On the Existence of Solutions to Vector Complementarity Problems

Chen, Guang-ya; Yang, Xiao Qi

doi:10.1007/978-1-4613-0299-5_6

Guang-ya Chen⁴ &
Xiao Qi Yang⁵

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 38))

407 Accesses
1 Citations

Abstract

It is known that there is a close relation between vector complementarity problems and vector variational inequalities. There are several types of existence results for vector variational inequalities. This paper aims to review some existence results on vector complementarity problems; it includes existence of solutions for vector complementarity problems, vector implicit complementarity problems, and generalized vector complementarity problems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 169.00; Price excludes VAT (USA)

Softcover Book: USD 219.99; Price excludes VAT (USA)

Hardcover Book: USD 219.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

References

Chen G.-Y. Yang X.Q., “The Vector Complementary Problems and Its Equivalences with Weak Minimal Element”. Jou. of Mathem. Analysis and Appls., Vol. 153, No. 1, 1990, pp. 136–158.
Article MATH Google Scholar
Cottle R.W., Giannessi F. and Lions J.-L. (Eds.), “Variational Inequalities and complementarity problems”. John Wiley, New York, 1980, pp. 151–186.
Google Scholar
Fu J., “Simultaneous vector variational inequalities and vector implicit complementarity problem”. Jou. of Optimiz. Theory and Appls., Vol. 93, 1997, pp. 141–151.
Article MATH Google Scholar
Giannessi F., “Theorems of the Alternative, Quadratic Programs, and Complementarity Problems”. In [2].
Google Scholar
Isac I., “On the implicit Complementarity problem in Hilbert spaces”. Bull. Austral. Mathem. Soc. Vol. 32, 1985, pp. 251–260.
Article MathSciNet Google Scholar
Rockafellar R.T., Convex Analysis. Princeton University Press, Princeton, New Jersey, 1970.
MATH Google Scholar
Yang X.Q., “Vector Complementarity and minimal element Problems”. Jou. of Optimiz. Theory and Appls., Vol. 77, No. 3, 1993, pp. 483–495.
Article MATH Google Scholar
Yu S.J. and Yao J.C., “On Vector variational inequalities”. Jou. of Optimiz. Theory and Appls., Vol. 89, 1996, pp. 749–769.
Article MathSciNet MATH Google Scholar

Download references

Author information

Authors and Affiliations

Institute of Systems Science, Chinese Academy of Sciences, Beijing, China
Guang-ya Chen
Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China
Xiao Qi Yang

Authors

Guang-ya Chen
View author publications
You can also search for this author in PubMed Google Scholar
Xiao Qi Yang
View author publications
You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

Department of Mathematics, University of Pisa, Pisa, Italy
Franco Giannessi

Rights and permissions

Reprints and permissions

Copyright information

About this chapter

Cite this chapter

Chen, Gy., Yang, X.Q. (2000). On the Existence of Solutions to Vector Complementarity Problems. In: Giannessi, F. (eds) Vector Variational Inequalities and Vector Equilibria. Nonconvex Optimization and Its Applications, vol 38. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0299-5_6

Download citation

DOI: https://doi.org/10.1007/978-1-4613-0299-5_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7985-0
Online ISBN: 978-1-4613-0299-5
eBook Packages: Springer Book Archive

Publish with us

Policies and ethics