SpringerLink
Log in

A New Approach on Multiobjective Higher-Order Symmetric Duality Under Cone-Invexity

  • Published:
Bulletin of the Malaysian Mathematical Sciences Society Aims and scope Submit manuscript

Abstract

In this paper, we introduce a new pair of multiobjective higher-order symmetric dual models with cone constraints. Weak, strong and converse duality theorems for a such pair are discussed under higher-order cone-invex functions. Three non-trivial examples are presented to show the uniqueness of higher-order cone-invex function and existence of the multiobjective higher-order symmetric dual model. Several known results are obtained as special cases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Agarwal, R.P., Ahmad, I., Jayswal, A.: Higher-order symmetric duality in nondifferentiable multiobjective programming problems involving generalized cone convex functions. Math. Comput. Model. 52, 1644–1650 (2010)

    Article  Google Scholar 

  2. Ahmad, I.: Unified higher order duality in nondifferentiable multiobjective programming involving cones. Math. Comput. Model. 55, 419–425 (2012)

    Article  MathSciNet  Google Scholar 

  3. Ahmad, I., Husain, Z.: Non-differentiable second order symmetric duality in multiobjective programming. Appl. Math. Lett. 18, 721–728 (2005)

    Article  MathSciNet  Google Scholar 

  4. Ahmad, I., Husain, Z.: On multiobjective second order symmetric duality with cone constraints. European J. Oper. Res. 204, 402–409 (2010)

    Article  MathSciNet  Google Scholar 

  5. Ahmad, I., Husain, Z., Sharma, S.: Higher-order duality in nondifferentiable multiobjective programming. Numer. Funct. Anal. Optim. 28, 989–1002 (2007)

    Article  MathSciNet  Google Scholar 

  6. Ahmad, I., Verma, K., Al-Homidan, S.: Mixed type nondifferentiable higher-order symmetric duality over cones. Symmetry 12, 274 (2020)

    Article  Google Scholar 

  7. Bector, C.R., Chandra, S.: Generalized bonvexity and higher order duality in fractional programming. Opsearch 24, 143–154 (1987)

    MathSciNet  MATH  Google Scholar 

  8. Chandra, S., Goyal, A., Husain, I.: On symmetric duality in mathematical programming with F-convexity. Optimization 43, 1–18 (1998)

    Article  MathSciNet  Google Scholar 

  9. Chen, X.: Higher order symmetric duality in non-differentiable multiobjective programming problems. J. Math. Anal. Appl. 290, 423–435 (2004)

    Article  MathSciNet  Google Scholar 

  10. Dantzig, G.B., Eisenberg, E., Cottle, R.W.: Symmetric dual nonlinear programs. Pacific J. Math. 15, 809–812 (1965)

    Article  MathSciNet  Google Scholar 

  11. Debnath, I.P., Gupta, S.K., Kumar, S.: Symmetric duality for a higher-order nondifferentiable multiobjective programming problem. J. Inequal. Appl. 3, 1–12 (2015)

    MathSciNet  MATH  Google Scholar 

  12. Gao, J.: Higher-order symmetric duality in multiobjective programming problems. Acta Math. Appl. Sin. Engl. Ser. 32, 485–494 (2016)

    Article  MathSciNet  Google Scholar 

  13. Gulati, T.R., Ahmad, I., Husain, I.: Second-order symmteric duality with generalized convexity. Opsearch 38, 210–222 (2001)

    Article  MathSciNet  Google Scholar 

  14. Gulati, T.R., Gupta, S.K., Ahmad, I.: Second-order symmteric duality with cone constraints. J. Comput. Appl. Math. 220(1–2), 347–354 (2008)

    Article  MathSciNet  Google Scholar 

  15. Gulati, T.R., Gupta, S.K.: Higher-order symmetric duality with cone constraints. Appl. Math. Lett. 22, 776–781 (2009)

    Article  MathSciNet  Google Scholar 

  16. Gulati, T.R., Verma, K.: Nondifferentiable higher-order symmetric duality under invexity/generalized invexity. Filomat 28, 1661–1674 (2014)

    Article  MathSciNet  Google Scholar 

  17. Gupta, S.K., Jayswal, A.: Multiobjective higher-order symmetric duality involving generalized cone-invex functions. Comput. Math. Appl. 60, 3187–3192 (2010)

    Article  MathSciNet  Google Scholar 

  18. Gupta, S.K., Kailey, N.: Second-order multiobjective symmetric duality involving cone-bonvex functions. J. Global Optim. 55(1), 125–140 (2013)

    Article  MathSciNet  Google Scholar 

  19. Khurana, S.: Symmetric duality in multiobjective programming involving generalized cone-invex functions. European J. Oper. Res. 165, 592–597 (2005)

    Article  MathSciNet  Google Scholar 

  20. Kim, D.S., Kang, H.S., Lee, Y.J., Seo, Y.Y.: Higher order duality in multiobjective programming with cone constraints. Optimization 59(1), 29–43 (2010)

    Article  MathSciNet  Google Scholar 

  21. Mangasarian, O.L.: Second and higher-order duality in nonlinear programming. J. Math. Anal. Appl. 51, 607–620 (1975)

    Article  MathSciNet  Google Scholar 

  22. Mond, B., Zhang, J.: Higher-order invexity and duality in mathematical programming. In: Crouzeix, J.P., et al. (eds.) Generalized convexity, generalized monotonicity: recent results, pp. 357–372. Kluwer Academic, Dordrecht (1998)

    Chapter  Google Scholar 

  23. Nahak, C., Padhan, S.K.: Higher-order symmetric duality in multiobjective programming problems under higher-order invexity. Appl. Math. Comput. 218, 1705–1712 (2011)

    MathSciNet  MATH  Google Scholar 

  24. Padhan, S.K., Nahak, C.: Higher-order symmetric duality with higher-order generalized invexity. J. Appl. Math. Comput. 48, 407–420 (2015)

    Article  MathSciNet  Google Scholar 

  25. Suneja, S.K., Aggarwal, S., Davar, S.: Multiobjective symmetric duality involving cones. European J. Oper. Res. 141, 471–479 (2002)

    Article  MathSciNet  Google Scholar 

  26. Suneja, S.K., Louhan, P.: Higher-order symmetric duality under cone-invexity and other related concepts. J. Comput. Appl. Math. 255, 825–836 (2014)

    Article  MathSciNet  Google Scholar 

  27. Verma, K., Gulati, T.R.: Wolfe type higher order symmetric duality under invexity. J. Appl. Math. Inform. 32, 153–159 (2014)

    Article  MathSciNet  Google Scholar 

  28. Yang, X.M., Teo, K.L., Yang, X.Q.: Higher order generalized convexity and duality in nondifferentiable multiobjective mathematical programming. J. Math. Anal. Appl. 297, 48–55 (2004)

    Article  MathSciNet  Google Scholar 

  29. Yang, X.M., Yang, X.Q., Teo, K.L., Hou, S.H.: Multiobjective second-order symmetric duality with F -convexity. European J. Oper. Res. 165, 585–591 (2005)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The third author would like to thank the King Fahd University of Petroleum and Minerals, Saudi Arabia, for providing the financial support under the Internal Research Project No. IN171012. The authors are thankful to referees for their valuable suggestions which improved the results and presentation of this article.

Author information

Authors and Affiliations

  1. Department of Applied Science and Humanities, Faculty of Engineering, University of Lucknow, Lucknow, 226 031, India

    Khushboo Verma

  2. Department of Economics, Netaji Subhash Chandra Bose Govt. Girls P.G. College, Lucknow, 226 024, India

    Jai Prakash Verma

  3. Also at affiliated to University of Lucknow, Lucknow, India

    Jai Prakash Verma

  4. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Izhar Ahmad

Authors
  1. Khushboo Verma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jai Prakash Verma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Izhar Ahmad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jai Prakash Verma.

Additional information

Communicated by Anton Abdulbasah Kamil.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Verma, K., Verma, J.P. & Ahmad, I. A New Approach on Multiobjective Higher-Order Symmetric Duality Under Cone-Invexity. Bull. Malays. Math. Sci. Soc. 44, 479–495 (2021). https://doi.org/10.1007/s40840-020-00952-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40840-020-00952-5

Keywords

Mathematics Subject Classification

Search

Navigation