IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v171y2016i1d10.1007_s10957-016-0991-1.html
   My bibliography  Save this article

New Augmented Lagrangian-Based Proximal Point Algorithm for Convex Optimization with Equality Constraints

Author

Listed:
  • Yuan Shen

    (Nanjing University of Finance and Economics)

  • Hongyong Wang

    (Nanjing University of Finance and Economics)

Abstract

The augmented Lagrangian method is a classic and efficient method for solving constrained optimization problems. However, its efficiency is still, to a large extent, dependent on how efficient the subproblem be solved. When an accurate solution to the subproblem is computationally expensive, it is more practical to relax the subproblem. Specifically, when the objective function has a certain favorable structure, the relaxed subproblem yields a closed-form solution that can be solved efficiently. However, the resulting algorithm usually suffers from a slower convergence rate than the augmented Lagrangian method. In this paper, based on the relaxed subproblem, we propose a new algorithm with a faster convergence rate. Numerical results using the proposed approach are reported for three specific applications. The output is compared with the corresponding results from state-of-the-art algorithms, and it is shown that the efficiency of the proposed method is superior to that of existing approaches.

Suggested Citation

  • Yuan Shen & Hongyong Wang, 2016. "New Augmented Lagrangian-Based Proximal Point Algorithm for Convex Optimization with Equality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 251-261, October.
  • Handle: RePEc:spr:joptap:v:171:y:2016:i:1:d:10.1007_s10957-016-0991-1
    DOI: 10.1007/s10957-016-0991-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-016-0991-1
    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/s10957-016-0991-1?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. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    2. R. S. Burachik & S. Scheimberg & B. F. Svaiter, 2001. "Robustness of the Hybrid Extragradient Proximal-Point Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 111(1), pages 117-136, October.
    3. NESTEROV, Yu., 2005. "Smooth minimization of non-smooth functions," LIDAM Reprints CORE 1819, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. R. T. Rockafellar, 1976. "Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 97-116, May.
    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. Feng Ma, 2019. "On relaxation of some customized proximal point algorithms for convex minimization: from variational inequality perspective," Computational Optimization and Applications, Springer, vol. 73(3), pages 871-901, July.

    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. Silvia Villa & Lorenzo Rosasco & Sofia Mosci & Alessandro Verri, 2014. "Proximal methods for the latent group lasso penalty," Computational Optimization and Applications, Springer, vol. 58(2), pages 381-407, June.
    2. Ya-Feng Liu & Xin Liu & Shiqian Ma, 2019. "On the Nonergodic Convergence Rate of an Inexact Augmented Lagrangian Framework for Composite Convex Programming," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 632-650, May.
    3. Yanlai Song & Mihai Postolache, 2021. "Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its Application," Mathematics, MDPI, vol. 9(12), pages 1-17, June.
    4. Yixuan Yang & Yuchao Tang & Chuanxi Zhu, 2019. "Iterative Methods for Computing the Resolvent of Composed Operators in Hilbert Spaces," Mathematics, MDPI, vol. 7(2), pages 1-16, February.
    5. Guoqiang Wang & Bo Yu, 2019. "PAL-Hom method for QP and an application to LP," Computational Optimization and Applications, Springer, vol. 73(1), pages 311-352, May.
    6. Pilar Lopez-Llompart & G. Mathias Kondolf, 2016. "Encroachments in floodways of the Mississippi River and Tributaries Project," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 81(1), pages 513-542, March.
    7. Cheng, Jianquan & Bertolini, Luca, 2013. "Measuring urban job accessibility with distance decay, competition and diversity," Journal of Transport Geography, Elsevier, vol. 30(C), pages 100-109.
    8. M. De Donno & M. Pratelli, 2006. "A theory of stochastic integration for bond markets," Papers math/0602532, arXiv.org.
    9. Prilly Oktoviany & Robert Knobloch & Ralf Korn, 2021. "A machine learning-based price state prediction model for agricultural commodities using external factors," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 1063-1085, December.
    10. Michelle Sheran Sylvester, 2007. "The Career and Family Choices of Women: A Dynamic Analysis of Labor Force Participation, Schooling, Marriage and Fertility Decisions," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(3), pages 367-399, July.
    11. Henrekson, Magnus & Johansson, Dan, 2010. "Firm Growth, Institutions and Structural Transformation," Ratio Working Papers 150, The Ratio Institute.
    12. Karen K. Lewis, 2011. "Global Asset Pricing," Annual Review of Financial Economics, Annual Reviews, vol. 3(1), pages 435-466, December.
    13. DAVID M. BLAU & WILBERT van der KLAAUW, 2013. "What Determines Family Structure?," Economic Inquiry, Western Economic Association International, vol. 51(1), pages 579-604, January.
    14. Panagiota DIONYSOPOULOU & Georgios SVARNIAS & Theodore PAPAILIAS, 2021. "Total Quality Management In Public Sector, Case Study: Customs Service," Regional Science Inquiry, Hellenic Association of Regional Scientists, vol. 0(1), pages 153-168, June.
    15. Mauricio Romero Sicre, 2020. "On the complexity of a hybrid proximal extragradient projective method for solving monotone inclusion problems," Computational Optimization and Applications, Springer, vol. 76(3), pages 991-1019, July.
    16. Afanasyev, Dmitriy O. & Fedorova, Elena A. & Popov, Viktor U., 2015. "Fine structure of the price–demand relationship in the electricity market: Multi-scale correlation analysis," Energy Economics, Elsevier, vol. 51(C), pages 215-226.
    17. Peter Viggo Jakobsen, 2009. "Small States, Big Influence: The Overlooked Nordic Influence on the Civilian ESDP," Journal of Common Market Studies, Wiley Blackwell, vol. 47(1), pages 81-102, January.
    18. Julie Holland Mortimer, 2007. "Price Discrimination, Copyright Law, and Technological Innovation: Evidence from the Introduction of DVDs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(3), pages 1307-1350.
    19. Suwan Shen & Xi Feng & Zhong Ren Peng, 2016. "A framework to analyze vulnerability of critical infrastructure to climate change: the case of a coastal community in Florida," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 84(1), pages 589-609, October.
    20. Jean-Bernard Chatelain & Kirsten Ralf, 2017. "Can We Identify the Fed's Preferences?," Working Papers halshs-01549908, HAL.

    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:joptap:v:171:y:2016:i:1:d:10.1007_s10957-016-0991-1. 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.