# OPTIMALITY AND DUALITY FOR NONDIFFERENTIABLE FRACTIONAL PROGRAMMING WITH GENERALIZED INVEXITY

• Kim, Gwi Soo (Department of Applied Mathematics Pukyong National University) ;
• Kim, Moon Hee (Department of Refrigeration Engineering Tongmyong University)
• Accepted : 2016.07.15
• Published : 2016.08.15

#### Abstract

We establish necessary and sufficient optimality conditions for a class of generalized nondifferentiable fractional optimization programming problems. Moreover, we prove the weak and strong duality theorems under (V, ${\rho}$)-invexity assumption.

#### References

1. R. P. Agarwal, I. Ahmad, and S. Al-Homidan, Optimality and duality for nondifferentiable multiobjective programming problems involving generalized d-$\rho$-(n, ${\theta}$) Type I invex functions, Journal of Nonlinear and Convex Analysis 13 (2012), no. 4, 733-744.
2. I. Ahmad, S. K. Gupta, and A. Jayswal, On sufficiency and duality for non-smooth multiobjective programming problems involving generalized V -r- invex functions, Nonlinear Analysis: Theory, Methods & Applications 74(17) (2011), 5920-5928. https://doi.org/10.1016/j.na.2011.05.058
3. R. P. Agarwal, I. Ahmad, Z. Husain, and A. Jayswal, Optimality and duality in nonsmooth multiobjective optimization involving V -type I invex functions, Journal of Inequalities and Applications 21 (2010).
4. I. Ahmad and S, Sharma, Optimality conditions and duality in nonsmooth multiobjective optimization, Journal of Nonlinear and Convex Analysis 8 (2007), 417-430.
5. F. H. Clarke, Optimization and Nonsmooth Analysis, A Wiley-Interscience Publication, John Wiley & Sons, 1983.
6. D. S. Kim, S. J. Kim, and M. H. Kim, Optimality and duality for a class of nondifferentiable multiobjective fractional programming problems, Journal of Optimization Theory and Applications 129 (2006), no. 1, 131-146. https://doi.org/10.1007/s10957-006-9048-1
7. M. H. Kim and G. S Kim, On optimality and duality for generalized nondifferentiable fractional optimization problems, Communications of the Korean Mathematical Society 25 (2010), 139-147. https://doi.org/10.4134/CKMS.2010.25.1.139
8. H. Kuk, G. M. Lee, and D. S. Kim, Nonsmooth multiobjective programs with (V, p)-invexity, Indian Journal of Pure and Applied Mathematics 29 (1998), 405-412.
9. H. Kuk, G. M. Lee, and T. Tanino, Optimality and duality for nonsmooth multiobjective fractional programming with generalized invexity, Journal of Mathematical Analysis and Applications 262 (2001), 365-375. https://doi.org/10.1006/jmaa.2001.7586
10. Z. Liang, H. Huang, and P. M. Pardalos, Optimality conditions and duality for a class of nonlinear fractional programming problems, Journal of Optimization Theory and Applications 110 (2001), 611-619. https://doi.org/10.1023/A:1017540412396
11. M. M. Maklela and P. Neittaanmaki, Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control, World Scientific Publishing Co. Pte. Ltd. 1992.
12. Z. Y. Peng and S. S. Chang, Some properties of semi-G-preinvex functions, Taiwan Journal of Mathematics 17 (2013), no. 3, 873-884. https://doi.org/10.11650/tjm.17.2013.2582