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Two types of duality in multiobjective fractional programming

Published online by Cambridge University Press:  17 April 2009

L. Coladas ,
Z. Li  and
S. Wang
L. Coladas
Affiliation:
Departament de Estadística e Investigación Operativa, Universidad de Santiago de Compostela, 15771 Santiago de Compostela, Spain, e-mail: coladas@zmat.usc.es
Z. Li
Affiliation:
Department of Mathematics, University of Inner Mongolia, Hohhot 010021, China
S. Wang
Affiliation:
Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080, China, e-mail: sywang@issO2.iss.ac.cn
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Abstract

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In this paper, we tire concerned with duality of a multiobjective fractional program. Two different dual problems are introduced with respect to the primal multiobjective fractional program. Under a mild assumption, we prove a weak duality theorem and a strong duality theorem for each type of duality. Finally, we explore some relations between these two types of duality.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 1 , August 1996 , pp. 99 - 114
Copyright
Copyright © Australian Mathematical Society 1996

References

REFERENCES

[1]Bazaraa, M.S. and Shetty, C.M., Nonlinear programming: theory and algorithms (John Wiley and Sons, New York, New York, 1979).Google Scholar
[2]Bector, C.R., Chandra, S. and Husain, I., ‘Optimality conditions and duality in subdif-ferentiable multiobjective fractional programming’, J. Optim. Theory Appl. 79 (1993), 105–125.CrossRefGoogle Scholar
[3]Bector, C.R., Chaudra, S. and Singh, C., ‘A linearization approach to multiobjective programming duality’, J. Math. Anal. Appl. 175 (1993), 268–279.CrossRefGoogle Scholar
[4]Coladas, L., Li, Z. and Wang, S., ‘Dualidad en programacion fracional multiobjetive’, in Proceedings of XXI Congreso Nacional de Estadistica e Investigation Operativa, Calella, Barcelona April 18–21., 1994, pp. 280–281.Google Scholar
[5]Craven, B.D. and Glover, B.M., ‘Invex functions and duality’, J. Austral. Math. Soc. Ser. A 39 (1985), 1–20.CrossRefGoogle Scholar
[6]Egudo, R.R., ‘Multiobjective fractional duality’, Bull. Austral. Math. Soc. 37 (1988), 367–378.CrossRefGoogle Scholar
[7]Egudo, R.R. and Hanson, M.A., ‘Multiobjective duality with invexity’, J. Math. Anal. Appl. 126 (1987), 469–477.CrossRefGoogle Scholar
[8]Hu, Y. and Zhang, F., ‘Two dual types of multiobjective programming’, Acta Math. Appl. Sinica 14 (1991), 128–135.Google Scholar
[9]Sawaragi, Y., Nakayama, H. and Tanino, T., Theory of multiobjective optimization (Academic Press, New York, New York, 1985).Google Scholar
[10]Singh, C., ‘A class of multiple-criteria fractional programming problem’, J. Math. Anal. Appl. 115 (1986), 202–213.CrossRefGoogle Scholar
[11]Wang, S., ‘Theory of the conjugate duality in multiobjective optimization’, J. Systems Sci. Math. Sci. 4 (1984), 303–312.Google Scholar
[12]Weir, T., ‘A duality theorem for a multiple objective fractional optimization problem’, Bull. Austral Math. Soc. 34 (1986), 415–425.CrossRefGoogle Scholar
[13]Weir, T. and Jeyakumar, V., ‘A class of nonconvex functions and mathematical programming’, Bull. Austral. Math. Soc. 38 (1988), 177–189.CrossRefGoogle Scholar