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Vector Variational Inequality and Vector Optimization Problem

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Toward Interactive and Intelligent Decision Support Systems

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 285))

Abstract

The theory as well as the application of the variational inequality have been well documented in the literature. In recent years, various extensions of this problems have been proposed and analyzed. Perhaps the most general extension of the variational inequality in the one studied by Giannessi [1]. Giannessi introduced the vector variational inequality.

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References

  1. F. Giannessi, Theorems of Alternative, Quadratic Programs, and Complementarity Problems, Variational Inequalities and Complementarity Problems, p.167, Edited R.W. Cottle, F. Giannessi, J-L. Lions, John Wiley & Sons, 1980.

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  2. R.T. Rockefellar, Lagrange Multipliers and Variational Inequality, Variational Inequalities and Complementarity Problems, p.305, Edited R.W. Cottle, F. Giannessi, J-L. Lions, John wiley & Sons, 1980.

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  3. Hildenbrand, W., (1974), Core and Equilibria of a Large Economy, Princeton University Press, Priceton.

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  4. Berge, C., (1963), Topological Spaces, the Macmillan Company, New York.

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  5. G. Jameson (1970), Ordered Linear Spaces, Springer-Verlag, Berlin.

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  6. D. Chan and J.S. Pang (1982), The Generalized Quasi-Variational Inequality Problems, Math. Oper. Res., Vol 7. No. 2.

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  7. Day, M.M., Normed Linear Spaces, Springer-Verlag, Berlin, 1962.

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Author information

Authors and Affiliations

  1. Institute of Systems Science, Academia Sinica, Beijing, China

    Guang-Ya Chen

  2. Institute of Traffic Systems Engineering, Beijing, China

    Ging-Min Cheng

Authors
  1. Guang-Ya Chen
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  2. Ging-Min Cheng
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Editor information

Editors and Affiliations

  1. Japan Institute of Systems Research, Nippon-Italy Kyoto Kaikan, 4 Ushinomiya-cho, Yoshida, Sakyo, Kyoto 606, Japan

    Yoshikazu Sawaragi

  2. Department of Aeronautical Engineering, Kyoto University, Yoshida-honmachi, Sakyo, Kyoto 606, Japan

    Koichi Inoue

  3. Department of Applied Mathematics, Konan University, 8-9-1 Okamoto, Higashinada, Kobe 658, Japan

    Hirotaka Nakayama

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© 1987 Springer-Verlag Berlin Heidelberg

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Chen, GY., Cheng, GM. (1987). Vector Variational Inequality and Vector Optimization Problem. In: Sawaragi, Y., Inoue, K., Nakayama, H. (eds) Toward Interactive and Intelligent Decision Support Systems. Lecture Notes in Economics and Mathematical Systems, vol 285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46607-6_44

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  • DOI: https://doi.org/10.1007/978-3-642-46607-6_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17718-0

  • Online ISBN: 978-3-642-46607-6

  • eBook Packages: Springer Book Archive

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