IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v154y2012i1d10.1007_s10957-012-9998-4.html
   My bibliography  Save this article

Calmness and Exact Penalization in Constrained Scalar Set-Valued Optimization

Author

Listed:
  • X. X. Huang

    (Chongqing University)

Abstract

In this paper, we study a class of constrained scalar set-valued optimization problems, which includes scalar optimization problems with cone constraints as special cases. We introduce (local) calmness of order α for this class of constrained scalar set-valued optimization problems. We show that the (local) calmness of order α is equivalent to the existence of a (local) exact set-valued penalty map.

Suggested Citation

  • X. X. Huang, 2012. "Calmness and Exact Penalization in Constrained Scalar Set-Valued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 108-119, July.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:1:d:10.1007_s10957-012-9998-4
    DOI: 10.1007/s10957-012-9998-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-012-9998-4
    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/s10957-012-9998-4?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. X. X. Huang & X. Q. Yang & K. L. Teo, 2007. "Lower-Order Penalization Approach to Nonlinear Semidefinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 1-20, January.
    2. Giovanni Crespi & Ivan Ginchev & Matteo Rocca, 2006. "First-order optimality conditions in set-valued optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 87-106, February.
    3. X. M. Yang & D. Li & S. Y. Wang, 2001. "Near-Subconvexlikeness in Vector Optimization with Set-Valued Functions," Journal of Optimization Theory and Applications, Springer, vol. 110(2), pages 413-427, August.
    4. A. Moldovan & L. Pellegrini, 2009. "On Regularity for Constrained Extremum Problems. Part 1: Sufficient Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 147-163, July.
    5. 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.
    6. A. Moldovan & L. Pellegrini, 2009. "On Regularity for Constrained Extremum Problems. Part 2: Necessary Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 165-183, July.
    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. X. Huang, 2013. "Convergence of a class of penalty methods for constrained scalar set-valued optimization," Journal of Global Optimization, Springer, vol. 56(4), pages 1501-1513, August.

    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. Lili Pan & Ziyan Luo & Naihua Xiu, 2017. "Restricted Robinson Constraint Qualification and Optimality for Cardinality-Constrained Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 104-118, October.
    2. Satoshi Suzuki & Daishi Kuroiwa, 2011. "On Set Containment Characterization and Constraint Qualification for Quasiconvex Programming," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 554-563, June.
    3. María C. Maciel & Sandra A. Santos & Graciela N. Sottosanto, 2011. "On Second-Order Optimality Conditions for Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 332-351, May.
    4. Letizia Pellegrini & Shengkun Zhu, 2018. "Constrained Extremum Problems, Regularity Conditions and Image Space Analysis. Part II: The Vector Finite-Dimensional Case," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 788-810, June.
    5. Stephan Dempe & Alain B. Zemkoho, 2011. "The Generalized Mangasarian-Fromowitz Constraint Qualification and Optimality Conditions for Bilevel Programs," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 46-68, January.
    6. Hui Hu & Qing Wang, 2011. "Closedness of a Convex Cone and Application by Means of the End Set of a Convex Set," Journal of Optimization Theory and Applications, Springer, vol. 150(1), pages 52-64, July.
    7. Yang-Dong Xu & Cheng-Ling Zhou & Sheng-Kun Zhu, 2021. "Image Space Analysis for Set Optimization Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 311-343, October.
    8. Leonid Minchenko, 2019. "Note on Mangasarian–Fromovitz-Like Constraint Qualifications," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1199-1204, September.
    9. L. Minchenko & A. Tarakanov, 2011. "On Error Bounds for Quasinormal Programs," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 571-579, March.
    10. Nguyen Huy Chieu & Gue Myung Lee, 2014. "Constraint Qualifications for Mathematical Programs with Equilibrium Constraints and their Local Preservation Property," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 755-776, December.
    11. Shengkun Zhu, 2018. "Image Space Analysis to Lagrange-Type Duality for Constrained Vector Optimization Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 743-769, June.
    12. M. Alavi Hejazi & N. Movahedian & S. Nobakhtian, 2018. "On Constraint Qualifications and Sensitivity Analysis for General Optimization Problems via Pseudo-Jacobians," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 778-799, December.
    13. Alexander Y. Kruger & Marco A. López, 2012. "Stationarity and Regularity of Infinite Collections of Sets," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 339-369, August.
    14. Hui Hu & Qing Wang, 2011. "Closedness of a Convex Cone and Application by Means of the End Set of a Convex Set," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 633-645, December.
    15. S. J. Li & Y. D. Xu & S. K. Zhu, 2012. "Nonlinear Separation Approach to Constrained Extremum Problems," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 842-856, September.
    16. Lei Guo & Gui-Hua Lin, 2013. "Notes on Some Constraint Qualifications for Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 600-616, March.
    17. Manxue You & Shengjie Li, 2017. "Separation Functions and Optimality Conditions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 527-544, November.
    18. Y. D. Xu & S. J. Li, 2013. "Optimality Conditions for Generalized Ky Fan Quasi-Inequalities with Applications," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 663-684, June.
    19. J. Li & N. J. Huang, 2010. "Image Space Analysis for Vector Variational Inequalities with Matrix Inequality Constraints and Applications," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 459-477, June.
    20. Shengjie Li & Yangdong Xu & Manxue You & Shengkun Zhu, 2018. "Constrained Extremum Problems and Image Space Analysis–Part I: Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 609-636, June.

    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:154:y:2012:i:1:d:10.1007_s10957-012-9998-4. 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.