Logarithmically concave function: Difference between revisions

Revision as of 19:23, 21 February 2011

Revision as of 08:37, 22 February 2011

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{{Unreferenced|date=December 2009}}

In [[mathematics]], a function {{nowrap|''f'' : '''R'''^''n'' → '''R'''⁺}} is '''logarithmically concave''' (or '''log-concave''' for short), if its [[natural logarithm]] {{nowrap|ln ''f''(''x'')}}, is [[concave function|concave]]. This means that it must befulfill the inequality (compare definition of [[concave function]]):

: <math>

f(\theta x + (1 - \theta) y) \geq f(x)^{\theta} f(y)^{1 - \theta} \qquad \theta \in [0, 1]

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{{DEFAULTSORT:Logarithmically Concave Function}}

[[Category:Mathematical analysis]]

[[Category:Convex analysis]]

[[eo:Logaritme konkava funkcio]]