IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v73y2019i1d10.1007_s10898-018-0682-6.html
   My bibliography  Save this article

Spectral projected gradient method for stochastic optimization

Author

Listed:
  • Nataša Krejić

    (University of Novi Sad)

  • Nataša Krklec Jerinkić

    (University of Novi Sad)

Abstract

We consider the Spectral Projected Gradient method for solving constrained optimization problems with the objective function in the form of mathematical expectation. It is assumed that the feasible set is convex, closed and easy to project on. The objective function is approximated by a sequence of different Sample Average Approximation functions with different sample sizes. The sample size update is based on two error estimates—SAA error and approximate solution error. The Spectral Projected Gradient method combined with a nonmonotone line search is used. The almost sure convergence results are achieved without imposing explicit sample growth condition. Preliminary numerical results show the efficiency of the proposed method.

Suggested Citation

  • Nataša Krejić & Nataša Krklec Jerinkić, 2019. "Spectral projected gradient method for stochastic optimization," Journal of Global Optimization, Springer, vol. 73(1), pages 59-81, January.
    • Handle: RePEc:spr:jglopt:v:73:y:2019:i:1:d:10.1007_s10898-018-0682-6
    DOI: 10.1007/s10898-018-0682-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-018-0682-6
    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/s10898-018-0682-6?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. Birgin, Ernesto G. & Martínez, Jose Mario & Raydan, Marcos, 2014. "Spectral Projected Gradient Methods: Review and Perspectives," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 60(i03).
    2. Bastin, Fabian & Cirillo, Cinzia & Toint, Philippe L., 2006. "Application of an adaptive Monte Carlo algorithm to mixed logit estimation," Transportation Research Part B: Methodological, Elsevier, vol. 40(7), pages 577-593, August.
    3. Güzin Bayraksan & David P. Morton, 2011. "A Sequential Sampling Procedure for Stochastic Programming," Operations Research, INFORMS, vol. 59(4), pages 898-913, August.
    4. Raghu Pasupathy, 2010. "On Choosing Parameters in Retrospective-Approximation Algorithms for Stochastic Root Finding and Simulation Optimization," Operations Research, INFORMS, vol. 58(4-part-1), pages 889-901, August.
    5. A. Shapiro & Y. Wardi, 1996. "Convergence Analysis of Stochastic Algorithms," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 615-628, August.
    6. Sigrún Andradöttir, 1996. "A Scaled Stochastic Approximation Algorithm," Management Science, INFORMS, vol. 42(4), pages 475-498, April.
    7. Fabian Bastin & Cinzia Cirillo & Philippe Toint, 2006. "An adaptive Monte Carlo algorithm for computing mixed logit estimators," Computational Management Science, Springer, vol. 3(1), pages 55-79, January.
    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. Emelogu, Adindu & Chowdhury, Sudipta & Marufuzzaman, Mohammad & Bian, Linkan & Eksioglu, Burak, 2016. "An enhanced sample average approximation method for stochastic optimization," International Journal of Production Economics, Elsevier, vol. 182(C), pages 230-252.
    2. Johannes Royset, 2013. "On sample size control in sample average approximations for solving smooth stochastic programs," Computational Optimization and Applications, Springer, vol. 55(2), pages 265-309, June.
    3. Stefania Bellavia & Nataša Krejić & Benedetta Morini, 2020. "Inexact restoration with subsampled trust-region methods for finite-sum minimization," Computational Optimization and Applications, Springer, vol. 76(3), pages 701-736, July.
    4. Johannes O. Royset & Roberto Szechtman, 2013. "Optimal Budget Allocation for Sample Average Approximation," Operations Research, INFORMS, vol. 61(3), pages 762-776, June.
    5. Wang, Honggang, 2012. "Retrospective optimization of mixed-integer stochastic systems using dynamic simplex linear interpolation," European Journal of Operational Research, Elsevier, vol. 217(1), pages 141-148.
    6. Carolina Osorio & Michel Bierlaire, 2013. "A Simulation-Based Optimization Framework for Urban Transportation Problems," Operations Research, INFORMS, vol. 61(6), pages 1333-1345, December.
    7. Suvrajeet Sen & Yifan Liu, 2016. "Mitigating Uncertainty via Compromise Decisions in Two-Stage Stochastic Linear Programming: Variance Reduction," Operations Research, INFORMS, vol. 64(6), pages 1422-1437, December.
    8. Powell, Warren B., 2019. "A unified framework for stochastic optimization," European Journal of Operational Research, Elsevier, vol. 275(3), pages 795-821.
    9. Bismark Singh & David P. Morton & Surya Santoso, 2018. "An adaptive model with joint chance constraints for a hybrid wind-conventional generator system," Computational Management Science, Springer, vol. 15(3), pages 563-582, October.
    10. Roberto Andreani & Marcos Raydan, 2021. "Properties of the delayed weighted gradient method," Computational Optimization and Applications, Springer, vol. 78(1), pages 167-180, January.
    11. Filippozzi, Rafaela & Gonçalves, Douglas S. & Santos, Luiz-Rafael, 2023. "First-order methods for the convex hull membership problem," European Journal of Operational Research, Elsevier, vol. 306(1), pages 17-33.
    12. Saurabh Bansal & James S. Dyer, 2017. "Technical Note—Multivariate Partial-Expectation Results for Exact Solutions of Two-Stage Problems," Operations Research, INFORMS, vol. 65(6), pages 1526-1534, December.
    13. Sun, Haoze & Weng, Chengguo & Zhang, Yi, 2017. "Optimal multivariate quota-share reinsurance: A nonparametric mean-CVaR framework," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 197-214.
    14. Flam, Sjur Didrik & Mirman, Leonard J., 1998. "Groping for optimal growth," Journal of Economic Dynamics and Control, Elsevier, vol. 23(2), pages 191-207, September.
    15. Andrej Čopar & Blaž Zupan & Marinka Zitnik, 2019. "Fast optimization of non-negative matrix tri-factorization," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-15, June.
    16. N. Krejić & E. H. M. Krulikovski & M. Raydan, 2023. "A Low-Cost Alternating Projection Approach for a Continuous Formulation of Convex and Cardinality Constrained Optimization," SN Operations Research Forum, Springer, vol. 4(4), pages 1-24, December.
    17. Chen, Shih-Pin, 2007. "Solving fuzzy queueing decision problems via a parametric mixed integer nonlinear programming method," European Journal of Operational Research, Elsevier, vol. 177(1), pages 445-457, February.
    18. Pospíšil, Lukáš & Dostál, Zdeněk, 2018. "The projected Barzilai–Borwein method with fall-back for strictly convex QCQP problems with separable constraints," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 145(C), pages 79-89.
    19. Na Zhao & Qingzhi Yang & Yajun Liu, 2017. "Computing the generalized eigenvalues of weakly symmetric tensors," Computational Optimization and Applications, Springer, vol. 66(2), pages 285-307, March.
    20. Akar, Gulsah & Clifton, Kelly J. & Doherty, Sean T., 2012. "Redefining activity types: Who participates in which leisure activity?," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(8), pages 1194-1204.

    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:1:d:10.1007_s10898-018-0682-6. 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.