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* A twice differentiable, nonnegative function with a convex ___domain is log-concave if and only if for all {{math|''x''}} satisfying {{math|''f''(''x'') > 0}},
::<math>f(x)\nabla^2f(x) \preceq \nabla f(x)\nabla f(x)^T</math>,<ref name=":0">{{cite book |first=Stephen |last=Boyd |authorlink=Stephen P. Boyd |first2=Lieven |last2=Vandenberghe |chapter=Log-concave and log-convex functions |title=Convex Optimization |___location= |publisher=Cambridge University Press |year=2004 |isbn=0-521-83378-7 |chapter-url=https://web.stanford.edu/~boyd/cvxbook/ |pages=104–108 }}</ref>
:i.e.
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==References==
* {{cite book|authorlink=Ole Barndorff-Nielsen|last=Barndorff-Nielsen|first=Ole|title=Information and exponential families in statistical theory|series=Wiley Series in Probability and Mathematical Statistics|publisher=John Wiley \& Sons, Ltd.|___location=Chichester|year=1978|pages=ix+238 pp
* {{cite book|title=Unimodality, convexity, and applications
|last1=Dharmadhikari|first1=Sudhakar
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|publisher=Academic Press, Inc.
|___location=Boston, MA
|year=1992|pages=xiv+467 pp
|isbn=0-12-549250-2
|mr=1162312}}
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