A p-norm Discrimination Model for Two Linearly Inseparable Sets

  • Pavlo Krokhmal
  • Robert Murphey
  • Panos M. Pardalos
  • Zhaohan Yu
Part of the Springer Optimization and Its Applications book series (SOIA, volume 40)


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.


Linear Programming Problem Discrimination Model Separation Model Conic Constraint Steiner Minimum Tree 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Pavlo Krokhmal
    • 1
  • Robert Murphey
    • 2
  • Panos M. Pardalos
    • 3
  • Zhaohan Yu
    • 1
  1. 1.Department of Mechanical and Industrial EngineeringUniversity of IowaIowa CityUSA
  2. 2.Air Force Research LabEglin AFBUSA
  3. 3.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA

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