mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph...

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

particular the subfields of convex analysis and optimization, a proper convex function is an extended real-valued convex function with a non-empty domain...

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...

the function f {\displaystyle f} is closed. This definition is valid for any function, but most used for convex functions. A proper convex function is...

functional on X . {\displaystyle X.} A function p : X → R {\displaystyle p:X\to \mathbb {R} } which is subadditive, convex, and satisfies p ( 0 ) ≤ 0 {\displaystyle...

the function) is a convex set. Convex minimization is a subfield of optimization that studies the problem of minimizing convex functions over convex sets...

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

In mathematics, a Schur-convex function, also known as S-convex, isotonic function and order-preserving function is a function f : R d → R {\displaystyle...

piecewise-differentiable functions, PDIFF. Important sub-classes of piecewise linear functions include the continuous piecewise linear functions and the convex piecewise...

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently...

Convex analysis is the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex...

optimization, the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex functions. It is also known...

manageable condition than a holomorphically convex. The subharmonic function looks like a kind of convex function, so it was named by Levi as a pseudoconvex...

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...

Examples of convex curves include the convex polygons, the boundaries of convex sets, and the graphs of convex functions. Important subclasses of convex curves...

mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906, building...

In the field of mathematics known as convex analysis, the characteristic function of a set is a convex function that indicates the membership (or non-membership)...

In convex analysis and the calculus of variations, both branches of mathematics, a pseudoconvex function is a function that behaves like a convex function...

In mathematics, the support function hA of a non-empty closed convex set A in R n {\displaystyle \mathbb {R} ^{n}} describes the (signed) distances of...

that point. Subderivatives arise in convex analysis, the study of convex functions, often in connection to convex optimization. Let f : I → R {\displaystyle...

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...

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept...

Generally, unless the objective function is convex in a minimization problem, there may be several local minima. In a convex problem, if there is a local...

Intuitively, subharmonic functions are related to convex functions of one variable as follows. If the graph of a convex function and a line intersect at...

K-convex functions, first introduced by Scarf, are a special weakening of the concept of convex function which is crucial in the proof of the optimality...

transformation on real-valued functions that are convex on a real variable. Specifically, if a real-valued multivariable function is convex on one of its independent...

y)=-(\cos(x^{2})+\cos(y^{2}))^{2}.} Asymptote Chart Plot Concave function Convex function Contour plot Critical point Derivative Epigraph Normal to a graph...

Invex functions were introduced by Hanson as a generalization of convex functions. Ben-Israel and Mond provided a simple proof that a function is invex...

compact and convex, and to functions that are concave in their first argument and convex in their second argument (known as concave-convex functions). Formally...