IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v57y2013i2p447-465.html
   My bibliography  Save this article

ε-Mixed type duality for nonconvex multiobjective programs with an infinite number of constraints

Author

Listed:
  • T. Son
  • D. Kim

Abstract

Using a scalarization method, approximate optimality conditions of a multiobjective nonconvex optimization problem which has an infinite number of constraints are established. Approximate duality theorems for mixed duality are given. Results on approximate duality in Wolfe type and Mond-Weir type are also derived. Approximate saddle point theorems of an approximate vector Lagrangian function are investigated. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • T. Son & D. Kim, 2013. "ε-Mixed type duality for nonconvex multiobjective programs with an infinite number of constraints," Journal of Global Optimization, Springer, vol. 57(2), pages 447-465, October.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:2:p:447-465
    DOI: 10.1007/s10898-012-9994-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-012-9994-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-012-9994-0?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. J. Dutta, 2005. "Necessary optimality conditions and saddle points for approximate optimization in banach spaces," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 127-143, June.
    2. T. Son & D. Kim & N. Tam, 2012. "Weak stability and strong duality of a class of nonconvex infinite programs via augmented Lagrangian," Journal of Global Optimization, Springer, vol. 53(2), pages 165-184, June.
    3. T. Son & N. Dinh, 2008. "Characterizations of optimal solution sets of convex infinite programs," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 147-163, 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. Thai Doan Chuong, 2022. "Approximate solutions in nonsmooth and nonconvex cone constrained vector optimization," Annals of Operations Research, Springer, vol. 311(2), pages 997-1015, April.
    2. C. Gutiérrez & L. Huerga & V. Novo & C. Tammer, 2016. "Duality related to approximate proper solutions of vector optimization problems," Journal of Global Optimization, Springer, vol. 64(1), pages 117-139, January.
    3. Xiangkai Sun & Kok Lay Teo & Xian-Jun Long, 2021. "Some Characterizations of Approximate Solutions for Robust Semi-infinite Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 281-310, October.
    4. N. V. Tuyen & C.-F. Wen & T. Q. Son, 2022. "An approach to characterizing $$\epsilon $$ ϵ -solution sets of convex programs," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 249-269, July.
    5. Zhe Hong & Kwan Deok Bae & Do Sang Kim, 2022. "Minimax programming as a tool for studying robust multi-objective optimization problems," Annals of Operations Research, Springer, vol. 319(2), pages 1589-1606, December.
    6. Liguo Jiao & Jae Hyoung Lee, 2018. "Approximate Optimality and Approximate Duality for Quasi Approximate Solutions in Robust Convex Semidefinite Programs," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 74-93, January.

    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. 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.
    2. T. Son & D. Kim & N. Tam, 2012. "Weak stability and strong duality of a class of nonconvex infinite programs via augmented Lagrangian," Journal of Global Optimization, Springer, vol. 53(2), pages 165-184, June.
    3. C. Gutiérrez & R. López & J. Martínez, 2022. "Generalized $${\varepsilon }$$ ε -quasi solutions of set optimization problems," Journal of Global Optimization, Springer, vol. 82(3), pages 559-576, March.
    4. V. Jeyakumar & G. M. Lee & G. Li, 2015. "Characterizing Robust Solution Sets of Convex Programs under Data Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 407-435, February.
    5. M. V. Dolgopolik, 2018. "Augmented Lagrangian functions for cone constrained optimization: the existence of global saddle points and exact penalty property," Journal of Global Optimization, Springer, vol. 71(2), pages 237-296, June.
    6. Liguo Jiao & Jae Hyoung Lee, 2018. "Approximate Optimality and Approximate Duality for Quasi Approximate Solutions in Robust Convex Semidefinite Programs," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 74-93, January.
    7. N. V. Tuyen & C.-F. Wen & T. Q. Son, 2022. "An approach to characterizing $$\epsilon $$ ϵ -solution sets of convex programs," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 249-269, July.
    8. Kin Keung Lai & Shashi Kant Mishra & Sanjeev Kumar Singh & Mohd Hassan, 2022. "Stationary Conditions and Characterizations of Solution Sets for Interval-Valued Tightened Nonlinear Problems," Mathematics, MDPI, vol. 10(15), pages 1-16, August.
    9. N. Q. Huy & J.-C. Yao, 2011. "Semi-Infinite Optimization under Convex Function Perturbations: Lipschitz Stability," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 237-256, February.
    10. C. Gutiérrez & L. Huerga & B. Jiménez & V. Novo, 2020. "Optimality conditions for approximate proper solutions in multiobjective optimization with polyhedral cones," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 526-544, July.
    11. Vsevolod I. Ivanov, 2019. "Characterizations of Solution Sets of Differentiable Quasiconvex Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 144-162, April.

    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:jglopt:v:57:y:2013:i:2:p:447-465. 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.