On p-norm linear discrimination

Yana Morenko; Alexander Vinel; Zhaohan Yu; Pavlo Krokhmal

doi:10.1016/j.ejor.2013.06.053

On p-norm linear discrimination

Yana Morenko, Alexander Vinel, Zhaohan Yu, Pavlo Krokhmal

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We consider a p-norm linear discrimination model that generalizes the model of Bennett and Mangasarian (1992) and reduces to a linear programming problem with p-order cone constraints. The proposed approach for handling linear programming problems with p-order cone constraints is based on reformulation of p-order cone optimization problems as second order cone programming (SOCP) problems when p is rational. Since such reformulations typically lead to SOCP problems with large numbers of second order cones, an "economical" representation that minimizes the number of second order cones is proposed. A case study illustrating the developed model on several popular data sets is conducted.

Original language	English (US)
Pages (from-to)	784-789
Number of pages	6
Journal	European Journal of Operational Research
Volume	231
Issue number	3
DOIs	https://doi.org/10.1016/j.ejor.2013.06.053
State	Published - Dec 16 2013
Externally published	Yes

Keywords

Linear separation
Second order cone programming
p-Order cone programming

ASJC Scopus subject areas

General Computer Science
Modeling and Simulation
Management Science and Operations Research
Information Systems and Management

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10.1016/j.ejor.2013.06.053

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title = "On p-norm linear discrimination",

abstract = "We consider a p-norm linear discrimination model that generalizes the model of Bennett and Mangasarian (1992) and reduces to a linear programming problem with p-order cone constraints. The proposed approach for handling linear programming problems with p-order cone constraints is based on reformulation of p-order cone optimization problems as second order cone programming (SOCP) problems when p is rational. Since such reformulations typically lead to SOCP problems with large numbers of second order cones, an {"}economical{"} representation that minimizes the number of second order cones is proposed. A case study illustrating the developed model on several popular data sets is conducted.",

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T1 - On p-norm linear discrimination

AU - Morenko, Yana

AU - Vinel, Alexander

AU - Yu, Zhaohan

AU - Krokhmal, Pavlo

N1 - Funding Information: The authors would like to acknowledge partial support of the US Air Force Office of Scientific Research and National Science Foundation.

PY - 2013/12/16

Y1 - 2013/12/16

N2 - We consider a p-norm linear discrimination model that generalizes the model of Bennett and Mangasarian (1992) and reduces to a linear programming problem with p-order cone constraints. The proposed approach for handling linear programming problems with p-order cone constraints is based on reformulation of p-order cone optimization problems as second order cone programming (SOCP) problems when p is rational. Since such reformulations typically lead to SOCP problems with large numbers of second order cones, an "economical" representation that minimizes the number of second order cones is proposed. A case study illustrating the developed model on several popular data sets is conducted.

AB - We consider a p-norm linear discrimination model that generalizes the model of Bennett and Mangasarian (1992) and reduces to a linear programming problem with p-order cone constraints. The proposed approach for handling linear programming problems with p-order cone constraints is based on reformulation of p-order cone optimization problems as second order cone programming (SOCP) problems when p is rational. Since such reformulations typically lead to SOCP problems with large numbers of second order cones, an "economical" representation that minimizes the number of second order cones is proposed. A case study illustrating the developed model on several popular data sets is conducted.

KW - Linear separation

KW - Second order cone programming

KW - p-Order cone programming

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M3 - Article

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EP - 789

JO - European Journal of Operational Research

JF - European Journal of Operational Research

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On p-norm linear discrimination

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Keywords

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