findInteriorPoint: Find an interior point

In hitandrun: "Hit and Run" and "Shake and Bake" for Sampling Uniformly from Convex Shapes

Find an interior point

Description

Find an interior point of a polytope given by a set of linear constraints along each dimension.

Usage

findInteriorPoint(constr, homogeneous=FALSE, randomize=FALSE)

Arguments

constr	Constraint definition
homogeneous	Whether constr is given in homogeneous coordinate representation
randomize	Whether the point should be randomized

Details

See har for a description of the constraint definition and the homogeneous coordinate representation.

Solves a slack-maximizing LP to find an interior point of the polytope defined by the given constraints. The randomized version randomly scales the slack on each (non-redundant) constraint.

Value

A vector.

Author(s)

Gert van Valkenhoef

See Also

har

findExtremePoints findVertices

lpcdd

Examples

# constraints: x_1 >= 0, x_2 >= 0, x_1 + x_2 <= 1
A <- rbind(c(-1, 0), c(0, -1), c(1, 1))
b <- c(0, 0, 1)
d <- c("<=", "<=", "<=")
constr <- list(constr=A, rhs=b, dir=d)

findInteriorPoint(constr, homogeneous=FALSE)

hitandrun documentation built on May 28, 2022, 1:09 a.m.