Convex sets (ConvexSet)

ConvexSet{N} <: LazySet{N}

Abstract type for convex sets, i.e., sets characterized by a (possibly infinite) intersection of halfspaces, or equivalently, sets $S$ such that for any two elements $x, y ∈ S$ and $0 ≤ λ ≤ 1$ it holds that $λ·x + (1-λ)·y ∈ S$.

Notes

Every concrete ConvexSet must define the following function:

• σ(::AbstractVector, ::LazySet) – return a support vector in the given direction

σ(d::AbstractVector, X::LazySet)

Compute a support vector of a set in a given direction.

Input

• d – direction
• X – set

Output

A support vector of X in direction d.

Notes

The convenience alias support_vector is also available.