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

## Synopsis

• Usage:
q = proximum(p,P)
q = proximum(p,C)
• Inputs:
• p, , over ZZ or QQ with only one column representing a point
• Outputs:
• q, , 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 euclidean distance to p.

 i1 : P = crossPolytope 3 o1 = P 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 | | 0 | | 1 | 3 1 o3 : Matrix QQ <--- QQ

## Ways to use proximum :

• "proximum(Matrix,Cone)"
• "proximum(Matrix,Polyhedron)"

## For the programmer

The object proximum is .