## Taiwanese Journal of Mathematics

### NONSMOOTH MULTIOBJECTIVE FRACTIONAL PROGRAMMING WITH GENERALIZED INVEXITY

Do Sang Kim

#### Abstract

In this paper, we consider nonsmooth multiobjective fractional programming problems involving locally Lipschitz functions. We introduce the property of generalized invexity for fractional function. We present necessary optimality conditions, sufficient optimality conditions and duality relations for nonsmooth multiobjective fractional programming problems, which is for a weakly efficient solution under suitable generalized invexity assumptions.

#### Article information

Source
Taiwanese J. Math., Volume 10, Number 2 (2006), 467-478.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500403837

Digital Object Identifier
doi:10.11650/twjm/1500403837

Mathematical Reviews number (MathSciNet)
MR2208279

Zentralblatt MATH identifier
1105.90093

#### Citation

Kim, Do Sang. NONSMOOTH MULTIOBJECTIVE FRACTIONAL PROGRAMMING WITH GENERALIZED INVEXITY. Taiwanese J. Math. 10 (2006), no. 2, 467--478. doi:10.11650/twjm/1500403837. https://projecteuclid.org/euclid.twjm/1500403837

#### References

• [1.] F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983.
• [2.] V. Jeyakumar, Equivalence of saddle-points and optima, and duality for a class of nonsmooth non-convex problems, J. Math. Anal. Appl., 130 (1988), 334-343.
• [3.] V. Jeyakumar and B. Mond, On generalized convex mathematical programming, J. Aust. Math. Soc., 34B (1992), 43-53.
• [4.] Z. A. Khan and M. A. Hanson, On ratio invexity in mathematical programming, J. Math. Anal. Appl., 205 (1997), 330-336.
• [5.] D. S. Kim and S. J. Kim, Nonsmooth fractional programming with generalized ratio invexity, RIMS Kokyuroku 1365, Proc. of RIMS Symposium "Nonlinear Analysis and Convex Analysis" (2004), 116-127.
• [6.] H. Kuk, G. M. Lee and D. S. Kim, Nonsmooth multiobjective programs with V-$\rho$-invexity, Indian J. Pure Appl. Math., 29 (1998), 405-412.
• [7.] 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.
• [8.] Z. A. Liang, H. X. Huang and P. M. Pardalos, Optimality conditions and duality for a class of nonlinear fractional programming problems, J. Optimization Theory Appl., 110 (2001) 611-619.
• [9.] Z. A. Liang, H. X. Huang and P. M. Pardalos, Efficiency conditions and duality for a class of multiobjective fractional programming problems, J. Global Optim., 27 (2003) 447-471.
• [10.] J. C. Liu, Optimality and duality for multiobjective fractional programming involving nonsmooth pseudo-invex functions, Optimization, 37 (1996) 27-39.
• [11.] J. C. Liu, Generalized minimax programming, Doctoral Dissertation, Niigata University, 2001.
• [12.] S. K. Mishra and R. N. Mukherjee, On generalized convex multi-objective nonsmooth programming, J. Aust. Math. Soc., 38B (1996) 140-148.
• [13.] V. Preda, On efficiency and duality for multiobjective programs, J. Math. Anal. Appl., 166 (1992) 365-377.
• [14.] R. L. Venkateswara and R. N. Mukherjee, Some results on mathematical programming with generalized ratio invexity, J. Math. Anal. Appl., 240 (1999) 299-310.