concave function
1Concave function — In mathematics, a concave function is the negative of a convex function. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap or upper convex. Contents 1 Definition 2 Properties 3 Examples …
2Logarithmically concave function — A function f : R^n o R^+ is logarithmically concave (or log concave for short), if its natural logarithm ln(f(x)), is concave. Note that we allow here concave functions to take value infty. Every concave function is log concave, however the… …
3Concave — A concave set. The word concave means curving in or hollowed inward, as opposed to convex. The former may be used in reference to: Concave lens, a lens with inward curving (concave) surfaces. Concave polygon, a polygon which is not convex.… …
4Concave set — In mathematics, the notion of a concave set is not correct.[citation needed] A set that is not convex, is a non convex set. See also Convex set Concave function References Categories: Convex geometry …
5Convex function — on an interval. A function (in black) is convex if and only i …
6Schur-convex function — In mathematics, a Schur convex function, also known as S convex, isotonic function and order preserving function is a function f: mathbb{R}^d ightarrow mathbb{R}, for which if forall x,yin mathbb{R}^d where x is majorized by y, then f(x)le f(y).… …
7Logarithmically concave measure — In mathematics, A Borel measure mu; on n dimensional Euclidean space R n is called logarithmically concave (or log concave for short) if, for any compact subsets A and B of R n and 0 lt; lambda; lt; 1, one has: mu(lambda A + (1 lambda) B) geq… …
8Log-concave — may refer to:* Logarithmically concave function * Logarithmically concave measure …
9Quasiconvex function — In mathematics, a quasiconvex function is a real valued function defined on an interval or on a convex subset of a real vector space such that the inverse image of any set of the form ( infty,a) is a convex set. Definition and… …
10Unimodal function — In mathematics, a function f ( x ) between two ordered sets is unimodal if for some value m (the mode), it is monotonically increasing for x ≤ m and monotonically decreasing for x ≥ m . In that case, the maximum value of f ( x ) is f ( m ) and… …
