Skip to main content

On Some Equivalent Conditions of Vector Variational Inequalities

  • Chapter

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

Abstract

In this paper, we discuss some equivalent conditions for weak vector variational inequality and vector variational inequality problems, such as relations among vector variational inequalities, vector optimization problems and gap functions. These results are useful in the design of solution methods for vector variational inequalities.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chen G-Y. and Yang X.Q., “The Vector Complementarity Problem and its Equivalences with Weak Minimal Element”. Jou. of Mathem. Analysis and Appls., Vol. 153, 1990, pp. 136–158.

    Article  MATH  Google Scholar 

  2. Chew, K.L., and Choo, E.V., “Pseudolinearity and Efficiency”, Mathematical Programming, Vol. 28, 1984, pp. 226–239.

    Article  MathSciNet  MATH  Google Scholar 

  3. Giannessi, F., “On Minty Variational Principle”. In “New Trends in Mathematical Programming”. Kluwer Academic Publishers, 1998, pp. 93–99.

    Google Scholar 

  4. Giannessi, F., “Theorems of the Alternative, Quadratic Programs, and Complementarity Problems”. In “Variational Inequalities and Complementarity Problems”, Edited by R.W. Cottle et al., J. Wiley, New York, New York, 1980, pp. 151–186.

    Google Scholar 

  5. Goh, C.J. and Yang, X.Q. “On the Solution of Vector Variational Inequalities”, Proceedings of ‘Optimization Techniques and Applications’, edited by Caccetta L. et al 1998, pp. 1158–1164.

    Google Scholar 

  6. Konno, I.V. and Yao, J.C., “On the Generalized Vecto Variational Inequality Problem”, J.u. of Mathem. Analysis and Appls., Vol. 206, 1997, pp. 42–58.

    Article  Google Scholar 

  7. Lee G.M., “Relations Between Vector Variational Inequality and Vector Optimization Problem”. To appear in ‘Progress in Optimization II - Contributions from Australasia’, (edited by Yang X.Q. et al) Kluwer.

    Google Scholar 

  8. Lee G.M., Lee B.S. and Chang S.S., “On Vector Quasivariational Inequalities”. Jou. Mathem. Analysis Appls., Vol. 203, 1996, pp. 626–638.

    Article  MATH  Google Scholar 

  9. Sawaragi Y., Nakayama H. and Tanino T., “Theory of multiobjective optimization”. Academic press, 1995.

    Google Scholar 

  10. Yang, X.Q., “Generalized Convex Functions and Vector Variational Inequalities,” Jou. of Optimiz. Theory and Appls., Vol. 79, 1993, pp. 563–580.

    Article  MATH  Google Scholar 

  11. Yang, X.Q., “Vector Variational Inequality and Vector Pseudolinear Optimization”. Jou. Optimiz. Theory Appls., Vol. 95, 1997, pp. 729–734.

    Article  MATH  Google Scholar 

  12. Yang, X.Q., and Goh, C.J., “On Vector Variational Inequality. Application to Vector Equilibria,” Jou. of Optimiz. Theory and Appls., Vol. 95, No. 2, 1997 pp. 431–443.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Kluwer Academic Publishers

About this chapter

Cite this chapter

Yang, X.Q. (2000). On Some Equivalent Conditions of Vector Variational Inequalities. 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_25

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-0299-5_25

  • 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