• Kim, Moon-Hee (Department of Multimedia Engineering, Tongmyong University) ;
  • Kim, Gwi-Soo (Department of Applied Mathematics, Pukyong National University)
  • Received : 2010.04.23
  • Accepted : 2010.06.23
  • Published : 2010.09.30


Sufficient optimality conditions for a class of generalized non-differentiable fractional optimization programming problems are established. Moreover, we prove the weak and strong duality theorems under (V, $\rho$)-invexity assumption.



Supported by : Korea Science and Engineering Foundation (KOSEF)


  1. F.H. Clarke, Optimization and Nonsmooth Analysis, A Wiley-Interscience Publication, John Wiley & Sons, 1983.
  2. D. S. Kim, S. J. Kim and M. H. Kim, Optimality and Duality for a Class of Non-differentiable Multiobjective Fractional Programming Problems, J. Optim. Theory Appl. 129(2006), 131-146. https://doi.org/10.1007/s10957-006-9048-1
  3. M. H. Kim and D. S. Kim, Non-differentiabel Symmetric Duality for Multiobjective Programming with Cone Constraints, European J. Oper. Res. 188(2008), 652-661. https://doi.org/10.1016/j.ejor.2007.05.005
  4. 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
  5. H. Kuk, G. M. Lee and D. S. Kim, Nonsmooth Multiobjective Programs with (V, $\rho$)-Invexity, Indian J. Pure and Appl. Math. 29(1998), 405-412.
  6. H. Kuk, G. M. Lee and T. Tanino, Optimality and Duality for Nonsmooth Multiobjective Fractional Programming with Generalized Invexity, J. Math. Anal. Appl. 262(2001), 365-375. https://doi.org/10.1006/jmaa.2001.7586
  7. Z. Liang, H. Huang and P. M. Pardalos, Optimality Conditions and Duality for a Class of Nonlinear Fractional Programming Problems, J. Optim. Theory Appl. 110(2001), 611-619.
  8. Z. Liang, H. Huang and P. M. Pardalos, Efficiency Conditions and Duality for a Class of Multiobjective Fractional Programming Problems, J. Global Optim. 27(2003), 444-417.
  9. X. J. Long, N. J. Huang and Z. B. Liu, Optimality conditions, duality ad saddle points for nondifferentiale multiobjective fractional programs, Journal of Industry Management and Optimization 4(2008), 287-298.
  10. Marko M. Maklela and Pekka Neittaanmaki, Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control, World Scientific Publishing Co. Pte. Ltd.,1992.
  11. X. M. Yang, X. Q. Yang and K. L. Teo, Duality and Saddle-point Type Optimality for Generalized Nonlinear Fractional Programming, J. Math. Anal. Appl. 289(2004), 100-109.