Matching with matrix norm minimization

Given (r1,r2,...rn) ∈ Rn, for any I=(I1,I2,...In) ∈ Zn, let EI=(eij), where eij=(ri−rj)−(Ii−Ii), find I ∈ Zn such that ∥EI∥ is minimized, where ∥·∥ is a matrix norm. This is a matching problem where, given a real-valued pattern, the goal is to find the best discrete pattern that matches the real-valued pattern. The criterion of the matching is based on the matrix norm minimization instead of simple pairwise distance minimization. This matching …