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Optimality Conditions and Duality for a Class of Nonlinear Fractional Programming Problems

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  • Z. A. Liang
  • H. X. Huang
  • P. M. Pardalos

Abstract

In this paper, we present sufficient optimality conditions and duality results for a class of nonlinear fractional programming problems. Our results are based on the properties of sublinear functionals and generalized convex functions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:110:y:2001:i:3:d:10.1023_a:1017540412396
    DOI: 10.1023/A:1017540412396
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    Cited by:

    1. 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.
    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.
    3. Arshpreet Kaur & Mahesh K Sharma, 2022. "Correspondence between a new class of generalized cone convexity and higher order duality," OPSEARCH, Springer;Operational Research Society of India, vol. 59(2), pages 550-560, June.
    4. Hong Yang & Angang Cui, 2023. "The Sufficiency of Solutions for Non-smooth Minimax Fractional Semi-Infinite Programming with ( B K ,ρ )−Invexity," Mathematics, MDPI, vol. 11(20), pages 1-13, October.
    5. Washington Alves Oliveira & Marko Antonio Rojas-Medar & Antonio Beato-Moreno & Maria Beatriz Hernández-Jiménez, 2019. "Necessary and sufficient conditions for achieving global optimal solutions in multiobjective quadratic fractional optimization problems," Journal of Global Optimization, Springer, vol. 74(2), pages 233-253, June.
    6. V. Jeyakumar & G. Y. Li, 2011. "Robust Duality for Fractional Programming Problems with Constraint-Wise Data Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 292-303, November.
    7. Abderrahman Bouhamidi & Mohammed Bellalij & Rentsen Enkhbat & Khalid Jbilou & Marcos Raydan, 2018. "Conditional Gradient Method for Double-Convex Fractional Programming Matrix Problems," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 163-177, January.
    8. D. S. Kim & S. J. Kim & M. H. Kim, 2006. "Optimality and Duality for a Class of Nondifferentiable Multiobjective Fractional Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 131-146, April.
    9. 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.
    10. Jeyakumar, V. & Li, G.Y. & Srisatkunarajah, S., 2013. "Strong duality for robust minimax fractional programming problems," European Journal of Operational Research, Elsevier, vol. 228(2), pages 331-336.
    11. Arun Kumar Tripathy, 2021. "The Study Higher-order Wolfe-type Non-differentiable Multiple Objective Symmetric Duality Involving Generalized Convex Functions," SN Operations Research Forum, Springer, vol. 2(4), pages 1-18, December.
    12. X. J. Long, 2011. "Optimality Conditions and Duality for Nondifferentiable Multiobjective Fractional Programming Problems with (C,α,ρ,d)-convexity," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 197-208, January.
    13. S. Mishra & S. Wang & K. Lai, 2008. "Optimality and duality for a nonsmooth multiobjective optimization involving generalized type I functions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(3), pages 493-504, June.
    14. Ching-Feng Wen & Hsien-Chung Wu, 2011. "Using the Dinkelbach-type algorithm to solve the continuous-time linear fractional programming problems," Journal of Global Optimization, Springer, vol. 49(2), pages 237-263, February.
    15. 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.
    16. P. Khanh & L. Tung, 2015. "First- and second-order optimality conditions for multiobjective fractional programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 419-440, July.
    17. Rongbo Wang & Qiang Feng, 2024. "Optimality and Duality of Semi-Preinvariant Convex Multi-Objective Programming Involving Generalized ( F , α , ρ , d )- I -Type Invex Functions," Mathematics, MDPI, vol. 12(16), pages 1-13, August.
    18. Xiaojun Lei & Zhian Liang, 2008. "Study on the Duality between MFP and ACP," Modern Applied Science, Canadian Center of Science and Education, vol. 2(6), pages 1-81, November.
    19. 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.
    20. Haijun Liu & Neng Fan & Panos M. Pardalos, 2012. "Generalized Lagrange Function and Generalized Weak Saddle Points for a Class of Multiobjective Fractional Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 370-381, August.
    21. I. Ahmad & Z. Husain & S. Sharma, 2009. "Higher-Order Duality in Nondifferentiable Minimax Programming with Generalized Type I Functions," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 1-12, April.
    22. Altannar Chinchuluun & Dehui Yuan & Panos Pardalos, 2007. "Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity," Annals of Operations Research, Springer, vol. 154(1), pages 133-147, October.

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