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On second order duality of minimax fractional programming with square root term involving generalized B-(p, r)-invex functions

Author

Listed:
  • Sonali

    (Thapar University)

  • N. Kailey

    (Thapar University)

  • V. Sharma

    (Thapar University)

Abstract

The advantage of second-order duality is that if a feasible point of the primal is given and first-order duality conditions are not applicable (infeasible), then we may use second-order duality to provide a lower bound for the value of primal problem. Consequently, it is quite interesting to discuss the duality results for the case of second order. Thus, we focus our study on a discussion of duality relationships of a minimax fractional programming problem under the assumptions of second order B-(p, r)-invexity. Weak, strong and strict converse duality theorems are established in order to relate the primal and dual problems under the assumptions. An example of a non trivial function has been given to show the existence of second order B-(p, r)-invex functions.

Suggested Citation

  • Sonali & N. Kailey & V. Sharma, 2016. "On second order duality of minimax fractional programming with square root term involving generalized B-(p, r)-invex functions," Annals of Operations Research, Springer, vol. 244(2), pages 603-617, September.
    • Handle: RePEc:spr:annopr:v:244:y:2016:i:2:d:10.1007_s10479-016-2147-y
    DOI: 10.1007/s10479-016-2147-y
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    References listed on IDEAS

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    1. Jin-Chirng Lee & Hang-Chin Lai, 2005. "Parameter-Free Dual Models for Fractional Programming with Generalized Invexity," Annals of Operations Research, Springer, vol. 133(1), pages 47-61, January.
    2. I. Ahmad & Z. Husain, 2006. "Optimality Conditions and Duality in Nondifferentiable Minimax Fractional Programming with Generalized Convexity," Journal of Optimization Theory and Applications, Springer, vol. 129(2), pages 255-275, May.
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    Cited by:

    1. Tadeusz Antczak & Najeeb Abdulaleem, 2021. "E-differentiable minimax programming under E-convexity," Annals of Operations Research, Springer, vol. 300(1), pages 1-22, May.
    2. Anurag Jayswal & Vivek Singh & Krishna Kummari, 2017. "Duality for nondifferentiable minimax fractional programming problem involving higher order $$(\varvec{C},\varvec{\alpha}, \varvec{\rho}, \varvec{d})$$ ( C , α , ρ , d ) -convexity," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 598-617, September.

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