:23–34, 1992) and reduces to linear programming problems with p-order conic constraints. We demonstrate that the developed model possesses excellent methodological and computational properties (e.g., it does not allow for a null separating hyperplane when the sets are linearly separable, etc.). The presented approach for handling linear programming problems with p-order conic constraints relies on construction of polyhedral approximations for p-order cones. A case study on several popular data sets that illustrates the advantages of the developed model is conducted.