In geometry, an orthant or hyperoctant is the analogue in n-dimensional Euclidean space of a quadrant in the plane or an octant in three dimensions. In...

and the one-dimensional ray. The generalization of an octant is called orthant or hyperoctant. A convention for naming an octant is to give its list of...

positive in quadrant IV. There are several variants of this mnemonic. Orthant Octant (solid geometry) Ray (geometry) Wikimedia Commons has media related...

variables only to get higher accuracy, and then repeating the process. Orthant-wise limited-memory quasi-Newton (OWL-QN) is an L-BFGS variant for fitting...

{\displaystyle P\hookrightarrow (\mathbf {R} _{\geq 0})^{f}} into the standard f-orthant, where f {\displaystyle f} is the number of constraints (facets of the...

finite sequences summing to 1), a cone is an algebra over the universal orthant (of finite sequences of nonnegative numbers), and a convex set is an algebra...

combination a i ≥ 0 {\displaystyle a_{i}\geq 0} Convex cone Quadrant, octant, or orthant Convex combination a i ≥ 0 {\displaystyle a_{i}\geq 0} and ∑ a i = 1 {\textstyle...

6-space as permutations of (0,1,1,1,1,2). This represents the positive orthant facet of the stericated 6-orthoplex. A second construction in 6-space,...

of the quadrant and octant to an arbitrary number of dimensions is the orthant, and a similar naming system applies. The Euclidean distance between two...

180 permutations of: (0,0,1,1,2,3) This construction exists as one of 64 orthant facets of the runcitruncated 6-orthoplex. Runcicantellated hexateron Biruncitruncated...

number of queueing nodes, with the diffusion restricted to the non-negative orthant. Fluid models are continuous deterministic analogs of queueing networks...

permutations of (0,0,0,1,1,2) or of (0,1,1,2,2,2). These represent positive orthant facets of the cantellated hexacross and bicantellated hexeract respectively...

{\displaystyle P\hookrightarrow (\mathbf {R} _{\geq 0})^{f}} into the f-orthant, where f is the number of faces (dual to the vertices). This map is one-to-one...

indexed by their highest weights. These weights are the lattice points in an orthant Q+ in the weight lattice of the Lie group consisting of the dominant integral...

f(x)} is smallest. Examples of C {\displaystyle C} include the positive orthant R + n = { x ∈ R n : x ≥ 0 } {\displaystyle \mathbb {R} _{+}^{n}=\left\{x\in...

program in standard form in the special case in which K is the nonnegative orthant of Rn. It is possible to convert a convex program in standard form, to...

always non-negative. A Metzler matrix has an eigenvector in the nonnegative orthant because of the corresponding property for nonnegative matrices. Perron–Frobenius...

understood to simply be the Euclidean metric restricted to a positive orthant (e.g. "quadrant" in R 2 {\displaystyle R^{2}} ) of a unit sphere, after...

vertex may be put into the standard form of the vertex of the positive orthant by the action of GL ⁡ ( n , Z ) {\displaystyle \operatorname {GL} (n,\mathbb...

multivariate stochastic orders exist. For instance the upper and lower orthant order which are similar to the usual one-dimensional stochastic order....

→ {\displaystyle {\vec {q}}} represent a discrete vector in the first orthant from the center structuring element to a point on the boundary of M N n...

consumption space is some set X {\displaystyle X} , usually the positive orthant of some vector space so that each x ∈ X {\displaystyle x\in X} represents...

with spherical base in Rn is equal to its internal dual. The nonnegative orthant of Rn and the space of all positive semidefinite matrices are self-dual...

original Farkas' lemma, S {\displaystyle \mathbf {S} } is the nonnegative orthant R + n , {\displaystyle \mathbb {R} _{+}^{n},} hence the closedness condition...

diagram. The two lines defining the center of the cycle divide the positive orthant into four regions. The figure below indicates with arrows the movement...

^{d}} and R + d {\displaystyle \mathbb {R} _{+}^{d}} is the non-negative orthant of R d {\displaystyle \mathbb {R} ^{d}} . Thus the minimizer of this vector...

then the signomial becomes a polynomial whose domain is the positive orthant. For example, f ( x 1 , x 2 , x 3 ) = 2.7 x 1 2 x 2 − 1 / 3 x 3 0.7 − 2...

scalarization. If the parameters/weights are drawn uniformly in the positive orthant, it is shown that this scalarization provably converges to the Pareto front...

… , a n ) {\displaystyle (a_{1},a_{2},\dots ,a_{n})} forms a positive orthant with its apex at the given tuple. With this notation, Dickson's lemma may...

permutations of (0,0,0,1,2,2) or of (0,0,1,2,2,2). These represent positive orthant facets of the bitruncated 6-orthoplex, and the tritruncated 6-cube respectively...