Logarithmically convex function information

In mathematics, a function f is logarithmically convex or superconvex if log ∘ f {\displaystyle {\log }\circ f} , the composition of the logarithm with...

In convex analysis, a non-negative function f : Rn → R+ is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it...

Karamata's inequality Logarithmically convex function Pseudoconvex function Quasiconvex function Subderivative of a convex function "Lecture Notes 2" (PDF)...

positive and logarithmically convex for positive z and whose value at 1 is 1 (a function is logarithmically convex if its logarithm is convex). Another characterisation...

of a quasiconvex function that is neither convex nor continuous. Convex function Concave function Logarithmically concave function Pseudoconvexity in...

properties of field of study of several complex variables, such as Logarithmically-convex, Hartogs's extension theorem, etc. , were given in the Reinhardt...

a concave function is one for which the value at any convex combination of elements in the domain is greater than or equal to the convex combination...

In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined...

asymptotes as x → ± ∞ {\displaystyle x\rightarrow \pm \infty } . A sigmoid function is convex for values less than a particular point, and it is concave for values...

measures is log-concave. Convex measure, a generalisation of this concept Logarithmically concave function Prékopa, A. (1980). "Logarithmic concave measures and...

completely monotonic function, logarithmically completely monotonic function, strongly logarithmically completely monotonic function, strongly completely...

power series is not necessarily an open ball; these regions are logarithmically-convex Reinhardt domains, the simplest example of which is a polydisk....

of barrier functions are inverse barrier functions and logarithmic barrier functions. Resumption of interest in logarithmic barrier functions was motivated...

and a convex class F {\displaystyle {\mathcal {F}}} of probability measures on ( Ω , A ) {\displaystyle (\Omega ,{\mathcal {A}})} . A function defined...

this formula internally. LSE is convex but not strictly convex. We can define a strictly convex log-sum-exp type function by adding an extra argument set...

} Thus, a measure being 0-convex is the same thing as it being a logarithmically concave measure. The classes of s-convex measures form a nested increasing...

) {\displaystyle \ln \Gamma (x)} is strictly convex. For m = 0 {\displaystyle m=0} , the digamma function, ψ ( x ) = ψ ( 0 ) ( x ) {\displaystyle \psi...

_{i}(\mathbf {x} ,\mathbf {y} ))} is the partition function. This density is a logarithmically convex function, and thus the common inference task in PSL of...

function of the shape parameters α and β. § Moments of logarithmically transformed random variables contains formulas for moments of logarithmically transformed...

functions that satisfy these conditions, but the gamma function is the unique one that is meromorphic in the whole complex plane, and logarithmically...

the term bidisc is sometimes used. A polydisc is an example of logarithmically convex Reinhardt domain. Poincare, H, Les fonctions analytiques de deux...

caveat: many terms in Riemannian and metric geometry, such as convex function, convex set and others, do not have exactly the same meaning as in general...