Skip to main content

Convexity

  • Chapter
  • First Online:
Optimization

Part of the book series: Springer Texts in Statistics ((STS,volume 95))

  • 12k Accesses

Abstract

Convexity is one of the cornerstones of mathematical analysis and has interesting consequences for optimization theory, statistical estimation, inequalities, and applied probability. Despite this fact, students seldom see convexity presented in a coherent fashion. It always seems to take a backseat to more pressing topics. The current chapter is intended as a partial remedy to this pedagogical gap.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
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

Institutional subscriptions

References

  1. Feller W (1971) An introduction to probability theory and its applications, vol 2, 2nd edn. Wiley, Hoboken

    Google Scholar 

  2. Franklin J (1983) Mathematical methods of economics. Am Math Mon 90:229–244

    Article  MathSciNet  MATH  Google Scholar 

  3. Hochstadt H (1986) The functions of mathematical physics. Dover, New York

    MATH  Google Scholar 

  4. Horn RA, Johnson CR (1985) Matrix analysis. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  5. Keener JP (1993) The Perron-Frobenius theorem and the ranking of football teams. SIAM Rev 35:80–93

    Article  MathSciNet  MATH  Google Scholar 

  6. Lax PD (2007) Linear algebra and its applications, 2nd edn. Wiley, Hoboken

    MATH  Google Scholar 

  7. Nedelman J, Wallenuis T (1986) Bernoulli trials, Poisson trials, surprising variances, and Jensen’s inequality. Am Stat 40:286–289

    Google Scholar 

  8. Seneta E (1973) Non-negative matrices: an introduction to theory and applications. Wiley, Hoboken

    MATH  Google Scholar 

  9. Steele JM (2004) The Cauchy-Schwarz master class: an introduction to the art of inequalities. Cambridge University Press and the Mathematical Association of America, Cambridge

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Lange, K. (2013). Convexity. In: Optimization. Springer Texts in Statistics, vol 95. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5838-8_6

Download citation

Publish with us

Policies and ethics