Skip to main content
SpringerLink
Log in

Optimality and duality for E-minimax fractional programming: application to multiobjective optimization

  • Original Research
  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

In this paper, we study the notion of strong invexity with respect to the E-operator. We discuss the necessary and sufficient conditions for the considered E-minimax fractional programming problem. Wolfe dual has been presented for the considered problem, and weak, strong, and strict converse duality theorems have been proved. Also, an application of the results derived is discussed in the context of a E-multiobjective fractional programming problem. At suitable places, nontrivial examples have been formulated with appropriate justification.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Abdulaleem, N.: \(E\)-invexity and generalized \(E\)-invexity in \(E\)-differentiable multiobjective programming. ITM Web Conf. EDP Sci. 24, 1–12 (2019)

    MATH  Google Scholar 

  2. Abdulaleem, N.: Optimality conditions for \(E\)-differentiable fractional optimization problems under \(E\)-invexity. J. Math. Anal. 11(6), 17–26 (2020)

    MathSciNet  Google Scholar 

  3. Ahmad, I., Al-Homidan, S.: Sufficiency and duality in nondifferentiable multiobjective programming involving higher order strong invexity. J. Ineq. Appl. 1, 1–12 (2015)

    MathSciNet  MATH  Google Scholar 

  4. Antczak, T., Abdulaleem, N.: Optimality and duality results for \(E\)-differentiable multiobjective fractional programming problems under \(E\)-convexity. J. Ineq. Appl. 2019(1), 1–24 (2019)

    MathSciNet  MATH  Google Scholar 

  5. Antczak, T., Abdulaleem, N.: \(E\)-optimality conditions and Wolfe \(E\)-duality for \(E\)-differentiable vector optimization problems with inequality and equality constraints. J. Nonlinear Sci. Appl. 12, 745–764 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  6. Antczak, T., Abdulaleem, N.: \(E\)-differentiable minimax programming under \(E\)-convexity. Ann. Oper. Res. 1–22 (2021)

  7. Barrodale, I.: Best rational approximation and strict quasi-convexity. SIAM J. Numer. Anal. 10(1), 8–12 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  8. Chandra, S., Craven, B.D., Mond, B.: Generalized fractional programming duablity: a ratio game approach. ANZIAM J. 28(2), 170–180 (1986)

    MATH  Google Scholar 

  9. Chuong, T.D.: Nondifferentiable minimax programming problems with applications. Ann. Oper. Res. 251(1–2), 73–87 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  10. Das, K., Nahak, C.: Optimality conditions for set-valued minimax fractional programming problems. SeMA J. 77(2), 161–179 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  11. Debnath, I.P., Qin, X.: Robust optimality and duality for minimax fractional programming problems with support functions. J. Nonlinear Funct. Anal. 5, 1–22 (2021)

    Google Scholar 

  12. Dubey, R., Mishra, V.N., Ali, R.: Duality for unified higher-order minimax fractional programming with support function under type-I assumptions. Mathematics 7(11), 1034 (2019)

    Article  Google Scholar 

  13. Hanson, M.A.: On sufficiency of the Kuhn–Tucker conditions. J. Math. Anal. Appl. 80(2), 545–550 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  14. Henrion, R.: On constraint qualifications. J. Optim. Theory Appl. 72(1), 187–197 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  15. Huang, T.Y.: Second-order parametric free dualities for complex minimax fractional programming. Mathematics 8(1), 67 (2020)

    Article  MathSciNet  Google Scholar 

  16. Karamardian, S., Schaible, S.: Seven kinds of monotone maps. J. Optim. Theory Appl. 66(1), 37–46 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  17. Kumar, P., Panda, G., Gupta, U.C.: Stochastic programming technique for portfolio optimization with minimax risk and bounded parameters. Sādhanā 43(9), 1–16 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  18. Levitin, E.S., Polyak, B.T.: Constrained minimization methods. USSR Comput. Math. Phys. 6(5), 1–50 (1966)

    Article  MATH  Google Scholar 

  19. Lin, G.H., Fukushima, M.: Some exact penalty results for nonlinear programs and mathematical programs with equilibrium constraints. J. Optim. Theory Appl. 118(1), 67–80 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  20. Mangasarian, O.L.: Nonlinear programming. SIAM. 1–239 (1994)

  21. Mishra, S.K., Lai, K.K., Singh, V.: Optimality and duality for minimax fractional programming with support function under \((C, \alpha, \rho, d)\)-convexity. J. Comput. Appl. Math. 274, 1–10 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  22. Megahed, A.E.M.A., Gomma, H.G., Youness, E.A., El-Banna, A.Z.H.: Optimality conditions of \(E\)-convex programming for an \(E\)-differentiable function. J. Inequ. Appl. 2013(1), 1–11 (2013)

    MathSciNet  MATH  Google Scholar 

  23. Nocedal, J., Wright, S.J.: Theory of constrained optimization. Numer. Optimiz. 304–354 (2006)

  24. Sahay, R.R., Bhatia, G.: Characterizations for the set of higher order global strict minimizers. J. Nonlinear Convex Anal. 15(6), 1293–1301 (2014)

    MathSciNet  MATH  Google Scholar 

  25. Stancu-Minasian, I.M., Tigan, S.: On some fractional programming models occurring in minimum-risk problems. In: Generalized Convexity and Fractional Programming with Economic Applications, pp. 295–324 (1990)

  26. Stancu-Minasian, I.M., Kummari, K., Jayswal, A.: Duality for semi-infinite minimax fractional programming problem involving higher-order \((\phi, \rho )\)-\(V\)-invexity. Numer. Funct. Anal. Optim. 38(7), 926–950 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  27. Stancu-Minasian, I.M.: A ninth bibliography of fractional programming. Optimization 68(11), 2125–2169 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  28. Vial, J.P.: Strong convexity of sets and functions. J. Math. Econ. 9(1–2), 187–205 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  29. Youness, E.A.: \(E\)-convex sets, \(E\)-convex functions, and \(E\)-convex programming. J. Optim. Theory Appl. 102(2), 439–450 (1999)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Humanities, SVNIT, Ichchhanath, Surat, Gujarat, 395007, India

    Nisha Pokharna & Indira P. Tripathi

Authors
  1. Nisha Pokharna
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Indira P. Tripathi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nisha Pokharna.

Ethics declarations

Conflict of interest

The authors declare that they have no conflicts of interest.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pokharna, N., Tripathi, I.P. Optimality and duality for E-minimax fractional programming: application to multiobjective optimization. J. Appl. Math. Comput. 69, 2361–2388 (2023). https://doi.org/10.1007/s12190-023-01838-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-023-01838-y

Keywords

Mathematics Subject Classification

Search

Navigation