IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v139y2008i1d10.1007_s10957-008-9431-1.html
   My bibliography  Save this article

Quasiconvex Minimization on a Locally Finite Union of Convex Sets

Author

Listed:
  • D. Aussel

    (Université de Perpignan)

  • J. J. Ye

    (University of Victoria)

Abstract

Extending the approach initiated in Aussel and Hadjisavvas (SIAM J. Optim. 16:358–367, 2005) and Aussel and Ye (Optimization 55:433–457, 2006), we obtain the existence of a local minimizer of a quasiconvex function on the locally finite union of closed convex subsets of a Banach space. We apply the existence result to some difficult nonconvex optimization problems such as the disjunctive programming problem and the bilevel programming problem.

Suggested Citation

  • D. Aussel & J. J. Ye, 2008. "Quasiconvex Minimization on a Locally Finite Union of Convex Sets," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 1-16, October.
    • Handle: RePEc:spr:joptap:v:139:y:2008:i:1:d:10.1007_s10957-008-9431-1
    DOI: 10.1007/s10957-008-9431-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-008-9431-1
    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/s10957-008-9431-1?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. Egon Balas, 2005. "Projection, Lifting and Extended Formulation in Integer and Combinatorial Optimization," Annals of Operations Research, Springer, vol. 140(1), pages 125-161, November.
    2. H. T. Jongen & J. J. Rückmann & O. Stein, 1997. "Disjunctive Optimization: Critical Point Theory," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 321-336, May.
    3. M. Gugat, 1997. "Parametric Disjunctive Programming: One-Sided Differentiability of the Value Function," Journal of Optimization Theory and Applications, Springer, vol. 92(2), pages 285-310, February.
    4. Jane J. Ye, 2006. "Constraint Qualifications and KKT Conditions for Bilevel Programming Problems," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 811-824, 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. D. Aussel & J. Cotrina, 2013. "Quasimonotone Quasivariational Inequalities: Existence Results and Applications," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 637-652, September.
    2. D. Aussel & J. Cotrina, 2011. "Semicontinuity of the solution map of quasivariational inequalities," Journal of Global Optimization, Springer, vol. 50(1), pages 93-105, May.
    3. Didier Aussel & Parin Chaipunya, 2024. "Variational and Quasi-Variational Inequalities Under Local Reproducibility: Solution Concept and Applications," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1531-1563, November.
    4. Wen Song & Qianqian Wang, 2015. "Optimality Conditions for Disjunctive Optimization in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 436-454, February.

    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. Wen Song & Qianqian Wang, 2015. "Optimality Conditions for Disjunctive Optimization in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 436-454, February.
    2. Lorenzo Lampariello & Simone Sagratella, 2015. "It is a matter of hierarchy: a Nash equilibrium problem perspective on bilevel programming," DIAG Technical Reports 2015-07, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    3. Kuo, R.J. & Lee, Y.H. & Zulvia, Ferani E. & Tien, F.C., 2015. "Solving bi-level linear programming problem through hybrid of immune genetic algorithm and particle swarm optimization algorithm," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1013-1026.
    4. Boris S. Mordukhovich & Nguyen Mau Nam & Hung M. Phan, 2012. "Variational Analysis of Marginal Functions with Applications to Bilevel Programming," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 557-586, March.
    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. Moeini, Asghar., 2017. "Identification of unidentified equality constraints for integer programming problems," European Journal of Operational Research, Elsevier, vol. 260(2), pages 460-467.
    7. STEPHAN, Rüdiger, 2010. "An extension of disjunctive programming and its impact for compact tree formulations," LIDAM Discussion Papers CORE 2010045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Filipa D. Carvalho & Maria Teresa Almeida, 2017. "The triangle k-club problem," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 814-846, April.
    9. Peter Kirst & Fabian Rigterink & Oliver Stein, 2017. "Global optimization of disjunctive programs," Journal of Global Optimization, Springer, vol. 69(2), pages 283-307, October.
    10. Leonardo Lozano & J. Cole Smith, 2017. "A Value-Function-Based Exact Approach for the Bilevel Mixed-Integer Programming Problem," Operations Research, INFORMS, vol. 65(3), pages 768-786, June.
    11. Yun Hui Lin & Qingyun Tian & Yanlu Zhao, 2022. "Locating facilities under competition and market expansion: Formulation, optimization, and implications," Production and Operations Management, Production and Operations Management Society, vol. 31(7), pages 3021-3042, July.
    12. 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.
    13. Taccari, Leonardo, 2016. "Integer programming formulations for the elementary shortest path problem," European Journal of Operational Research, Elsevier, vol. 252(1), pages 122-130.
    14. Lin, Yun Hui & Tian, Qingyun, 2023. "Facility location and pricing problem: Discretized mill price and exact algorithms," European Journal of Operational Research, Elsevier, vol. 308(2), pages 568-580.
    15. L. Foulds & B. Toklu & J. Wilson, 2009. "Modelling either-or relations in integer programming," Annals of Operations Research, Springer, vol. 166(1), pages 203-222, February.
    16. Alexander Mitsos, 2010. "Global solution of nonlinear mixed-integer bilevel programs," Journal of Global Optimization, Springer, vol. 47(4), pages 557-582, August.
    17. 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.
    18. Jan Rückmann & Juan Alfredo Gómez, 2006. "On generalized semi-infinite programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 1-32, June.
    19. Bodur, Merve & Dash, Sanjeeb & Günlük, Oktay, 2017. "A new lift-and-project operator," European Journal of Operational Research, Elsevier, vol. 257(2), pages 420-428.
    20. Lorenzo Lampariello & Simone Sagratella, 2017. "A Bridge Between Bilevel Programs and Nash Games," Journal of Optimization Theory and Applications, Springer, vol. 174(2), pages 613-635, August.

    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:139:y:2008:i:1:d:10.1007_s10957-008-9431-1. 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.