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Optimized choice of parameters in interior-point methods for linear programming

Author

Listed:
  • Luiz-Rafael Santos

    (Federal University of Santa Catarina)

  • Fernando Villas-Bôas

    (IMECC, University of Campinas)

  • Aurelio R. L. Oliveira

    (IMECC, University of Campinas)

  • Clovis Perin

    (IMECC, University of Campinas)

Abstract

In this work, we propose a predictor–corrector interior point method for linear programming in a primal–dual context, where the next iterate is chosen by the minimization of a polynomial merit function of three variables: the first is the steplength, the second defines the central path and the third models the weight of a corrector direction. The merit function minimization is performed by restricting it to constraints defined by a neighborhood of the central path that allows wide steps. In this framework, we combine different directions, such as the predictor, the corrector and the centering directions, with the aim of producing a better one. The proposed method generalizes most of predictor–corrector interior point methods, depending on the choice of the variables described above. Convergence analysis of the method is carried out, considering an initial point that has a good practical performance, which results in Q-linear convergence of the iterates with polynomial complexity. Numerical experiments using the Netlib test set are made, which show that this approach is competitive when compared to well established solvers, such as PCx.

Suggested Citation

  • Luiz-Rafael Santos & Fernando Villas-Bôas & Aurelio R. L. Oliveira & Clovis Perin, 2019. "Optimized choice of parameters in interior-point methods for linear programming," Computational Optimization and Applications, Springer, vol. 73(2), pages 535-574, June.
    • Handle: RePEc:spr:coopap:v:73:y:2019:i:2:d:10.1007_s10589-019-00079-9
    DOI: 10.1007/s10589-019-00079-9
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    References listed on IDEAS

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    1. Renato D. C. Monteiro & Ilan Adler & Mauricio G. C. Resende, 1990. "A Polynomial-Time Primal-Dual Affine Scaling Algorithm for Linear and Convex Quadratic Programming and Its Power Series Extension," Mathematics of Operations Research, INFORMS, vol. 15(2), pages 191-214, May.
    2. Gondzio, Jacek, 2012. "Interior point methods 25 years later," European Journal of Operational Research, Elsevier, vol. 218(3), pages 587-601.
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    Cited by:

    1. Fabio Vitor & Todd Easton, 2022. "Projected orthogonal vectors in two-dimensional search interior point algorithms for linear programming," Computational Optimization and Applications, Springer, vol. 83(1), pages 211-246, September.

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