Logarithmically concave function
- Logarithmically concave function
A function is logarithmically concave (or log-concave for short), if its natural logarithm , is concave. Note that we allow here concave functions to take value . Every concave function is log-concave, however the reverse does not necessarily hold (e.g., ).
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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