Abstract
Some relations are obtained between weak vector minimization, a vector variational inequality, and the optimization of a utility function over a set of efficient points.
Zusammenfassung
Es werden einige Beziehungen über schwache Vektorminimierung, einer vektoriellen Variationsgleichung und der Optimierung einer Nutzenfunktion über einer Menge effizienter Punkte hergeleitet.
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References
Benson HP (1984) Optimization over the efficient set. J Math Anal Appl 98:562–580
Benson HP (1986) An algorithm for optimizing over the weakly efficient set. European J Operational Research 25(2):192–199
Chen Guang-Ya, Cheng Ging-Min (1987) Vector variational inequality and vector optimization problems. Proceedings of 7th MCDM Conference, Kyoto, Japan. Springer-Verlag, Berlin, pp 408–416
Craven BD (1978) Mathematical programming and control theory. Chapman & Hall, London
Craven BD (1977) Lagrangean conditions and quasiduality. Bull Austral Math Soc 16:325–339
Giles JR (1982) Convex analysis with application in differentiation of convex functions. Pitman Advanced Publishing Program, Boston
Jameson G (1970) Ordered linear spaces. Lectture Notes in Mathematics 141. Springer-Verlag, Berlin
Philip J (1972) Algorithms for one vector maximization problem. Math Programming 2:207–229
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Chen, G.Y., Craven, B.D. A vector variational inequality and optimization over an efficient set. ZOR - Methods and Models of Operations Research 34, 1–12 (1990). https://doi.org/10.1007/BF01415945
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DOI: https://doi.org/10.1007/BF01415945