IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v73y2019i3d10.1007_s10898-018-0721-3.html
   My bibliography  Save this article

A generic interval branch and bound algorithm for parameter estimation

Author

Listed:
  • Bertrand Neveu

    (Université Paris–Est)

  • Martin Gorce

    (Université Paris–Est)

  • Pascal Monasse

    (Université Paris–Est)

  • Gilles Trombettoni

    (University of Montpellier, CNRS)

Abstract

In engineering sciences, parameter estimation is a challenging problem consisting in computing the parameters of a parametric model that fit observed data. The system is defined by unknown parameters and sometimes internal constraints. The observed data provide constraints on the parameters. This problem is particularly difficult when some observation constraints correspond to outliers and/or the constraints are non convex. The ransac randomized algorithm can efficiently handle it, but is non deterministic and must be specialized for every problem. This paper presents the first generic interval branch and bound algorithm that produces a model maximizing the number of observation constraints satisfied within a given tolerance. This tool is inspired by the IbexOpt branch and bound algorithm for constrained global optimization (NLP) and is endowed with an improved version of a relaxed intersection operator applied to observations. Experiments have been carried out on two different computer vision problems. They highlight a significant speedup w.r.t. Jaulin et al.’s interval method in 2D and 3D shape recognition problems (having three parameters). We have also obtained promising results on a stereo vision problem where the essential matrix (five parameters) is estimated exactly at a good accuracy in hours for models having a thousand points, a typical size for such problems.

Suggested Citation

  • Bertrand Neveu & Martin Gorce & Pascal Monasse & Gilles Trombettoni, 2019. "A generic interval branch and bound algorithm for parameter estimation," Journal of Global Optimization, Springer, vol. 73(3), pages 515-535, March.
    • Handle: RePEc:spr:jglopt:v:73:y:2019:i:3:d:10.1007_s10898-018-0721-3
    DOI: 10.1007/s10898-018-0721-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-018-0721-3
    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/s10898-018-0721-3?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. Bertrand Neveu & Gilles Trombettoni & Ignacio Araya, 2016. "Node selection strategies in interval Branch and Bound algorithms," Journal of Global Optimization, Springer, vol. 64(2), pages 289-304, February.
    2. Ruth Misener & Christodoulos Floudas, 2014. "ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations," Journal of Global Optimization, Springer, vol. 59(2), pages 503-526, July.
    3. Ignacio Araya & Gilles Trombettoni & Bertrand Neveu & Gilles Chabert, 2014. "Upper bounding in inner regions for global optimization under inequality constraints," Journal of Global Optimization, Springer, vol. 60(2), pages 145-164, October.
    Full references (including those not matched with items on IDEAS)

    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. Ignacio Araya & Jose Campusano & Damir Aliquintui, 2019. "Nonlinear biobjective optimization: improvements to interval branch & bound algorithms," Journal of Global Optimization, Springer, vol. 75(1), pages 91-110, September.
    2. Ignacio Araya & Bertrand Neveu, 2018. "lsmear: a variable selection strategy for interval branch and bound solvers," Journal of Global Optimization, Springer, vol. 71(3), pages 483-500, July.
    3. Bertrand Neveu & Gilles Trombettoni & Ignacio Araya, 2016. "Node selection strategies in interval Branch and Bound algorithms," Journal of Global Optimization, Springer, vol. 64(2), pages 289-304, February.
    4. Stuart M. Harwood & Paul I. Barton, 2017. "How to solve a design centering problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 215-254, August.
    5. Jaromił Najman & Alexander Mitsos, 2019. "On tightness and anchoring of McCormick and other relaxations," Journal of Global Optimization, Springer, vol. 74(4), pages 677-703, August.
    6. Lingxun Kong & Christos T. Maravelias, 2020. "On the Derivation of Continuous Piecewise Linear Approximating Functions," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 531-546, July.
    7. Victor Reyes & Ignacio Araya, 2021. "AbsTaylor: upper bounding with inner regions in nonlinear continuous global optimization problems," Journal of Global Optimization, Springer, vol. 79(2), pages 413-429, February.
    8. Emily Speakman & Jon Lee, 2018. "On branching-point selection for trilinear monomials in spatial branch-and-bound: the hull relaxation," Journal of Global Optimization, Springer, vol. 72(2), pages 129-153, October.
    9. Farough Motamed Nasab & Zukui Li, 2023. "Multistage Adaptive Robust Binary Optimization: Uncertainty Set Lifting versus Partitioning through Breakpoints Optimization," Mathematics, MDPI, vol. 11(18), pages 1-24, September.
    10. Jaromił Najman & Dominik Bongartz & Alexander Mitsos, 2021. "Linearization of McCormick relaxations and hybridization with the auxiliary variable method," Journal of Global Optimization, Springer, vol. 80(4), pages 731-756, August.
    11. Liang, Zheng & Liang, Yingzong & Luo, Xianglong & Chen, Jianyong & Yang, Zhi & Wang, Chao & Chen, Ying, 2022. "Superstructure-based mixed-integer nonlinear programming framework for hybrid heat sources driven organic Rankine cycle optimization," Applied Energy, Elsevier, vol. 307(C).
    12. Iosif Pappas & Nikolaos A. Diangelakis & Efstratios N. Pistikopoulos, 2021. "The exact solution of multiparametric quadratically constrained quadratic programming problems," Journal of Global Optimization, Springer, vol. 79(1), pages 59-85, January.
    13. Ricardo M. Lima & Ignacio E. Grossmann, 2017. "On the solution of nonconvex cardinality Boolean quadratic programming problems: a computational study," Computational Optimization and Applications, Springer, vol. 66(1), pages 1-37, January.
    14. Yi Zhang & Nikolaos V. Sahinidis & Carlos Nohra & Gang Rong, 2020. "Optimality-based domain reduction for inequality-constrained NLP and MINLP problems," Journal of Global Optimization, Springer, vol. 77(3), pages 425-454, July.
    15. Fränk Plein & Johannes Thürauf & Martine Labbé & Martin Schmidt, 2022. "A bilevel optimization approach to decide the feasibility of bookings in the European gas market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(3), pages 409-449, June.
    16. Ivo Nowak & Norman Breitfeld & Eligius M. T. Hendrix & Grégoire Njacheun-Njanzoua, 2018. "Decomposition-based Inner- and Outer-Refinement Algorithms for Global Optimization," Journal of Global Optimization, Springer, vol. 72(2), pages 305-321, October.
    17. Luo, Xianglong & Huang, Xiaojian & El-Halwagi, Mahmoud M. & Ponce-Ortega, José María & Chen, Ying, 2016. "Simultaneous synthesis of utility system and heat exchanger network incorporating steam condensate and boiler feedwater," Energy, Elsevier, vol. 113(C), pages 875-893.
    18. Artur M. Schweidtmann & Alexander Mitsos, 2019. "Deterministic Global Optimization with Artificial Neural Networks Embedded," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 925-948, March.
    19. Ignacio Araya & Damir Aliquintui & Franco Ardiles & Braulio Lobo, 2021. "Nonlinear biobjective optimization: improving the upper envelope using feasible line segments," Journal of Global Optimization, Springer, vol. 79(2), pages 503-520, February.
    20. Ignacio Araya & Victor Reyes, 2016. "Interval Branch-and-Bound algorithms for optimization and constraint satisfaction: a survey and prospects," Journal of Global Optimization, Springer, vol. 65(4), pages 837-866, August.

    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:jglopt:v:73:y:2019:i:3:d:10.1007_s10898-018-0721-3. 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.