Logarithmically concave function: Difference between revisions

Revision as of 20:50, 15 November 2021

Revision as of 02:17, 24 August 2022

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Examples of log-concave functions are the 0-1 [[indicator function]]s of convex sets (which requires the more flexible definition), and the [[Gaussian function]].

Similarly, a function is '''[[log-convex]]''' if it satisfies the reverse inequality

: <math>

f(\theta x + (1 - \theta) y) \leq f(x)^{\theta} f(y)^{1 - \theta}