Research and Innovation Articles
Published 2008-02-29
Keywords
- Vector fractional programming,
- Clarke generalized gradient,
- duality,
- weak efficiency,
- optimality conditions
How to Cite
Batista Santos, L., Osuna-Gómez, R., & Rojas-Medar, M. A. (2008). Nonsmooth multiobjective fractional programming with generalized convexity. Revista Integración, Temas De matemáticas, 26(1), 1–12. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/52
Abstract
In this paper we study a class of nonconvex and nondifferentiable multiobjective fractional problems. We use the transformation proposed by Dinkelbach [2] and Jagannathan [4] and we obtain optimality conditions for weakly efficient solutions for these problems. Furthermore, we define a dual problem and we establish some results on duality. To obtain our results, we use a notion of generalized convexity, called KT-invexity. Our paper generalizes the results given by Osuna-Gómez et al. in [6], where the authors considered smooth problems.
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References
[1] F.H. Clarke, Optimization and nonsmooth analysis, Wiley, 1983.
[2] W. Dinklebach, “On nonlinear fractional programming”, Manegement Science, 137, pp. 492-498, 1967.
[3] A.M. Geoffrion, “Proper efficiency and the theory of vector maximization”, J. Math.Anal. Appl., 22, pp. 618-630, 1968.
[4] R. Jagannathan, “Duality for nonlinear fractional programs”, Zeitschrift fur Operations
Research, 17, pp. 1-3, 1973.
[5] D.H. Martin, “The essence of invexity”, J. Math. Anal. Appl. 47, pp. 65-76, 1985.
[6] R. Osuna-Gómez, A. Rufián-Lizana, P. Ruiz-Canales, “Multiobjective fractional programming with generalized invexity”, Sociedad de Estadística e Investigación Operativa TOP, vol. 8, no. 1, pp. 97-110, 2000.
[7] R. Osuna-Gómez, A. Rufián-Lizana, A. Beato-Moreno, “Generalized convexity in multiobjective programming”, Journal of Mathematical Analysis and Applications, vol. 23, pp. 467-475, 1999.
[8] P.H. Sach, D.S. Kim, G.M. Lee, “Invexity as necessary optimality condition in nonsmooth programs”, J. Korean Math. Soc. 43, no.2, pp. 241-258, 2006.
[9] S. Schaible, “A survey of fractional programming”, In: Generalized Convexity in Optimization and Economics. Eds. S. Schaible, W. T. Ziemba. Academic Press.
[2] W. Dinklebach, “On nonlinear fractional programming”, Manegement Science, 137, pp. 492-498, 1967.
[3] A.M. Geoffrion, “Proper efficiency and the theory of vector maximization”, J. Math.Anal. Appl., 22, pp. 618-630, 1968.
[4] R. Jagannathan, “Duality for nonlinear fractional programs”, Zeitschrift fur Operations
Research, 17, pp. 1-3, 1973.
[5] D.H. Martin, “The essence of invexity”, J. Math. Anal. Appl. 47, pp. 65-76, 1985.
[6] R. Osuna-Gómez, A. Rufián-Lizana, P. Ruiz-Canales, “Multiobjective fractional programming with generalized invexity”, Sociedad de Estadística e Investigación Operativa TOP, vol. 8, no. 1, pp. 97-110, 2000.
[7] R. Osuna-Gómez, A. Rufián-Lizana, A. Beato-Moreno, “Generalized convexity in multiobjective programming”, Journal of Mathematical Analysis and Applications, vol. 23, pp. 467-475, 1999.
[8] P.H. Sach, D.S. Kim, G.M. Lee, “Invexity as necessary optimality condition in nonsmooth programs”, J. Korean Math. Soc. 43, no.2, pp. 241-258, 2006.
[9] S. Schaible, “A survey of fractional programming”, In: Generalized Convexity in Optimization and Economics. Eds. S. Schaible, W. T. Ziemba. Academic Press.