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On the Complexity of a Linear Programming Predictor-Corrector Algorithm Using the Two Norm Neighborhood

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Optimization, Learning Algorithms and Applications (OL2A 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1754))

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Abstract

In this work the complexity of a feasible variant of a Linear Programming Predictor-Corrector algorithm specialized for transportation and assignment problems is explored. A \(O(n |\log (\epsilon )|)\) iteration complexity was achieved by proving that the step size computed by the studied algorithm is bounded at each iteration by \(\frac{\theta (4-3\theta )(1-\theta )^2}{n}\), where \(\theta \in [0,1[\). Therefore, allowing to conclude that the analyzed Predictor-Corrector algorithm that uses the 2-norm neighborhood has polynomial iteration complexity and is Q-linearly convergent.

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Acknowledgements

The research was partially financed by the Portuguese Funds through FCT (Fundação para a Ciência e a Tecnologia), within the Projects UIDB/00013/2020 and UIDP/00013/2020.

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Authors and Affiliations

  1. Mathematics Centre, University of Minho - Pole CMAT - UTAD, Braga, Portugal

    Ana Teixeira & R. Almeida

  2. Department of Mathematics, University of Trás-os-Montes e Alto Douro, 5000-801, Vila Real, Portugal

    Ana Teixeira & R. Almeida

Authors
  1. Ana Teixeira
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  2. R. Almeida
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Corresponding author

Correspondence to R. Almeida .

Editor information

Editors and Affiliations

  1. Instituto Politécnico de Bragança, Bragança, Portugal

    Ana I. Pereira

  2. University of Ljubljana, Ljubljana, Slovenia

    Andrej Košir

  3. Instituto Politécnico de Bragança, Bragança, Portugal

    Florbela P. Fernandes

  4. Instituto Politécnico de Bragança, Bragança, Portugal

    Maria F. Pacheco

  5. Instituto Politécnico de Bragança, Bragança, Portugal

    João P. Teixeira

  6. Instituto Politécnico de Bragança, Bragança, Portugal

    Rui P. Lopes

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Teixeira, A., Almeida, R. (2022). On the Complexity of a Linear Programming Predictor-Corrector Algorithm Using the Two Norm Neighborhood. In: Pereira, A.I., Košir, A., Fernandes, F.P., Pacheco, M.F., Teixeira, J.P., Lopes, R.P. (eds) Optimization, Learning Algorithms and Applications. OL2A 2022. Communications in Computer and Information Science, vol 1754. Springer, Cham. https://doi.org/10.1007/978-3-031-23236-7_37

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  • DOI: https://doi.org/10.1007/978-3-031-23236-7_37

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-23235-0

  • Online ISBN: 978-3-031-23236-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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