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A Primal–Dual Smooth Perceptron–von Neumann Algorithm

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Discrete Geometry and Optimization

Part of the book series: Fields Institute Communications ((FIC,volume 69))

Abstract

We propose an elementary algorithm for solving a system of linear inequalities A T y>0 or its alternative Ax=0,x≥0,x≠0. Our algorithm is a smooth version of the perceptron and von Neumann algorithms. Our algorithm retains the simplicity of these algorithms but has a significantly improved convergence rate. Our approach also extends to more general conic systems provided a suitable smoothing oracle is available.

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Authors and Affiliations

  1. Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, 15213, USA

    Negar Soheili & Javier Peña

Authors
  1. Negar Soheili
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  2. Javier Peña
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Corresponding author

Correspondence to Javier Peña .

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Editors and Affiliations

  1. , Mathematics & Statistics, University of Calgary, University Drive NW, Calgary, T2N 1N4, Alberta, Canada

    Karoly Bezdek

  2. , Department of Computing, McMaster University, Main Street West 1280, Hamilton, L8S 4K1, Ontario, Canada

    Antoine Deza

  3. School of Engineering, Department of Management Science and Eng, Stanford University, Via Ortega 475, Stanford, 94305, California, USA

    Yinyu Ye

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Soheili, N., Peña, J. (2013). A Primal–Dual Smooth Perceptron–von Neumann Algorithm. In: Bezdek, K., Deza, A., Ye, Y. (eds) Discrete Geometry and Optimization. Fields Institute Communications, vol 69. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00200-2_17

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