IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v198y2023i3d10.1007_s10957-023-02260-x.html
   My bibliography  Save this article

Optimality Conditions in DC-Constrained Mathematical Programming Problems

Author

Listed:
  • Rafael Correa

    (Universidad de O’Higgins
    DIM-CMM of Universidad de Chile)

  • Marco A. López

    (University of Alicante
    Federation University Australia)

  • Pedro Pérez-Aros

    (Universidad de O’Higgins)

Abstract

This paper provides necessary and sufficient optimality conditions for abstract-constrained mathematical programming problems in locally convex spaces under new qualification conditions. Our approach exploits the geometrical properties of certain mappings, in particular their structure as difference of convex functions, and uses techniques of generalized differentiation (subdifferential and coderivative). It turns out that these tools can be used fruitfully out of the scope of Asplund spaces. Applications to infinite, stochastic and semi-definite programming are developed in separate sections.

Suggested Citation

  • Rafael Correa & Marco A. López & Pedro Pérez-Aros, 2023. "Optimality Conditions in DC-Constrained Mathematical Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1191-1225, September.
    • Handle: RePEc:spr:joptap:v:198:y:2023:i:3:d:10.1007_s10957-023-02260-x
    DOI: 10.1007/s10957-023-02260-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-023-02260-x
    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/s10957-023-02260-x?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. Lopez, Marco & Still, Georg, 2007. "Semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 180(2), pages 491-518, July.
    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. Li Wang & Feng Guo, 2014. "Semidefinite relaxations for semi-infinite polynomial programming," Computational Optimization and Applications, Springer, vol. 58(1), pages 133-159, May.
    2. S. Mishra & M. Jaiswal & H. Le Thi, 2012. "Nonsmooth semi-infinite programming problem using Limiting subdifferentials," Journal of Global Optimization, Springer, vol. 53(2), pages 285-296, June.
    3. Cao Thanh Tinh & Thai Doan Chuong, 2022. "Conic Linear Programming Duals for Classes of Quadratic Semi-Infinite Programs with Applications," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 570-596, August.
    4. Duarte, Belmiro P.M. & Sagnol, Guillaume & Wong, Weng Kee, 2018. "An algorithm based on semidefinite programming for finding minimax optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 99-117.
    5. Nazih Abderrazzak Gadhi, 2019. "Necessary optimality conditions for a nonsmooth semi-infinite programming problem," Journal of Global Optimization, Springer, vol. 74(1), pages 161-168, May.
    6. Jan Schwientek & Tobias Seidel & Karl-Heinz Küfer, 2021. "A transformation-based discretization method for solving general semi-infinite optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(1), pages 83-114, February.
    7. Engau, Alexander & Sigler, Devon, 2020. "Pareto solutions in multicriteria optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 357-368.
    8. Aguiar, Victor H. & Kashaev, Nail & Allen, Roy, 2023. "Prices, profits, proxies, and production," Journal of Econometrics, Elsevier, vol. 235(2), pages 666-693.
    9. Hassan Bakhtiari & Hossein Mohebi, 2021. "Lagrange Multiplier Characterizations of Constrained Best Approximation with Infinite Constraints," Journal of Optimization Theory and Applications, Springer, vol. 189(3), pages 814-835, June.
    10. Tran Van Su, 2023. "Optimality and duality for nonsmooth mathematical programming problems with equilibrium constraints," Journal of Global Optimization, Springer, vol. 85(3), pages 663-685, March.
    11. Mohammad R. Oskoorouchi & Hamid R. Ghaffari & Tamás Terlaky & Dionne M. Aleman, 2011. "An Interior Point Constraint Generation Algorithm for Semi-Infinite Optimization with Health-Care Application," Operations Research, INFORMS, vol. 59(5), pages 1184-1197, October.
    12. S. Rivaz & M. A. Yaghoobi & M. Hladík, 2016. "Using modified maximum regret for finding a necessarily efficient solution in an interval MOLP problem," Fuzzy Optimization and Decision Making, Springer, vol. 15(3), pages 237-253, September.
    13. Zhi Guo Feng & Fei Chen & Lin Chen & Ka Fai Cedric Yiu, 2020. "Optimality Analysis of a Class of Semi-infinite Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 398-411, August.
    14. Boris S. Mordukhovich & T. T. A. Nghia, 2014. "Nonsmooth Cone-Constrained Optimization with Applications to Semi-Infinite Programming," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 301-324, May.
    15. J. O. Royset & E. Y. Pee, 2012. "Rate of Convergence Analysis of Discretization and Smoothing Algorithms for Semiinfinite Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 855-882, December.
    16. Sönke Behrends & Anita Schöbel, 2020. "Generating Valid Linear Inequalities for Nonlinear Programs via Sums of Squares," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 911-935, September.
    17. Holger Berthold & Holger Heitsch & René Henrion & Jan Schwientek, 2022. "On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(1), pages 1-37, August.
    18. Ariel Neufeld & Antonis Papapantoleon & Qikun Xiang, 2023. "Model-Free Bounds for Multi-Asset Options Using Option-Implied Information and Their Exact Computation," Management Science, INFORMS, vol. 69(4), pages 2051-2068, April.
    19. 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.
    20. Tadeusz Antczak, 2022. "Optimality conditions and Mond–Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints," 4OR, Springer, vol. 20(3), pages 417-442, 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:198:y:2023:i:3:d:10.1007_s10957-023-02260-x. 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.