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Journals / An International Journal of Optimization and Control: Theories & Applications (IJOCTA) / 2013 / Cilt: 3 - Sayı: 1

Minimax fractional programming problem involving nonsmooth generalized ?-univex functions

Anurag JAYSWALA
Dilip KUMAR
Rajnish KUMAR
Pages
7–22
Publication Date
2022-10-11
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The results in this paper extend some known results in the literature.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we introduce a new class of generalized ?-univex functions where the involved functions are locally Lipschitz.
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Key Findings & Data:Comput. 31 (2009) 317-334] to ?-univexity and an example is provided to show that there exist functions that are ?-univex but not ?-type I invex.
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Conclusion & Impact:The results in this paper extend some known results in the literature.
🔬Design:Modeling & Simulation
📍Scope:2009 Verileri
⚙️Variables:Domain Parameters

Abstract

In this paper, we introduce a new class of generalized ?-univex functions where the involved functions are locally Lipschitz. We extend the concept of ?-type I invex [S. K. Mishra, J. S. Rautela, On nondifferentiable minimax fractional programming under generalized ?-type I invexity, J. Appl. Math. Comput. 31 (2009) 317-334] to ?-univexity and an example is provided to show that there exist functions that are ?-univex but not ?-type I invex. Furthermore, Karush-Kuhn-Tuckertype sufficient optimality conditions and duality results for three different types of dual models are obtained for nondifferentiable minimax fractional programming problem involving generalized ?univex functions. The results in this paper extend some known results in the literature.

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Cite This Article

JAYSWALA, A., KUMAR, D., KUMAR, R. (2022). Minimax fractional programming problem involving nonsmooth generalized ?-univex functions. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 3 - Sayı: 1, 7–22. https://ajindex.com/articles/440737

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References (18)

  1. C. R. Bector, B. L. Bhatia, Sufficient optimality and duality for a minimax problems. Utilitas Math., 27, 229-247 (1985)
  2. C. R. Bector, S. K. Suneja, S. Gupta, Univex functions and univex nonlinear programming. Proceedings of the Administrative Sciences Association of Canada, 115-124, (1992)
  3. S. Chandra, B. D. Craven, B. Mond, Generalized fractional programming duality: A ratio game approach. J. Austral. Math. Soc. Ser. B, 28, 170-180 (1986)
  4. Charnes, W. W. Copper, Goal programming and multi-objective optimization. Part I, European J. Oper. Res.1, 39-54 (1977)
  5. S. Chandra, V. Kumar, Duality in fractional minimax programming. J. Austral. Math. Soc. Ser. A, 58, 376-386 (1995)
  6. F. H. Clarke, Optimization and Nonsmooth Analysis. Wiley, New York, (1983)
  7. L. Fan, Y. Guo, On strongly ?-preinvex functions. J. Math. Anal. Appl., 330, 1412- 1425 (2007)
  8. M. A. Hanson, On sufficiency of the KuhnTucker conditions. J. Math. Anal. Appl., 80, 545-550 (1981)
  9. M. A. Hanson, B. Mond, Further generalizations of convexity in mathematical programming. J. Inform. Optim. Sci., 3, 25-32 (1982)
  10. A. Jayswal, Non-differentiable minimax fractional programming with generalized ? -univexity. J. Comput. Appl. Math., 214, 121-135 (2008)
  11. H. C. Lai, J. C. Liu, K. Tanaka, Necessary and sufficient conditions for minimax fractional programming. J. Math. Anal. Appl., 230, 311-328 (1999)
  12. H. C. Lai, J. C. Lee, On duality theorems for a nondifferentiable minimax fractional programming. J. Comput. Appl. Math., 146, 115-126 (2002)
  13. J. C. Liu, Optimality and duality for multiobjective fractional programming involving nonsmooth ?F, ?? -convex functions. Optimization, 36, 333-346 (1996)
  14. J. C. Liu, Optimality and duality for multiobjective fractional programming involving nonsmooth pseudoinvex functions. Optimization, 37, 27-39 (1996)
  15. X. J. Long, J. Quan, Optimality conditions and duality for minimax fractional programming involving nonsmooth generalized univexity, Numerical Algebra, Control and Optimization. 1, 361-370 (2011)
  16. S. K. Mishra, R. P. Pant, J. S. Rautela, Generalized ? -invexity and nondifferentiable minimax fractional programming. J. Comput. Appl. Math., 206, 122-135 (2007)
  17. S. K. Mishra, J. S. Rautela, On nondifferentiable minimax fractional programming under generalized ? -type I invexity. J. Appl. Math. Comput., 31, 317- 334 (2009)
  18. M. A. Noor, On generalized preinvex functions and monotonicities. J. In