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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Feller W (1971) An introduction to probability theory and its applications, vol 2, 2nd edn. Wiley, Hoboken
Franklin J (1983) Mathematical methods of economics. Am Math Mon 90:229–244
Hochstadt H (1986) The functions of mathematical physics. Dover, New York
Horn RA, Johnson CR (1985) Matrix analysis. Cambridge University Press, Cambridge
Keener JP (1993) The Perron-Frobenius theorem and the ranking of football teams. SIAM Rev 35:80–93
Lax PD (2007) Linear algebra and its applications, 2nd edn. Wiley, Hoboken
Nedelman J, Wallenuis T (1986) Bernoulli trials, Poisson trials, surprising variances, and Jensen’s inequality. Am Stat 40:286–289
Seneta E (1973) Non-negative matrices: an introduction to theory and applications. Wiley, Hoboken
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
Author information
Authors and Affiliations
Rights 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
DOI: https://doi.org/10.1007/978-1-4614-5838-8_6
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-5837-1
Online ISBN: 978-1-4614-5838-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)