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...

narrowly to either a convex cone or projective cone. Cones can be generalized to higher dimensions. The perimeter of the base of a cone is called the directrix...

Dual cone and polar cone are closely related concepts in convex analysis, a branch of mathematics. The dual cone C* of a subset C in a linear space X...

invariant convex cone is a closed convex cone in a Lie algebra of a connected Lie group that is invariant under inner automorphisms. The study of such cones was...

convexity Convex cone Convex series Convex metric space Carathéodory's theorem (convex hull) Choquet theory Helly's theorem Holomorphically convex hull Integrally-convex...

convex program can be presented in a conic form, which means minimizing a linear objective over the intersection of an affine plane and a convex cone:: 5...

bundles are described by a convex cone, and the possible contractions of the variety correspond to certain faces of the nef cone. In view of the correspondence...

subsets, convex cones, and convex sets are generalizations of vector subspaces: a vector subspace is also an affine subspace, a convex cone, and a convex set...

A second-order cone program (SOCP) is a convex optimization problem of the form minimize   f T x   {\displaystyle \ f^{T}x\ } subject to ‖ A i x + b i...

tangent cone, including the adjacent cone, Bouligand's contingent cone, and the Clarke tangent cone. These three cones coincide for a convex set, but...

again a cone (resp. convex cone); the same is true of the union of an increasing (under set inclusion) family of cones (resp. convex cones). A cone C {\displaystyle...

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...

the convex cone of positive semi-definite matrices. This order is usually employed to generalize the definitions of monotone and concave/convex scalar...

cone is a kind of a convex cone that is particularly important in modeling convex optimization problems. It is a generalization of the quadratic cone:...

Thus we can take, for example, y1 = 1, y2 = −2. Consider the closed convex cone C ( A ) {\displaystyle C(\mathbf {A} )} spanned by the columns of A;...

semidefinite matrices forms a convex cone in Rn × n, and a spectrahedron is a shape that can be formed by intersecting this cone with an affine subspace. Spectrahedra...

then the closed cone of curves is the closure of the positive cone. Otherwise, the closed cone of curves is the closed convex cone spanned by all elements...

of convex optimization that studies problems consisting of minimizing a convex function over the intersection of an affine subspace and a convex cone. The...

hence they are members of the convex cone of nonnegative real numbers (whose nonzero members have reciprocals in this same cone). For several parameters,...

positive definite matrices is an open convex cone, while the set of positive semi-definite matrices is a closed convex cone. In the following definitions, x...

matrix if the space of covariance matrices is viewed as an extrinsic convex cone in Rp×p; however, measured using the intrinsic geometry of positive-definite...

Affine cone may refer to: Convex cone § Affine convex cones Cone (algebraic geometry) This disambiguation page lists articles associated with the title...

used to reduce affine geometry to linear algebra, and reduce convex bodies to convex cones. Explicitly, let S ⊂ R d {\displaystyle S\subset \mathbb {R}...

{\displaystyle \mathbb {Z} ^{n}} . A strongly convex rational polyhedral cone in N {\displaystyle N} is a convex cone (of the real vector space of N {\displaystyle...

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

define a convex cone, which contains all non-negative linear combinations of its vectors. Corresponding concept in an affine space is a convex set, which...

prism), and a polyhedral cone (infinite cone) defined by three or more half-spaces passing through a common point. A convex polytope may be defined in...

b+L is an affine plane), and K is a closed pointed convex cone with a nonempty interior. Every convex program can be converted to the conic form. To use...

allows color to be represented as a convex cone in the 3- D linear space, which is referred to as the color cone. Colors can be created in printing with...

on an (abstract) convex cone of nonempty compact convex sets. The mapping τ {\displaystyle \tau } is an isometry between this cone, endowed with the...