Skip to main content

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 319))

Abstract

In mathematical programming duality means that corresponding to every optimization (say minimization) problem, one relates a maximization problem in such a manner that by solving the latter problem it is possible to get the optimal value of the first one. To see the crucial ideas of this method let us consider a linear mathematical programming problem, denoted by (LP):

$$ \begin{gathered} \min {\kern 1pt} {\kern 1pt} cx \hfill \\ s.t.{\kern 1pt} x \in {R^{n}},{\kern 1pt} Ax \geqslant b \hfill \\ \end{gathered} $$

, where cRn, bRm and A is an (n × m)-matrix.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

eBook
USD 9.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Luc, D.T. (1989). Duality. In: Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Systems, vol 319. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-50280-4_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-50280-4_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50541-9

  • Online ISBN: 978-3-642-50280-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics