be convex, or even look like a cone in Euclidean space. When the scalars are real numbers, or belong to an ordered field, one generally calls a cone a...

a pyramid. Depending on the context, "cone" may also mean specifically a convex cone or a projective cone. Cones can also be generalized to higher dimensions...

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...

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

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...

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...

a set of points is convex if it contains every line segment between two points in the set. Equivalently, a convex set or a convex region is a set that...

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...

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

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...

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...

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;...

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...

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...

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

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

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...

In mathematics, especially convex analysis, the recession cone of a set A {\displaystyle A} is a cone containing all vectors such that A {\displaystyle...

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

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...

functional and convex analysis, and related disciplines of mathematics, the polar set A ∘ {\displaystyle A^{\circ }} is a special convex set associated...

positive definite matrices is an open convex cone, while the set of positive semi-definite matrices is a closed convex cone. Some authors use more general definitions...

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:...

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

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...

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...

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

interest to markets with transaction costs. Specifically, it is the convex cone of portfolios that can be exchanged to portfolios of non-negative components...

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