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...

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...

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...

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...

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

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...

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

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...

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

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...

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

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

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

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...

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)...

Strictly convex may refer to: Strictly convex function, a function having the line between any two points above its graph Strictly convex polygon, a polygon...

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...

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

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...

Convex function, when the line segment between any two points on the graph of the function lies above or on the graph Convex conjugate, of a function...

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...

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

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...

relation is convex, but not strictly-convex. 3. A preference relation represented by linear utility functions is convex, but not strictly convex. Whenever...

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...

Rastrigin function of two variables In mathematical optimization, the Rastrigin function is a non-convex function used as a performance test problem for...