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A new proposal to improve the early iterations in the interior point method

Author

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  • Manolo Rodriguez Heredia

    (Federal University of Southern and Southeastern Pará)

  • Aurelio Ribeiro Leite Oliveira

    (University of Campinas)

Abstract

We propose a modification that allows reducing the number of restarts in the computation of the Controlled Cholesky Factorization preconditioner. We use this preconditioner in the solution of linear systems arising from primal-dual interior point method. The Controlled Cholesky Factorization preconditioner depends on the fill-in parameter and the correction parameter that controls diagonal fault. We use geometric and algebraic tools to modify these parameters. In particular, we determine an equation whose exact solution avoids the diagonal fault. Numerical experiments with large-scale problems show that these modifications reduce the number of restarts. These experiments indicate that the new approach is robust and competitive.

Suggested Citation

  • Manolo Rodriguez Heredia & Aurelio Ribeiro Leite Oliveira, 2020. "A new proposal to improve the early iterations in the interior point method," Annals of Operations Research, Springer, vol. 287(1), pages 185-208, April.
    • Handle: RePEc:spr:annopr:v:287:y:2020:i:1:d:10.1007_s10479-019-03254-7
    DOI: 10.1007/s10479-019-03254-7
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    References listed on IDEAS

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    1. Gondzio, Jacek, 2012. "Interior point methods 25 years later," European Journal of Operational Research, Elsevier, vol. 218(3), pages 587-601.
    2. Porfirio Suñagua & Aurelio R. L. Oliveira, 2017. "A new approach for finding a basis for the splitting preconditioner for linear systems from interior point methods," Computational Optimization and Applications, Springer, vol. 67(1), pages 111-127, May.
    3. Jacek Gondzio, 2012. "Matrix-free interior point method," Computational Optimization and Applications, Springer, vol. 51(2), pages 457-480, March.
    4. Anibal Azevedo & Aurelio Oliveira & Secundino Soares, 2009. "Interior point method for long-term generation scheduling of large-scale hydrothermal systems," Annals of Operations Research, Springer, vol. 169(1), pages 55-80, July.
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