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Clarified examples, added Properties section, added twice differentiable property, fixed integration statement (integration only preserves log-concavity in special cases) |
→Properties: add simplified twice differentiable condition |
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* A twice differentiable function with convex ___domain is log-concave if and only if for all <math>x\in\operatorname{dom} f</math>
:<math>f(x)\nabla^2f(x) \preceq \nabla f(x)\nabla f(x)^T</math> <ref> Stephen Boyd and Lieven Vandenberghe, [http://www.stanford.edu/~boyd/cvxbook/ Convex Optimization] (PDF) p.105</ref>
If <math>f:\mathbb{R}\to\mathbb{R}</math>, this condition simplifies to
:<math>f(x)f''(x) \leq (f'(x))^2</math>
==Operations preserving the log-concavity==
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