volesti (version 1.1.2-9)

Spectrahedron-class: An R class to represent a Spectrahedron

Description

A spectrahedron is a convex body defined by a linear matrix inequality of the form \(A_0 + x_1 A_1 + ... + x_n A_n \preceq 0\). The matrices \(A_i\) are symmetric \(m \times m\) real matrices and \(\preceq 0\) denoted negative semidefiniteness.

Details

matrices

A List that contains the matrices \(A_0, A_1, ..., A_n\).

Examples

A0 = matrix(c(-1,0,0,0,-2,1,0,1,-2), nrow=3, ncol=3, byrow = TRUE)
A1 = matrix(c(-1,0,0,0,0,1,0,1,0), nrow=3, ncol=3, byrow = TRUE)
A2 = matrix(c(0,0,-1,0,0,0,-1,0,0), nrow=3, ncol=3, byrow = TRUE)
lmi = list(A0, A1, A2)
S = Spectrahedron(matrices = lmi);