In convex geometry and vector algebra, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points...

one can define the related concepts of affine combination, conical combination, and convex combination, and the associated notions of sets closed under...

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...

this property characterizes convex sets. Such an affine combination is called a convex combination of u1, ..., ur. The convex hull of a subset S of a real...

non-empty convex compact set which does not contain the origin, then the convex conical hull of S is a closed set. Affine combination Convex combination Linear...

{\displaystyle P} . Equivalently, x {\displaystyle x} can be written as the convex combination of d + 1 {\displaystyle d+1} or fewer points in P {\displaystyle P}...

combinations of b→ with coefficients from the rows in A. Convex combination Conical combination Linear combination Affine space Affine geometry Affine hull Gallier...

A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n {\displaystyle n} -dimensional...

analysis and related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces...

the function value at any convex combination of elements in the domain is greater than or equal to that convex combination of those domain elements. Equivalently...

expressed using coefficients that sum to one. Such a linear combination is called a convex combination. Using the previous example, we would get the following...

combinations with positive coefficients. It follows that convex cones are convex sets. The definition of a convex cone makes sense in a vector space over any ordered...

is a state that can not be written as a probabilistic mixture, or convex combination, of other quantum states. There are several equivalent characterizations...

tight curves Combination – One edge of the blade is convexed, the opposite edge concaved, so the tool can be used on concaved and convexed surfaces. Spokeshaves...

can be defined as a set X {\displaystyle X} equipped with a binary convex combination operation c λ : X × X → X {\displaystyle c_{\lambda }:X\times X\rightarrow...

more precise by generalizing the notion of weighted average from a convex combination to an integral taken over the set E of extreme points. Here C is a...

the convex combination 0.5 x + 0.5 y = ( 4 , 4 ) {\displaystyle 0.5x+0.5y=(4,4)} is worse than both of them since its utility is 4. A set of convex-shaped...

probability density function if it exists) can be expressed as a convex combination (i.e. a weighted sum, with non-negative weights that sum to 1) of...

induction, a set Q is convex if and only if every convex combination of members of Q also belongs to Q. By definition, a convex combination of an indexed subset {v0...

problems in mathematical programming can be formulated as problems on convex sets or convex bodies. Six kinds of problems are particularly important:: Sec.2 ...

it. For any system, the state space is a convex set: Any mixed state can be written as a convex combination of pure states, though not in a unique way...

In mathematics, an extreme point of a convex set S {\displaystyle S} in a real or complex vector space is a point in S {\displaystyle S} that does not...

for constrained convex optimization. Also known as the conditional gradient method, reduced gradient algorithm and the convex combination algorithm, the...

algorithm) is an algorithm for decomposing a bistochastic matrix into a convex combination of permutation matrices. It was published by Garrett Birkhoff in 1946...

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...

_{1}P_{1}+\cdots +\theta _{k}P_{k}.} (Such a decomposition of X is known as a 'convex combination'.) A proof of the theorem based on Hall's marriage theorem is given...

of the option is given by a closed form formula and it is a linear convex combination of Black Scholes prices of call options with volatilities σ 1 , …...

Equivalently, a line segment is the convex hull of two points. Thus, the line segment can be expressed as a convex combination of the segment's two end points...

background color, thereby producing a new blended color. This is a convex combination of two colors allowing for transparency effects in computer graphics...

d-dimensional polytope, then every point in P can be written as a convex combination of at most d+1 affinely-independent vertices of P. The theorem can...