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- Convex_function abstract "In mathematics, a real-valued function f (x) defined on an interval is called convex (or convex downward or concave upward) if the line segment between any two points on the graph of the function lies above the graph, in a Euclidean space (or more generally a vector space) of at least two dimensions. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. Well-known examples of convex functions are the quadratic function and the exponential function for any real number x.Convex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties. For instance, a (strictly) convex function on an open set has no more than one minimum. Even in infinite-dimensional spaces, under suitable additional hypotheses, convex functions continue to satisfy such properties and, as a result, they are the most well-understood functionals in the calculus of variations. In probability theory, a convex function applied to the expected value of a random variable is always less or equal to the expected value of the convex function of the random variable. This result, known as Jensen's inequality underlies many important inequalities (including, for instance, the arithmetic-geometric mean inequality and Hölder's inequality).Exponential growth is a special case of convexity. Exponential growth narrowly means "increasing at a rate proportional to the current value", while convex growth generally means "increasing at an increasing rate (but not necessarily proportionally to current value)".".
- Convex_function thumbnail ConvexFunction.svg?width=300.
- Convex_function wikiPageExternalLink cvxbook.
- Convex_function wikiPageID "245568".
- Convex_function wikiPageRevisionID "603056790".
- Convex_function hasPhotoCollection Convex_function.
- Convex_function id "p/c026230".
- Convex_function id "p/c026240".
- Convex_function title "Convex function".
- Convex_function subject Category:Convex_analysis.
- Convex_function subject Category:Generalized_convexity.
- Convex_function subject Category:Types_of_functions.
- Convex_function comment "In mathematics, a real-valued function f (x) defined on an interval is called convex (or convex downward or concave upward) if the line segment between any two points on the graph of the function lies above the graph, in a Euclidean space (or more generally a vector space) of at least two dimensions. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set.".
- Convex_function label "Convex function".
- Convex_function label "Convexe functie".
- Convex_function label "Fonction convexe".
- Convex_function label "Función convexa".
- Convex_function label "Funzione convessa".
- Convex_function label "Função convexa".
- Convex_function label "Konvexe und konkave Funktionen".
- Convex_function label "Wypukłość funkcji".
- Convex_function label "Выпуклая функция".
- Convex_function label "دالة محدبة".
- Convex_function label "凸函数".
- Convex_function label "凸関数".
- Convex_function sameAs Konvexe_und_konkave_Funktionen.
- Convex_function sameAs Función_convexa.
- Convex_function sameAs Fonction_convexe.
- Convex_function sameAs Funzione_convessa.
- Convex_function sameAs 凸関数.
- Convex_function sameAs 볼록함수.
- Convex_function sameAs Convexe_functie.
- Convex_function sameAs Wypukłość_funkcji.
- Convex_function sameAs Função_convexa.
- Convex_function sameAs m.01kjxx.
- Convex_function sameAs Q319913.
- Convex_function sameAs Q319913.
- Convex_function wasDerivedFrom Convex_function?oldid=603056790.
- Convex_function depiction ConvexFunction.svg.
- Convex_function isPrimaryTopicOf Convex_function.
