Logarithmically concave function: Difference between revisions

Revision as of 00:13, 18 April 2019

Revision as of 00:19, 18 April 2019

Line 25:

* 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 and|authorlink=Stephen P. Boyd |first2=Lieven |last2=Vandenberghe, [http|chapter=Log-concave and log-convex functions |title=Convex Optimization |___location= |publisher=Cambridge University Press |year=2004 |isbn=0-521-83378-7 |url=https://wwwweb.stanford.edu/~boyd/cvxbook/ Convex Optimization]|pages=104–108 (PDF) Section 3.5}}</ref>

:i.e.