On the Minimum Rank of a Generalized Matrix Approximation Problem in the Maximum Singular Value Norm

Kin Sou, Anders Rantzer
In this paper theoretical results regarding a generalized minimum rank matrix approximation problem in the maximum singular value norm are presented. Using the idea of projection, the considered problem can be shown to be equivalent to a classical minimum rank matrix approximation which can be solved efficiently using singular value decomposition. In addition, as long as the generalized problem is feasible, it is shown to have exactly the same optimal objective value as that of the classical
more » ... of the classical problem. Certain comments and extensions of the presented theorem are included in the end of the paper.