The Lorentz cone, also called second order cone or ice-cream cone, is the set C_n of vectors in IRⁿ such that the Euclidian norm of the n-1 first components is less than or equal to the n^th component:

 C_n = {  [u^T v]^T  s.t.  u є IR^n-1 ,  v є IR   and   ||u||≤v }

This cone arises in the conic constraints of Second Order Cone Programs (SOCP).