Logarithmically concave function

Logarithmically concave function

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

Examples of log-concave functions are the indicator functions of convex sets.

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

See also

*Convex function
*Logarithmically concave measure


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