IDEAS home Printed from https://ideas.repec.org/a/spr/snopef/v5y2024i2d10.1007_s43069-024-00323-x.html
   My bibliography  Save this article

On the Convergence of Inexact Alternate Minimization in Problems with $$\ell _0$$ ℓ 0 Penalties

Author

Listed:
  • Matteo Lapucci

    (Università di Firenze)

  • Alessio Sortino

    (Università di Firenze)

Abstract

In this work, we consider unconstrained nonlinear optimization problems where the objective function presents a penalty term on the cardinality of a subset of the variables vector; specifically, we prove that an alternate minimization scheme has global asymptotic convergence guarantees towards points satisfying first-order optimality conditions, even when the optimization step with respect to one of the blocks of variables is inexact and without introducing proximal terms. This result, supported by numerical evidence, justifies the use of pure alternate minimization in applications, even in absence of convexity assumptions.

Suggested Citation

  • Matteo Lapucci & Alessio Sortino, 2024. "On the Convergence of Inexact Alternate Minimization in Problems with $$\ell _0$$ ℓ 0 Penalties," SN Operations Research Forum, Springer, vol. 5(2), pages 1-11, June.
    • Handle: RePEc:spr:snopef:v:5:y:2024:i:2:d:10.1007_s43069-024-00323-x
    DOI: 10.1007/s43069-024-00323-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s43069-024-00323-x
    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/s43069-024-00323-x?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. Nicholas Gould & Dominique Orban & Philippe Toint, 2015. "CUTEst: a Constrained and Unconstrained Testing Environment with safe threads for mathematical optimization," Computational Optimization and Applications, Springer, vol. 60(3), pages 545-557, April.
    2. Christian Kanzow & Matteo Lapucci, 2023. "Inexact penalty decomposition methods for optimization problems with geometric constraints," Computational Optimization and Applications, Springer, vol. 85(3), pages 937-971, July.
    3. Matteo Lapucci & Tommaso Levato & Marco Sciandrone, 2021. "Convergent Inexact Penalty Decomposition Methods for Cardinality-Constrained Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 473-496, February.
    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. Yutao Zheng & Bing Zheng, 2017. "Two New Dai–Liao-Type Conjugate Gradient Methods for Unconstrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 502-509, November.
    2. Giovanni Fasano & Massimo Roma, 2016. "A novel class of approximate inverse preconditioners for large positive definite linear systems in optimization," Computational Optimization and Applications, Springer, vol. 65(2), pages 399-429, November.
    3. Yonggang Pei & Shaofang Song & Detong Zhu, 2023. "A sequential adaptive regularisation using cubics algorithm for solving nonlinear equality constrained optimization," Computational Optimization and Applications, Springer, vol. 84(3), pages 1005-1033, April.
    4. Mehiddin Al-Baali & Andrea Caliciotti & Giovanni Fasano & Massimo Roma, 2017. "Exploiting damped techniques for nonlinear conjugate gradient methods," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(3), pages 501-522, December.
    5. Nicholas I. M. Gould & Daniel P. Robinson, 2017. "A dual gradient-projection method for large-scale strictly convex quadratic problems," Computational Optimization and Applications, Springer, vol. 67(1), pages 1-38, May.
    6. Charles Audet & Kwassi Joseph Dzahini & Michael Kokkolaras & Sébastien Le Digabel, 2021. "Stochastic mesh adaptive direct search for blackbox optimization using probabilistic estimates," Computational Optimization and Applications, Springer, vol. 79(1), pages 1-34, May.
    7. Caliciotti, Andrea & Fasano, Giovanni & Roma, Massimo, 2018. "Preconditioned Nonlinear Conjugate Gradient methods based on a modified secant equation," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 196-214.
    8. Jianjun Liu & Xiangmin Xu & Xuehui Cui, 2018. "An accelerated nonmonotone trust region method with adaptive trust region for unconstrained optimization," Computational Optimization and Applications, Springer, vol. 69(1), pages 77-97, January.
    9. Rujun Jiang & Man-Chung Yue & Zhishuo Zhou, 2021. "An accelerated first-order method with complexity analysis for solving cubic regularization subproblems," Computational Optimization and Applications, Springer, vol. 79(2), pages 471-506, June.
    10. Andrea Cristofari & Marianna Santis & Stefano Lucidi & Francesco Rinaldi, 2017. "A Two-Stage Active-Set Algorithm for Bound-Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 369-401, February.
    11. Christian Kanzow & Matteo Lapucci, 2023. "Inexact penalty decomposition methods for optimization problems with geometric constraints," Computational Optimization and Applications, Springer, vol. 85(3), pages 937-971, July.
    12. S. Gratton & C. W. Royer & L. N. Vicente & Z. Zhang, 2019. "Direct search based on probabilistic feasible descent for bound and linearly constrained problems," Computational Optimization and Applications, Springer, vol. 72(3), pages 525-559, April.
    13. Sven Leyffer & Charlie Vanaret, 2020. "An augmented Lagrangian filter method," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(2), pages 343-376, October.
    14. David Ek & Anders Forsgren, 2021. "Approximate solution of system of equations arising in interior-point methods for bound-constrained optimization," Computational Optimization and Applications, Springer, vol. 79(1), pages 155-191, May.
    15. David J. Eckman & Shane G. Henderson & Sara Shashaani, 2023. "Diagnostic Tools for Evaluating and Comparing Simulation-Optimization Algorithms," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 350-367, March.
    16. Brian Irwin & Eldad Haber, 2023. "Secant penalized BFGS: a noise robust quasi-Newton method via penalizing the secant condition," Computational Optimization and Applications, Springer, vol. 84(3), pages 651-702, April.
    17. S. Gratton & Ph. L. Toint, 2020. "A note on solving nonlinear optimization problems in variable precision," Computational Optimization and Applications, Springer, vol. 76(3), pages 917-933, July.
    18. M. Ahmadvand & M. Esmaeilbeigi & A. Kamandi & F. M. Yaghoobi, 2019. "A novel hybrid trust region algorithm based on nonmonotone and LOOCV techniques," Computational Optimization and Applications, Springer, vol. 72(2), pages 499-524, March.
    19. Nicolas Boutet & Rob Haelterman & Joris Degroote, 2021. "Secant Update generalized version of PSB: a new approach," Computational Optimization and Applications, Springer, vol. 78(3), pages 953-982, April.
    20. E. G. Birgin & J. L. Gardenghi & J. M. Martínez & S. A. Santos, 2021. "On the solution of linearly constrained optimization problems by means of barrier algorithms," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 417-441, July.

    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:snopef:v:5:y:2024:i:2:d:10.1007_s43069-024-00323-x. 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.