proximum -- computes the proximum of the Polyhedron/Cone to a point in euclidian metric

Synopsis

• Usage:

  q = proximum(p,P)

  q = proximum(p,C)

• Inputs:
  • p, a matrix, over ZZ or QQ with only one column representing a point
  • P, a convex polyhedron
  • C, a convex rational cone
• Outputs:
  • q, a matrix, over QQ with only one column representing the closest point

Description

For a point p and a Polyhedron P or a Cone C, proximum computes the point in P or C with minimal euclidian distance to p.

i1 : P = crossPolytope 3

o1 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of polyhedron => 3
      number of facets => 8
      number of rays => 0
      number of vertices => 6

o1 : Polyhedron

i2 : p = matrix {{1},{2},{3}}

o2 = | 1 |
     | 2 |
     | 3 |

              3        1
o2 : Matrix ZZ  <--- ZZ

i3 : q = proximum(p,P)

o3 = | 0 |
     | 1 |
     | 0 |

              3        1
o3 : Matrix QQ  <--- QQ