Abstract
G.S.Rubinstein in his paper [1] has introduced a universal scheme for constructing a dual problem to a given optimization problem with a real valued objective function. T.Q. Chien in his dissertation [2] has extended the Rubinstein scheme for optimization problems with vector valued objective functions. In this paper the basic ideas of Rubinstein’s approach are expounded and its application potency is illustrated by means of fractional programming problems with vector valued objective functions.
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References
Rubinstein G.S., Duality in Mathematical Programming and Some Questions of Convex Analysis (in Russian), Uspechi mat. nauk (1970), pp. 171–201.
Tran Quoc Chien, Duality Theory in Vector Optimization. Thesis, Charles University, Prague, 1985.
Tran Quoc Chien, Fenchel-Lagranee Duality in Vector Fractional Programming via Abstract Duality Scheme. Kybernetika 22 (1986), pp.289–319.
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© 1990 Springer-Verlag Berlin Heidelberg
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Vlach, M. (1990). Rubinstein Duality Scheme for Vector Optimization. In: Cambini, A., Castagnoli, E., Martein, L., Mazzoleni, P., Schaible, S. (eds) Generalized Convexity and Fractional Programming with Economic Applications. Lecture Notes in Economics and Mathematical Systems, vol 345. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46709-7_18
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DOI: https://doi.org/10.1007/978-3-642-46709-7_18
Publisher Name: Springer, Berlin, Heidelberg
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