IDEAS home Printed from https://ideas.repec.org/a/spr/opsear/v57y2020i1d10.1007_s12597-019-00401-3.html
   My bibliography  Save this article

Optimality and duality for vector optimization problem with non-convex feasible set

Author

Listed:
  • S. K. Suneja

    (University of Delhi)

  • Sunila Sharma

    (University of Delhi)

  • Priyanka Yadav

    (University of Delhi)

Abstract

The Karush–Kuhn–Tucker (KKT) optimality conditions are necessary and sufficient for a convex programming problem under suitable constraint qualification. Recently, several papers (Dutta and Lalitha in Optim Lett 7(2):221–229, 2013; Lasserre in Optim Lett 4(1):1–5, 2010; Suneja et al. Am J Oper Res 3(6):536–541, 2013) have appeared wherein the convexity of constraint function has been replaced by convexity of the feasible set. Further, Ho (Optim Lett 11(1):41–46, 2017) studied nonlinear programming problem with non-convex feasible set. We have used this modified approach in the present paper to study vector optimization problem over cones. The KKT optimality conditions are proved by replacing the convexity of the objective function with convexity of strict level set, convexity of feasible set is replaced by a weaker condition and no condition is assumed on the constraint function. We have also formulated a Mond–Weir type dual and proved duality results in the modified setting. Our results directly extend the work of Ho (2017) Suneja et al. (2013) and Lasserre (2010).

Suggested Citation

  • S. K. Suneja & Sunila Sharma & Priyanka Yadav, 2020. "Optimality and duality for vector optimization problem with non-convex feasible set," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 1-12, March.
    • Handle: RePEc:spr:opsear:v:57:y:2020:i:1:d:10.1007_s12597-019-00401-3
    DOI: 10.1007/s12597-019-00401-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12597-019-00401-3
    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/s12597-019-00401-3?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. Altannar Chinchuluun & Panos Pardalos, 2007. "A survey of recent developments in multiobjective optimization," Annals of Operations Research, Springer, vol. 154(1), pages 29-50, October.
    2. Suneja, S. K. & Aggarwal, Sunila & Davar, Sonia, 2002. "Multiobjective symmetric duality involving cones," European Journal of Operational Research, Elsevier, vol. 141(3), pages 471-479, September.
    3. Khanh, Phan Quoc & Quyen, Ho Thuc & Yao, Jen-Chih, 2011. "Optimality conditions under relaxed quasiconvexity assumptions using star and adjusted subdifferentials," European Journal of Operational Research, Elsevier, vol. 212(2), pages 235-241, 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. S. K. Suneja & Sunila Sharma & Priyanka Yadav, 2018. "Generalized higher-order cone-convex functions and higher-order duality in vector optimization," Annals of Operations Research, Springer, vol. 269(1), pages 709-725, October.
    2. Podinovski, Vladislav V., 2013. "Non-dominance and potential optimality for partial preference relations," European Journal of Operational Research, Elsevier, vol. 229(2), pages 482-486.
    3. Wassila Drici & Fatma Zohra Ouail & Mustapha Moulaï, 2018. "Optimizing a linear fractional function over the integer efficient set," Annals of Operations Research, Springer, vol. 267(1), pages 135-151, August.
    4. Duque, Daniel & Lozano, Leonardo & Medaglia, Andrés L., 2015. "An exact method for the biobjective shortest path problem for large-scale road networks," European Journal of Operational Research, Elsevier, vol. 242(3), pages 788-797.
    5. Shahryar Rahnamayan & Sedigheh Mahdavi & Kalyanmoy Deb & Azam Asilian Bidgoli, 2020. "Ranking Multi-Metric Scientific Achievements Using a Concept of Pareto Optimality," Mathematics, MDPI, vol. 8(6), pages 1-46, June.
    6. Thai Doan Chuong, 2021. "Optimality and duality in nonsmooth composite vector optimization and applications," Annals of Operations Research, Springer, vol. 296(1), pages 755-777, January.
    7. Lee, Soonhui & Turner, Jonathan & Daskin, Mark S. & Homem-de-Mello, Tito & Smilowitz, Karen, 2012. "Improving fleet utilization for carriers by interval scheduling," European Journal of Operational Research, Elsevier, vol. 218(1), pages 261-269.
    8. Ahmad, I. & Husain, Z., 2007. "Minimax mixed integer symmetric duality for multiobjective variational problems," European Journal of Operational Research, Elsevier, vol. 177(1), pages 71-82, February.
    9. C. Gutiérrez & B. Jiménez & V. Novo, 2011. "A generic approach to approximate efficiency and applications to vector optimization with set-valued maps," Journal of Global Optimization, Springer, vol. 49(2), pages 313-342, February.
    10. Xu Lei & Tang Shiyun & Deng Yanfei & Yuan Yuan, 2020. "Sustainable operation-oriented investment risk evaluation and optimization for renewable energy project: a case study of wind power in China," Annals of Operations Research, Springer, vol. 290(1), pages 223-241, July.
    11. Walter Gutjahr & Alois Pichler, 2016. "Stochastic multi-objective optimization: a survey on non-scalarizing methods," Annals of Operations Research, Springer, vol. 236(2), pages 475-499, January.
    12. S. Gupta & N. Kailey, 2013. "Second-order multiobjective symmetric duality involving cone-bonvex functions," Journal of Global Optimization, Springer, vol. 55(1), pages 125-140, January.
    13. Walter J. Gutjahr & Alois Pichler, 2016. "Stochastic multi-objective optimization: a survey on non-scalarizing methods," Annals of Operations Research, Springer, vol. 236(2), pages 475-499, January.
    14. Ahmad, I. & Husain, Z., 2010. "On multiobjective second order symmetric duality with cone constraints," European Journal of Operational Research, Elsevier, vol. 204(3), pages 402-409, August.
    15. Xu, Pan & Wang, Lizhi & Beavis, William D., 2011. "An optimization approach to gene stacking," European Journal of Operational Research, Elsevier, vol. 214(1), pages 168-178, October.
    16. Tariq Mumtaz & Shahabuddin Muhammad & Muhammad Imran Aslam & Irfan Ahmed, 2022. "Inter-slice resource management for 5G radio access network using markov decision process," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 79(4), pages 541-557, April.
    17. Amir Elalouf, 2014. "Fast approximation algorithms for routing problems with hop-wise constraints," Annals of Operations Research, Springer, vol. 222(1), pages 279-291, November.
    18. Ahmad, I. & Sharma, Sarita, 2008. "Symmetric duality for multiobjective fractional variational problems involving cones," European Journal of Operational Research, Elsevier, vol. 188(3), pages 695-704, August.
    19. Thai Doan Chuong, 2022. "Second-order cone programming relaxations for a class of multiobjective convex polynomial problems," Annals of Operations Research, Springer, vol. 311(2), pages 1017-1033, April.
    20. Anurag Jayswal, 2010. "On sufficiency and duality in multiobjective programming problem under generalized α-type I univexity," Journal of Global Optimization, Springer, vol. 46(2), pages 207-216, February.

    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:opsear:v:57:y:2020:i:1:d:10.1007_s12597-019-00401-3. 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.