Abstract
This paper derives several results regarding the optimality conditions and duality properties for the class of multiobjective fractional programs under generalized convexity assumptions. These results are obtained by applying a parametric approach to reduce the problem to a more conventional form.
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Bector, C.R. and S. Chandra (1987).Multiobjective Fractional Programming Duality: A parametric Approach. Research Report, Faculty of Management, University of Manitoba.
Ben-Israel, A. and B. Mond (1986). What is the invexity?.J. Austral. Math. Soc. Ser. B,28, 1–9.
Dinklebach, W. (1967). On nonlinear fractional programming.Management Science,137, 492–498.
Elster, K.H. and R. Nehse (1980).Optimality Conditions for some Nonconvex problems, Springer-Verlag, New York.
Geoffrion, A. M. (1968). Proper efficiency and the theory of vector maximization.J. Math. Ana. App.,22, 618–630.
Hanson, M. A. and B. Mond (1987). Convex Transformable Problems and Invexity.J. Inf. opt. Sci. 8, 201–206.
Jagannathan, R. (1973). Duality for nonlinear fractional programs.Zeitschrift fur Operations Research,17, 1–3.
Kaul, R.N. and V. Lyall (1989). A note on nonlinear fractional vector maximization.Opsearch,26, No. 2, 108–121.
Martin, D.H. (1985). The essence of invexity.Journal of Optimization Theory and Applications,47, No. 1, 65–76.
Mukherjee, R.N. (1991). Generalized convex duality for multiobjective fractional programs.J. Math. Ana. Appl.,162, 309–316.
Osuna-Gómez, R., A. Beato-Moreno and A. Rufián-Lizana (1999). Generalized convexity in multiobjective programming.Journal of Mathematical Analysis and Applications,233, 205–220.
Osuna-Gómez, R., A. Rufián-Lizana and P. Ruíz-Canales (1998). Invex functions and generalized convexity in multiobjective programming.Journal of Optimization Theory and Applications,24, No. 3, 651–661.
Schaible, S. (1976). Fractional programming 1, duality.Mangement Science,22, 858–867.
Singh, C. (1986). A class of multiple criteria fractional programming problems.Math. Ana. Appl.,115, 202–213.
Singh, C., S.K. Suneja and N.G. Rueda (1991). Preinvexity in Multiobjective Programming.J. Inf. and Opt. Sciences,13, No. 2, 293–302.
Suneja, S.K. and S. Gupta (1990). Duality in multiple objective fractional programming problems involving non-convex functions.Opsearch,27, No. 4, 239–253.
Suneja, S.K. and M.K. Srivastava (1994). Duality in multiobjective fractional programming involving generalized invexity.Opsearch,31, No. 2, 127–143.
Weir, T. (1986). A dual for a multiple objective fractional programming problem.J. Inf. Opti. Sci.,7, 261–269.
Weir, T. (1986). A duality theorem for a multiobjective fractional optimization.Bull. Aust. Math. Soc.,24, 415–425.
Weir, T. (1989). On duality in multiobjective fractional programming.Opsearch,26, No. 3, 151–158.
Yang, X. (1992). Alternative theorems and optimality conditions with weakened convexity.Opsearch,29, No. 2, 125–135.
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Osuna-Gómez, R., Rufián-Lizana, A. & Ruíz-Canales, P. Multiobjective fractional programming with generalized convexity. Top 8, 97–110 (2000). https://doi.org/10.1007/BF02564830
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DOI: https://doi.org/10.1007/BF02564830