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Duality for nondifferentiable minimax fractional programming problem involving higher order $$(\varvec{C},\varvec{\alpha}, \varvec{\rho}, \varvec{d})$$ ( C , α , ρ , d ) -convexity

Author

Listed:
  • Anurag Jayswal

    (Indian Institute of Technology (Indian School of Mines))

  • Vivek Singh

    (Indian Institute of Technology (Indian School of Mines))

  • Krishna Kummari

    (Indian Institute of Technology (Indian School of Mines))

Abstract

In this paper, we present new class of higher-order $$(C, \alpha , \rho , d)$$ ( C , α , ρ , d ) -convexity and formulate two types of higher-order duality for a nondifferentiable minimax fractional programming problem. Based on the higher-order $$(C, \alpha , \rho , d)$$ ( C , α , ρ , d ) -convexity, we establish appropriate higher-order duality results. These results extend several known results to a wider class of programs.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:opsear:v:54:y:2017:i:3:d:10.1007_s12597-016-0295-0
    DOI: 10.1007/s12597-016-0295-0
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    References listed on IDEAS

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    1. D. H. Yuan & X. L. Liu & A. Chinchuluun & P. M. Pardalos, 2006. "Nondifferentiable Minimax Fractional Programming Problems with (C, α, ρ, d)-Convexity," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 185-199, April.
    2. Z. A. Liang & H. X. Huang & P. M. Pardalos, 2001. "Optimality Conditions and Duality for a Class of Nonlinear Fractional Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 611-619, September.
    3. Jean-Philippe Vial, 1983. "Strong and Weak Convexity of Sets and Functions," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 231-259, May.
    4. VIAL, Jean-Philippe, 1983. "Strong and weak convexity of sets and functions," LIDAM Reprints CORE 529, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. 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.
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