IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v73y2019i2d10.1007_s10589-019-00079-9.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-019-00079-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-019-00079-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Castro, Jordi & Escudero, Laureano F. & Monge, Juan F., 2023. "On solving large-scale multistage stochastic optimization problems with a new specialized interior-point approach," European Journal of Operational Research, Elsevier, vol. 310(1), pages 268-285.
    2. Luciana Casacio & Aurelio R. L. Oliveira & Christiano Lyra, 2018. "Using groups in the splitting preconditioner computation for interior point methods," 4OR, Springer, vol. 16(4), pages 401-410, December.
    3. Stefano Cipolla & Jacek Gondzio, 2023. "Proximal Stabilized Interior Point Methods and Low-Frequency-Update Preconditioning Techniques," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1061-1103, June.
    4. Bittencourt, Tiberio & Ferreira, Orizon Pereira, 2015. "Local convergence analysis of Inexact Newton method with relative residual error tolerance under majorant condition in Riemannian manifolds," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 28-38.
    5. Fatemeh Marzbani & Akmal Abdelfatah, 2024. "Economic Dispatch Optimization Strategies and Problem Formulation: A Comprehensive Review," Energies, MDPI, vol. 17(3), pages 1-31, January.
    6. Stefania Bellavia & Valentina De Simone & Daniela di Serafino & Benedetta Morini, 2016. "On the update of constraint preconditioners for regularized KKT systems," Computational Optimization and Applications, Springer, vol. 65(2), pages 339-360, November.
    7. Yu, Jianxi & Liu, Pei & Li, Zheng, 2021. "Data reconciliation of the thermal system of a double reheat power plant for thermal calculation," Renewable and Sustainable Energy Reviews, Elsevier, vol. 148(C).
    8. de Groot, Oliver & Mazelis, Falk & Motto, Roberto & Ristiniemi, Annukka, 2021. "A toolkit for computing Constrained Optimal Policy Projections (COPPs)," Working Paper Series 2555, European Central Bank.
    9. Martijn H. H. Schoot Uiterkamp & Marco E. T. Gerards & Johann L. Hurink, 2022. "On a Reduction for a Class of Resource Allocation Problems," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1387-1402, May.
    10. E. de Klerk & C. Roos & T. Terlaky, 1998. "Polynomial Primal-Dual Affine Scaling Algorithms in Semidefinite Programming," Journal of Combinatorial Optimization, Springer, vol. 2(1), pages 51-69, March.
    11. Michaël Allouche & Emmanuel Gobet & Clara Lage & Edwin Mangin, 2024. "Structured dictionary learning of rating migration matrices for credit risk modeling," Computational Statistics, Springer, vol. 39(6), pages 3431-3456, September.
    12. Cecilia Orellana Castro & Manolo Rodriguez Heredia & Aurelio R. L. Oliveira, 2023. "Recycling basic columns of the splitting preconditioner in interior point methods," Computational Optimization and Applications, Springer, vol. 86(1), pages 49-78, September.
    13. repec:hal:wpaper:hal-03715954 is not listed on IDEAS
    14. Enrico Bettiol & Lucas Létocart & Francesco Rinaldi & Emiliano Traversi, 2020. "A conjugate direction based simplicial decomposition framework for solving a specific class of dense convex quadratic programs," Computational Optimization and Applications, Springer, vol. 75(2), pages 321-360, March.
    15. Camila de Lima & Antonio Roberto Balbo & Thiago Pedro Donadon Homem & Helenice de Oliveira Florentino Silva, 2017. "A hybrid approach combining interior-point and branch-and-bound methods applied to the problem of sugar cane waste," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(2), pages 147-164, February.
    16. 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.
    17. Dominik Garmatter & Margherita Porcelli & Francesco Rinaldi & Martin Stoll, 2023. "An improved penalty algorithm using model order reduction for MIPDECO problems with partial observations," Computational Optimization and Applications, Springer, vol. 84(1), pages 191-223, January.
    18. Fabio Vitor & Todd Easton, 2018. "The double pivot simplex method," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 109-137, February.
    19. Gondzio, Jacek, 2016. "Crash start of interior point methods," European Journal of Operational Research, Elsevier, vol. 255(1), pages 308-314.
    20. Coralia Cartis & Yiming Yan, 2016. "Active-set prediction for interior point methods using controlled perturbations," Computational Optimization and Applications, Springer, vol. 63(3), pages 639-684, April.
    21. Belli, Edoardo, 2022. "Smoothly adaptively centered ridge estimator," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:73:y:2019:i:2:d:10.1007_s10589-019-00079-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.