Halfspace given by a normal and an offset — halfspace

The unbounded case: \(\{\theta : a^\top \theta \le b\}\) (H-representation). The plurality region \(\{\theta : \theta_1 \le \theta_j\}\) is normal = e_1 - e_j, offset = 0.

Usage

halfspace_region(normal, offset = 0)

Arguments

normal: Normal vector a; must be non-zero.
offset: Offset b.

Value

A halfspace_region.

Details

Coordinates are (z, c): z positions a point on the bounding hyperplane in an orthonormal basis, and c >= 0 is the distance inward.

A halfspace cannot yet be certified; see polytope_region() for the bounded alternative.

Examples

# `{theta : theta_1 <= theta_2}`
halfspace_region(normal = c(1, -1), offset = 0)
#> <halfspace_region>
#>   the halfspace normal . theta <= 0, normal (1, -1), unbounded
#>   facets: 1 inequality