Logarithmically concave function: Difference between revisions

Revision as of 00:09, 5 May 2007

Revision as of 02:00, 14 April 2009

Line 1:

A function <math>f : \R^n \to \R^+</math> is '''logarithmically concave''' (or '''log-concave''' for short), if its [[natural logarithm]] <math>\ln(f(x))</math>, is [[concave function|concave]]. Note that we allow here concave functions to take value <math>-\infty</math>. Every concave function is log-concave, however the reverse does not necessarily hold (e.g., <math>\exp\e^{-x^2\}</math>).

Examples of log-concave functions are the [[indicator function|indicator functions]] of convex sets.