objectiveVector -- computes an objective vector of a face of a polyhedron

Synopsis

Usage:

v = objectiveVector(P,Q)
Inputs:
- P, a convex polyhedron
- Q, a convex polyhedron, which must be a face of P
Outputs:
- v, a matrix, one column vector over QQ representing a vector

Description

An objective vector v of a face Q of a polyhedron P is vector such that Q = {p in P | v*p = max over P} i.e. it is the face on which v attains its maximum.

i1 : P = hypercube 3

o1 = P

o1 : Polyhedron

i2 : Q = convexHull matrix {{1,1,-1,-1},{1,-1,1,-1},{1,1,1,1}}

o2 = Q

o2 : Polyhedron

i3 : v = objectiveVector(P,Q)

o3 = | 0 |
     | 0 |
     | 1 |

              3       1
o3 : Matrix QQ  <-- QQ

Since it is the face on which v attains its maximum it can be recovered with maxFace:

i4 : Q == maxFace(v,P)

o4 = true

Ways to use objectiveVector :

objectiveVector(Polyhedron,Polyhedron)

For the programmer

The object objectiveVector is a method function.