Skip to main content

Existence of Solutions for Vector Saddle-Point Problems

  • Chapter

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

Abstract

In this paper, we establish an existence theorem for weak saddle points of a vector valued function by making use for vector variational-like inequality and non-convex functions.

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. Ben-Israel A., and Neogy S.K., “What is Invexity?” Jou. of Australian Mathem. Society, Vol. 28, 1986, pp. 1–9.

    Article  MATH  Google Scholar 

  2. Chen G.-Y., “Existence of Solutions for a Vector Variational Inequality: An Existence of the Hartmann-Stampacchia Theorem”. Jou. of Optimiz. Theory and Appls., Vol. 74, 1992, pp. 445–456.

    Article  MATH  Google Scholar 

  3. Craven B.D., “Invex Functions and Constrained Local Minima”. Bull. of Australian Mathem. Society, Vol. 39, 1985, pp. 1–20.

    Article  MathSciNet  MATH  Google Scholar 

  4. Fan K., “A Generalization of Tychonoff’s Fixed Point Theorem”. Mathematische Annalen, Vol. 142, 1961, pp. 305–310.

    Article  MathSciNet  MATH  Google Scholar 

  5. Kazmi K.R., “Some Remarks on Vector Optimization Problems”. Jou. of Optimiz. Theory and Appls., Vol. 96, No. 1, 1998, pp. 133–138.

    Article  MathSciNet  MATH  Google Scholar 

  6. Mohan S.R., and Neogy S.K., “On Invex Sets and Preinvex Functions”. Jou. of Mathem. Analysis and Appls., Vol. 189, 1995, pp. 901–908.

    Article  MathSciNet  MATH  Google Scholar 

  7. Parida J., and Sen A., “A Variational-Like Inequality for Multifunctions with Applications”. Jou. of Mathem. Analysis and Appls., Vol. 124, 1987, pp. 73–81.

    Article  MathSciNet  MATH  Google Scholar 

  8. Tanaka T., “Generalised Quasiconvexities, Cone Saddle Points, and Minimax Theorem for Vector Valued Functions”. Jou. of Optimiz. Theory and Appls., Vol. 81, 1994, pp. 355–377.

    Article  MATH  Google Scholar 

  9. Weir T., and Jeyakumar V., “A Class of Nonconvex Functions and Mathematical Programming”. Jou. of Australian Mathem. Society, Vol. 38, 1988, pp. 177–189.

    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

Kazmi, K.R. (2000). Existence of Solutions for Vector Saddle-Point 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_15

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-0299-5_15

  • 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