IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v175y2017i1d10.1007_s10957-017-1150-z.html
   My bibliography  Save this article

Optimality Conditions for Convex Semi-infinite Programming Problems with Finitely Representable Compact Index Sets

Author

Listed:
  • Olga Kostyukova

    (National Academy of Sciences of Belarus)

  • Tatiana Tchemisova

    (University of Aveiro)

Abstract

In the present paper, we analyze a class of convex semi-infinite programming problems with arbitrary index sets defined by a finite number of nonlinear inequalities. The analysis is carried out by employing the constructive approach, which, in turn, relies on the notions of immobile indices and their immobility orders. Our previous work showcasing this approach includes a number of papers dealing with simpler cases of semi-infinite problems than the ones under consideration here. Key findings of the paper include the formulation and the proof of implicit and explicit optimality conditions under assumptions, which are less restrictive than the constraint qualifications traditionally used. In this perspective, the optimality conditions in question are also compared to those provided in the relevant literature. Finally, the way to formulate the obtained optimality conditions is demonstrated by applying the results of the paper to some special cases of the convex semi-infinite problems.

Suggested Citation

  • Olga Kostyukova & Tatiana Tchemisova, 2017. "Optimality Conditions for Convex Semi-infinite Programming Problems with Finitely Representable Compact Index Sets," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 76-103, October.
    • Handle: RePEc:spr:joptap:v:175:y:2017:i:1:d:10.1007_s10957-017-1150-z
    DOI: 10.1007/s10957-017-1150-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-017-1150-z
    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/s10957-017-1150-z?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. Sanjay Mehrotra & David Papp, 2013. "A cutting surface algorithm for semi-infinite convex programming with an application to moment robust optimization," Papers 1306.3437, arXiv.org, revised Aug 2014.
    2. Xiaoqi Yang & Zhangyou Chen & Jinchuan Zhou, 2016. "Optimality Conditions for Semi-Infinite and Generalized Semi-Infinite Programs Via Lower Order Exact Penalty Functions," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 984-1012, June.
    3. O. I. Kostyukova & T. V. Tchemisova & S. A. Yermalinskaya, 2010. "Convex Semi-Infinite Programming: Implicit Optimality Criterion Based on the Concept of Immobile Indices," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 325-342, May.
    4. G. Stein & G. Still, 2000. "On Optimality Conditions for Generalized Semi-Infinite Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 443-458, February.
    5. J. J. Rückmann & A. Shapiro, 1999. "First-Order Optimality Conditions in Generalized Semi-Infinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 101(3), pages 677-691, June.
    6. Peter Kirst & Oliver Stein, 2016. "Solving Disjunctive Optimization Problems by Generalized Semi-infinite Optimization Techniques," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1079-1109, June.
    7. P. Parpas & B. Rustem, 2009. "An Algorithm for the Global Optimization of a Class of Continuous Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 461-473, May.
    8. Lopez, Marco & Still, Georg, 2007. "Semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 180(2), pages 491-518, July.
    9. O. Kostyukova & T. Tchemisova, 2012. "Implicit optimality criterion for convex SIP problem with box constrained index set," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 475-502, July.
    10. Faizan Ahmed & Mirjam Dür & Georg Still, 2013. "Copositive Programming via Semi-Infinite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 322-340, November.
    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. Tamanna Yadav & S. K. Gupta & Sumit Kumar, 2024. "Optimality analysis and duality conditions for a class of conic semi-infinite program having vanishing constraints," Annals of Operations Research, Springer, vol. 340(2), pages 1091-1123, September.
    2. O. I. Kostyukova & T. V. Tchemisova, 2022. "On strong duality in linear copositive programming," Journal of Global Optimization, Springer, vol. 83(3), pages 457-480, July.
    3. Olga Kostyukova & Tatiana Tchemisova, 2021. "Structural Properties of Faces of the Cone of Copositive Matrices," Mathematics, MDPI, vol. 9(21), pages 1-21, October.

    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. Stein, Oliver, 2012. "How to solve a semi-infinite optimization problem," European Journal of Operational Research, Elsevier, vol. 223(2), pages 312-320.
    2. O. Stein, 2004. "On Constraint Qualifications in Nonsmooth Optimization," Journal of Optimization Theory and Applications, Springer, vol. 121(3), pages 647-671, June.
    3. Kanzi, N. & Nobakhtian, S., 2010. "Necessary optimality conditions for nonsmooth generalized semi-infinite programming problems," European Journal of Operational Research, Elsevier, vol. 205(2), pages 253-261, September.
    4. Li Wang & Feng Guo, 2014. "Semidefinite relaxations for semi-infinite polynomial programming," Computational Optimization and Applications, Springer, vol. 58(1), pages 133-159, May.
    5. O. Kostyukova & T. Tchemisova, 2012. "Implicit optimality criterion for convex SIP problem with box constrained index set," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 475-502, July.
    6. J. J. Ye & S. Y. Wu, 2008. "First Order Optimality Conditions for Generalized Semi-Infinite Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 419-434, May.
    7. Bo Wei & William B. Haskell & Sixiang Zhao, 2020. "An inexact primal-dual algorithm for semi-infinite programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(3), pages 501-544, June.
    8. Li-Ping Pang & Qi Wu & Jin-He Wang & Qiong Wu, 2020. "A discretization algorithm for nonsmooth convex semi-infinite programming problems based on bundle methods," Computational Optimization and Applications, Springer, vol. 76(1), pages 125-153, May.
    9. Oliver Stein, 2001. "First-Order Optimality Conditions for Degenerate Index Sets in Generalized Semi-Infinite Optimization," Mathematics of Operations Research, INFORMS, vol. 26(3), pages 565-582, August.
    10. M. A. Goberna & M. A. López, 2018. "Recent contributions to linear semi-infinite optimization: an update," Annals of Operations Research, Springer, vol. 271(1), pages 237-278, December.
    11. Stein, Oliver & Still, Georg, 2002. "On generalized semi-infinite optimization and bilevel optimization," European Journal of Operational Research, Elsevier, vol. 142(3), pages 444-462, November.
    12. Li-Ping Pang & Jian Lv & Jin-He Wang, 2016. "Constrained incremental bundle method with partial inexact oracle for nonsmooth convex semi-infinite programming problems," Computational Optimization and Applications, Springer, vol. 64(2), pages 433-465, June.
    13. Feng Guo & Xiaoxia Sun, 2020. "On semi-infinite systems of convex polynomial inequalities and polynomial optimization problems," Computational Optimization and Applications, Springer, vol. 75(3), pages 669-699, April.
    14. T. Q. Son & J. J. Strodiot & V. H. Nguyen, 2009. "ε-Optimality and ε-Lagrangian Duality for a Nonconvex Programming Problem with an Infinite Number of Constraints," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 389-409, May.
    15. O. I. Kostyukova & T. V. Tchemisova & S. A. Yermalinskaya, 2010. "Convex Semi-Infinite Programming: Implicit Optimality Criterion Based on the Concept of Immobile Indices," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 325-342, May.
    16. Feng Guo & Liguo Jiao, 2021. "On solving a class of fractional semi-infinite polynomial programming problems," Computational Optimization and Applications, Springer, vol. 80(2), pages 439-481, November.
    17. Bo Wei & William B. Haskell & Sixiang Zhao, 2020. "The CoMirror algorithm with random constraint sampling for convex semi-infinite programming," Annals of Operations Research, Springer, vol. 295(2), pages 809-841, December.
    18. Xiaoqi Yang & Zhangyou Chen & Jinchuan Zhou, 2016. "Optimality Conditions for Semi-Infinite and Generalized Semi-Infinite Programs Via Lower Order Exact Penalty Functions," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 984-1012, June.
    19. Souvik Das & Ashwin Aravind & Ashish Cherukuri & Debasish Chatterjee, 2022. "Near-optimal solutions of convex semi-infinite programs via targeted sampling," Annals of Operations Research, Springer, vol. 318(1), pages 129-146, November.
    20. Groetzner, Patrick & Werner, Ralf, 2022. "Multiobjective optimization under uncertainty: A multiobjective robust (relative) regret approach," European Journal of Operational Research, Elsevier, vol. 296(1), pages 101-115.

    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:175:y:2017:i:1:d:10.1007_s10957-017-1150-z. 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.