IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v111y2001i1d10.1023_a1017575415432.html
   My bibliography  Save this article

Minimizing and Stationary Sequences of Convex Constrained Minimization Problems

Author

Listed:
  • Y. R. He

    (Chinese University of Hong Kong)

Abstract

In the asymptotic analysis of the minimization problem for a nonsmooth convex function on a closed convex set X in ℝn, one can consider the corresponding problem of minimizing a smooth convex function F on ℝn, where F denotes the Moreau–Yosida regularization of f. We study the interrelationship between the minimizing/stationary sequence for f and that for F. An algorithm is given to generate iteratively a possibly unbounded sequence, which is shown to be a minimizing sequence of f under certain regularity and uniform continuity assumptions.

Suggested Citation

  • Y. R. He, 2001. "Minimizing and Stationary Sequences of Convex Constrained Minimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 111(1), pages 137-153, October.
    • Handle: RePEc:spr:joptap:v:111:y:2001:i:1:d:10.1023_a:1017575415432
    DOI: 10.1023/A:1017575415432
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1017575415432
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1017575415432?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. Correa Romar, 2014. "Mathematical Foci," Mathematical Economics Letters, De Gruyter, vol. 2(1-2), pages 5-11, August.
    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. J. R. Birge & L. Qi & Z. Wei, 1998. "Convergence Analysis of Some Methods for Minimizing a Nonsmooth Convex Function," Journal of Optimization Theory and Applications, Springer, vol. 97(2), pages 357-383, May.
    2. Jinpeng Ma & Qiongling Li, 2016. "Convergence of price processes under two dynamic double auctions," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 1-44, December.
    3. Gürkan, G. & Ozge, A.Y., 1996. "Sample-Path Optimization of Buffer Allocations in a Tandem Queue - Part I : Theoretical Issues," Other publications TiSEM 77da022b-635b-46fd-bf4a-f, Tilburg University, School of Economics and Management.
    4. J.-P. Penot & P. H. Quang, 1997. "Generalized Convexity of Functions and Generalized Monotonicity of Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 92(2), pages 343-356, February.
    5. R. Cominetti, 1997. "Coupling the Proximal Point Algorithm with Approximation Methods," Journal of Optimization Theory and Applications, Springer, vol. 95(3), pages 581-600, December.
    6. A. I. Rauf & M. Fukushima, 2000. "Globally Convergent BFGS Method for Nonsmooth Convex Optimization1," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 539-558, March.
    7. E. Mijangos, 2006. "Approximate Subgradient Methods for Nonlinearly Constrained Network Flow Problems," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 167-190, January.
    8. Larsson, Torbjorn & Patriksson, Michael & Stromberg, Ann-Brith, 2003. "On the convergence of conditional [var epsilon]-subgradient methods for convex programs and convex-concave saddle-point problems," European Journal of Operational Research, Elsevier, vol. 151(3), pages 461-473, December.
    9. Jie Shen & Ya-Li Gao & Fang-Fang Guo & Rui Zhao, 2018. "A Redistributed Bundle Algorithm for Generalized Variational Inequality Problems in Hilbert Spaces," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(04), pages 1-18, August.
    10. K. C. Kiwiel, 2000. "Efficiency of Proximal Bundle Methods," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 589-603, March.
    11. Sitters, R.A., 2009. "Efficient algorithms for average completion time scheduling," Serie Research Memoranda 0058, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    12. Z. Wei & L. Qi & H. Jiang, 1997. "Some Convergence Properties of Descent Methods," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 177-188, October.
    13. J. P. Penot & P. H. Sach, 1997. "Generalized Monotonicity of Subdifferentials and Generalized Convexity," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 251-262, July.
    14. Zhou, Bojian & Bliemer, Michiel & Yang, Hai & He, Jie, 2015. "A trial-and-error congestion pricing scheme for networks with elastic demand and link capacity constraints," Transportation Research Part B: Methodological, Elsevier, vol. 72(C), pages 77-92.
    15. Gürkan, G. & Ozge, A.Y., 1996. "Sample-Path Optimization of Buffer Allocations in a Tandem Queue - Part I : Theoretical Issues," Discussion Paper 1996-98, Tilburg University, Center for Economic Research.
    16. T. T. Hue & J. J. Strodiot & V. H. Nguyen, 2004. "Convergence of the Approximate Auxiliary Problem Method for Solving Generalized Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 119-145, April.
    17. Zengru Cui & Gonglin Yuan & Zhou Sheng & Wenjie Liu & Xiaoliang Wang & Xiabin Duan, 2015. "A Modified BFGS Formula Using a Trust Region Model for Nonsmooth Convex Minimizations," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-15, October.
    18. O. Cornejo & A. Jourani & C. Zălinescu, 1997. "Conditioning and Upper-Lipschitz Inverse Subdifferentials in Nonsmooth Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 127-148, October.

    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:111:y:2001:i:1:d:10.1023_a:1017575415432. 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.