IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v162y2014i2d10.1007_s10957-013-0288-6.html
   My bibliography  Save this article

An Approximate Exact Penalty in Constrained Vector Optimization on Metric Spaces

Author

Listed:
  • A. J. Zaslavski

    (Technion)

Abstract

In this paper, we use the penalty approach in order to study a class of constrained vector minimization problems on complete metric spaces. A penalty function is said to have the generalized exact penalty property iff there is a penalty coefficient for which approximate solutions of the unconstrained penalized problem are close enough to approximate solutions of the corresponding constrained problem. For our class of problems, we establish the generalized exact penalty property and obtain an estimation of the exact penalty.

Suggested Citation

  • A. J. Zaslavski, 2014. "An Approximate Exact Penalty in Constrained Vector Optimization on Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 649-664, August.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:2:d:10.1007_s10957-013-0288-6
    DOI: 10.1007/s10957-013-0288-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-013-0288-6
    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/s10957-013-0288-6?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. Alexander J. Zaslavski, 2007. "Existence of Approximate Exact Penalty in Constrained Optimization," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 484-495, May.
    2. Alexander J. Zaslavski, 2010. "Optimization on Metric and Normed Spaces," Springer Optimization and Its Applications, Springer, number 978-0-387-88621-3, September.
    3. R. S. Burachik & A. N. Iusem & J. G. Melo, 2010. "Duality and Exact Penalization for General Augmented Lagrangians," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 125-140, October.
    4. X. X. Huang & X. Q. Yang, 2003. "A Unified Augmented Lagrangian Approach to Duality and Exact Penalization," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 533-552, August.
    5. Willard I. Zangwill, 1967. "Non-Linear Programming Via Penalty Functions," Management Science, INFORMS, vol. 13(5), pages 344-358, January.
    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. Amos Uderzo, 2016. "A Strong Metric Subregularity Analysis of Nonsmooth Mappings Via Steepest Displacement Rate," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 573-599, November.

    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. Kaiwen Meng & Xiaoqi Yang, 2015. "First- and Second-Order Necessary Conditions Via Exact Penalty Functions," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 720-752, June.
    2. M. V. Dolgopolik, 2018. "A Unified Approach to the Global Exactness of Penalty and Augmented Lagrangian Functions I: Parametric Exactness," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 728-744, March.
    3. Yu Zhou & Jin Zhou & Xiao Yang, 2014. "Existence of augmented Lagrange multipliers for cone constrained optimization problems," Journal of Global Optimization, Springer, vol. 58(2), pages 243-260, February.
    4. Regina S. Burachik & Alfredo N. Iusem & Jefferson G. Melo, 2013. "An Inexact Modified Subgradient Algorithm for Primal-Dual Problems via Augmented Lagrangians," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 108-131, April.
    5. C. Y. Wang & X. Q. Yang & X. M. Yang, 2013. "Nonlinear Augmented Lagrangian and Duality Theory," Mathematics of Operations Research, INFORMS, vol. 38(4), pages 740-760, November.
    6. M. V. Dolgopolik, 2018. "Augmented Lagrangian functions for cone constrained optimization: the existence of global saddle points and exact penalty property," Journal of Global Optimization, Springer, vol. 71(2), pages 237-296, June.
    7. X. Q. Yang & Y. Y. Zhou, 2010. "Second-Order Analysis of Penalty Function," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 445-461, August.
    8. Changyu Wang & Qian Liu & Biao Qu, 2017. "Global saddle points of nonlinear augmented Lagrangian functions," Journal of Global Optimization, Springer, vol. 68(1), pages 125-146, May.
    9. Yaohua Hu & Carisa Kwok Wai Yu & Xiaoqi Yang, 2019. "Incremental quasi-subgradient methods for minimizing the sum of quasi-convex functions," Journal of Global Optimization, Springer, vol. 75(4), pages 1003-1028, December.
    10. Y. Y. Zhou & X. Q. Yang, 2009. "Duality and Penalization in Optimization via an Augmented Lagrangian Function with Applications," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 171-188, January.
    11. S. K. Zhu & S. J. Li, 2014. "Unified Duality Theory for Constrained Extremum Problems. Part II: Special Duality Schemes," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 763-782, June.
    12. Qian Liu & Wan Tang & Xin Yang, 2009. "Properties of saddle points for generalized augmented Lagrangian," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 111-124, March.
    13. Regina Burachik & Wilhelm Freire & C. Kaya, 2014. "Interior Epigraph Directions method for nonsmooth and nonconvex optimization via generalized augmented Lagrangian duality," Journal of Global Optimization, Springer, vol. 60(3), pages 501-529, November.
    14. Boshi Tian & Yaohua Hu & Xiaoqi Yang, 2015. "A box-constrained differentiable penalty method for nonlinear complementarity problems," Journal of Global Optimization, Springer, vol. 62(4), pages 729-747, August.
    15. Angelia Nedić & Asuman Ozdaglar, 2008. "Separation of Nonconvex Sets with General Augmenting Functions," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 587-605, August.
    16. Yaohua Hu & Chong Li & Kaiwen Meng & Xiaoqi Yang, 2021. "Linear convergence of inexact descent method and inexact proximal gradient algorithms for lower-order regularization problems," Journal of Global Optimization, Springer, vol. 79(4), pages 853-883, April.
    17. Ma, Jun & Nault, Barrie R. & Tu, Yiliu (Paul), 2023. "Customer segmentation, pricing, and lead time decisions: A stochastic-user-equilibrium perspective," International Journal of Production Economics, Elsevier, vol. 264(C).
    18. R. S. Burachik & X. Q. Yang & Y. Y. Zhou, 2017. "Existence of Augmented Lagrange Multipliers for Semi-infinite Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 471-503, May.
    19. Antczak, Tadeusz, 2009. "Exact penalty functions method for mathematical programming problems involving invex functions," European Journal of Operational Research, Elsevier, vol. 198(1), pages 29-36, October.
    20. Tiago Andrade & Nikita Belyak & Andrew Eberhard & Silvio Hamacher & Fabricio Oliveira, 2022. "The p-Lagrangian relaxation for separable nonconvex MIQCQP problems," Journal of Global Optimization, Springer, vol. 84(1), pages 43-76, September.

    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:162:y:2014:i:2:d:10.1007_s10957-013-0288-6. 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.