IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v63y2016i3d10.1007_s10589-015-9791-z.html
   My bibliography  Save this article

Active-set prediction for interior point methods using controlled perturbations

Author

Listed:
  • Coralia Cartis

    (University of Oxford)

  • Yiming Yan

    (University of Edinburgh)

Abstract

We propose the use of controlled perturbations to address the challenging question of optimal active-set prediction for interior point methods. Namely, in the context of linear programming, we consider perturbing the inequality constraints/bounds so as to enlarge the feasible set. We show that if the perturbations are chosen appropriately, the solution of the original problem lies on or close to the central path of the perturbed problem. We also find that a primal-dual path-following algorithm applied to the perturbed problem is able to accurately predict the optimal active set of the original problem when the duality gap for the perturbed problem is not too small; furthermore, depending on problem conditioning, this prediction can happen sooner than predicting the active set for the perturbed problem or when the original one is solved. Encouraging preliminary numerical experience is reported when comparing activity prediction for the perturbed and unperturbed problem formulations.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:63:y:2016:i:3:d:10.1007_s10589-015-9791-z
    DOI: 10.1007/s10589-015-9791-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-015-9791-z
    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/s10589-015-9791-z?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. Kevin A. McShane & Clyde L. Monma & David Shanno, 1989. "An Implementation of a Primal-Dual Interior Point Method for Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 1(2), pages 70-83, May.
    2. Z.-Q. Luo & O. L. Mangasarian & J. Ren & M. V. Solodov, 1994. "New Error Bounds for the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 880-892, November.
    3. Gondzio, Jacek, 2012. "Interior point methods 25 years later," European Journal of Operational Research, Elsevier, vol. 218(3), pages 587-601.
    4. Yinyu Ye & Michael J. Todd & Shinji Mizuno, 1994. "An O(√nL)-Iteration Homogeneous and Self-Dual Linear Programming Algorithm," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 53-67, February.
    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. M. Paul Laiu & André L. Tits, 2019. "A constraint-reduced MPC algorithm for convex quadratic programming, with a modified active set identification scheme," Computational Optimization and Applications, Springer, vol. 72(3), pages 727-768, April.

    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. 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.
    2. Lorenzo Fiaschi & Marco Cococcioni, 2022. "A Non-Archimedean Interior Point Method and Its Application to the Lexicographic Multi-Objective Quadratic Programming," Mathematics, MDPI, vol. 10(23), pages 1-34, November.
    3. 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.
    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. Enzo Busseti, 2019. "Derivative of a Conic Problem with a Unique Solution," Papers 1903.05753, arXiv.org, revised Mar 2019.
    6. Luo, Z-Q. & Sturm, J.F. & Zhang, S., 1998. "Conic convex programming and self-dual embedding," Econometric Institute Research Papers EI 9815, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    7. 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.
    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. R. Almeida & A. Teixeira, 2015. "On the convergence of a predictor-corrector variant algorithm," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 401-418, July.
    11. Mehdi Karimi & Levent Tunçel, 2020. "Primal–Dual Interior-Point Methods for Domain-Driven Formulations," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 591-621, May.
    12. Michaël Allouche & Emmanuel Gobet & Clara Lage & Edwin Mangin, 2023. "Structured Dictionary Learning of Rating Migration Matrices for Credit Risk Modeling," Working Papers hal-03715954, HAL.
    13. 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.
    14. Duarte Jr, A. M., 2000. "Fast Computation of Efficient Portfolios," Finance Lab Working Papers flwp_32, Finance Lab, Insper Instituto de Ensino e Pesquisa.
    15. 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.
    16. 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.
    17. Gondzio, Jacek, 2016. "Crash start of interior point methods," European Journal of Operational Research, Elsevier, vol. 255(1), pages 308-314.
    18. Freund, Robert Michael. & Mizuno, Shinji., 1996. "Interior point methods : current status and future directions," Working papers 3924-96., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    19. Belli, Edoardo, 2022. "Smoothly adaptively centered ridge estimator," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    20. Quoc Tran-Dinh & Anastasios Kyrillidis & Volkan Cevher, 2018. "A Single-Phase, Proximal Path-Following Framework," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1326-1347, November.

    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:63:y:2016:i:3:d:10.1007_s10589-015-9791-z. 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.