Logarithmically concave function: Difference between revisions

Revision as of 15:16, 26 January 2007

Revision as of 15:17, 26 January 2007

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A function <math>f : \mathcal{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]]. Every concave function is log-concave, however the reverse does not necessarily hold (e.g., <math>\exp\{-x^2\}</math>).

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

In parallel, a function is '''[[log-convex]]''' if its natural log is convex.