Vol. 5 (10) pp. 279-290 DOI: 10.21474/IJAR01/5531

ON NONDIFFERENTIABLE MULTIOBJECTIVE PROGRAMMING INVOLVING TYPE-I -INVEX FUNCTIONS.

and
  • Department of Mathematics, Vyasangar Autonomous College, Odisha, India.
  • Principal, Govt. Junior College, Ayeba, Kendrapada, Odisha, India.
10 Downloads 98 Views
Crossref

Download Full Paper (PDF)

Abstract

The aim of this paper is to study a nondifferentialblemultiobjective programming problem with inequality constraints. In this paper we introduce the concept to type-I -invex, weak strictly pseudo-quasi type-I -invex, strong pseudo-quasi type-I -invex, weak quasi-strictly-pseudo type-I -invex and weak strictly-pseudo type-I -invex functions. By utilizing these new notions we derive a Fritz John type sufficient optimality condition and establish Mond-Weir type and Mond-Weir type duality results for the nondiffferentiablemultiobjective programming problem.

Keywords

Article Analytics

References

  1. Aghezzaf and M. Hachimi, Generalized invexity and duality in multiobjcctive pro?gramming problems, Journal of Global Optimization 18 (2000), 91-101.
  2. Antezak, Multiobjective programming under d-invexity, European Journal of Op?erational Research 137 (2002), 28-36.
  3. S. Bazaraa, H. D. Sherali and C. M. Shetty, Nonlinear Programming: Theory and Algorithms, Wiley, New York, 1991.
  4. R. Bector, S. K. Suneja and S. Gupta, Univex functions and univex nonlinear pro?gramming. In: Proceedings of the Administrative Sciences Association of Canada (1992), pp.115-124.
  5. D. Craven, Invex functions and constrained local minima, Bulletin of Australian Mathematical Society 24 (1981), 357-366.
  6. D. Craven, Nondifferentiable optimization by smooth approximation, Optimization 17(1986),3-17,
  7. R. Egudo and M. A. Hanson, Multi-objective duality with invexity, Journal of Mathematical Analysis and Applications 80 (1987), 469-477.
  8. A. Hanson. On sufficiency of the Kuhn-Tucker conditions. Journal of Mathematical Analysis and Applications 80 (1981), 545-550.
  9. A. Hanson and B. Mond, Necessary and sufficient conditions in constrained optimization, Mathematical programming 37 (1987), 51-58.
  10. Jeyakumar and B. Mond, On generalized convex mathematical programming, Jour?nal of Australian Mathematical Society Series B 34 (1992), 43-53.
  11. N. Kaul, S. K. Suneja and M. K. Srivastava, Optimality criteria and duality in multiple objective optimization involving generalized invexity. Journal of Optimization Theory and Applications 80 (1994), 465-482.
  12. L. Manga sari an, Nonlinear Programming, McGraw Hill. New York, 5969.
  13. K. Mishra, Lagrange multipliers saddle point and scalarizations in composite miltiobjectivenonsmooth programming, Optimization 38 (1996), 93-105.
  14. K. Mishra, On sufficiency and duality in nonsmoothmultiobjectivc programming, Opsearch34 (1997), 221-231.
  15. K. Mishra, On multiple objective optimization with generalized univexity. Journal of Mathematical Analysis and Applications 224 (1998), 131-148.
  16. K. Mishra and G. Giorgi, Optimality and duality with generalized semi-univexity. Opsearch37 (2000), 340-350.
  17. Mishra and R. N. Mukherjee, On generalized convex multiobjectivenonsmoothprogramming, Journal of Australian Mathematical Society Series B 38 (1996), 140-148.
  18. K. Mishra and M. A. Noor, On vector variational-like inequality problems. Journal of Mathematical Analysis and Applications 311 (2005), 69-75.
  19. K. Mislira, G. Giorgi and S. Y Wang, Duality in vector optimization in Banachspaces with generalized convexity. Journal of Global Optimization 29 (2004), 415-424
  20. Mishra, R.P. Pant and J.S. Rautela, Generalized α-invexity and nondifferentiableminimax fractional programming, Journal of Computational and Applied Mathematics 206,(2007), 122-135.
  21. K. Mishira, S. V. Wang and K. K. Lai, Complex minimax programming under generalized convexity. Journal of Computational and Applied Mathematics 167 (2004), 89-71
  22. K. Mishra, S.Y Wang and K.K.Lai, Optimality and duality in nondifferentiable and multiobjective programming under generalized d-invexity, Journal of Global Optimization 29(2004),425-438.
  23. K. Mishra, S.Y. Wang and K.K. Lai, Optimality and duality for multiple objective optimization under generalized type-I univexity. Journal of Mathematical Analysis and Applications303 (2005), 315-326.
  24. K. Mishra, S.Y. WangandK.K. Lai, Multiple objective fractional programming involving semilocally type-I preinvex and related functions. Journal of Mathematical Analysis and Applications 310 (2005), 626-640.
  25. Mond and T. Weir, Generalized concavity and duality. In: Schaible, S. and Zieniba. W.T. (eds.), Generalized concavity Optimization and Economics, Academic Press, New York (1981), pp. 263-280.
  26. A. Noon, ?On generalized preinvex functions and monotonicities?, Journal of lnequalities in Pure and Applied Mathematics 5 (2004), 1-9.
  27. P. Pant and J.S. Rautela, α-invexity and duality in mathematical programming, Journal of Mathematical Analysis and Approximation Theory 1(2006), 14-114.
  28. W. Reiland, Nonsmoothinvexity, Bulletin of the Australian Mathematical Society 42 (I 990;. 437-446.
  29. G. Rueda and M. A. Hanson, Optimality criteria in mathematical programming involving generalized invexity. Journal of Mathematical Analysis and Applications 130 (1988), 375-385.
  30. G. Rueda, M. A. Hanson and C. Singh, Optimality and duality with generalized convexity, Journal of Optimization Theory and Applications 86 (1995) 491-500.
  31. K. Suneja and M. K. Srivastava, Optimality and duality in nondifferentiablemultiobjective optimization involving d-type-I and related functions, Journal of Mathematical Analysis and Applications 206(1997), 465-479.
  32. Weir and B. Mond, Preinvex functions in multiple objective optimization, Journal of Mathematical Analysis and Applications 136 (1988), 29-38.
  33. L. Ye, d-invexity and optimally conditions. Journal of Mathematical Analysis and Applications 162 (1991), 242-249.
  34. K. Mishra, J.S. Rautela and R.P. Pant, On nondifferentiablemultiobjective programming involving type-I invex function, Applied Mathematics and Information Science, 2(3), (2008), 317-333.

How to Cite This Article

R. K. Sahu and D. K. Dalai. (2017); ON NONDIFFERENTIABLE MULTIOBJECTIVE PROGRAMMING INVOLVING TYPE-I -INVEX FUNCTIONS., Int. J. of Adv. Res., 5 (10), 279-290, ISSN 2320-5407. DOI: https://doi.org/10.21474/IJAR01/5531

Corresponding Author

R.K. Sahu
Department of Mathematics, Vyasangar Autonomous College, Odisha, India.
Creative Commons Attribution 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.