VectorGreaterEqual

yields True for vectors of length n if x_i≥y_i for all components .

x_κy or VectorGreaterEqual[{x,y},κ]

yields True for x and y if x-y∈κ, where κ is a proper convex cone.

Details

VectorGreaterEqual gives a partial ordering of elements in a vector space that is still compatible with vector space operations.
VectorGreaterEqual is typically used to specify vector inequalities for constrained optimization, inequality solving and integration.
By using the character , entered as v>= or \[VectorGreaterEqual], with subscripts vector inequalities can be entered as follows:
VectorGreaterEqual[{x,y}] the standard vector inequality

VectorGreaterEqual[{x,y},κ] vector inequality defined by a cone κ
xy remains unevaluated if x or y has a non-numeric element; typically gives True or False otherwise.
When x and y are n-vectors, xy yields False if x_i>y_i for any component .
When x is an n-vector and y is a scalar, xy yields True if x_i≥y for all components .
Possible cone specifications κ in for vectors x include:

Possible cone specifications κ in for matrices x include:
"NonNegativeCone" such that

{"SemidefiniteCone", n} symmetric positive semidefinite matrices
Possible cone specifications κ in for arrays x include:
"NonNegativeCone" such that
For exact numeric quantities, VectorGreaterEqual internally uses numerical approximations to establish numerical ordering. This process can be affected by the setting of the global variable $MaxExtraPrecision.