On certain optimization problems related to matrix norms. (2nd October 2016) - Wei, Ning
Abstract : In this paper, first, we show that the following optimization problem always has an optimal solution which does not depend on the matrix norm, and give a sufficient condition for the uniqueness of optimal solutions: (Section.Display) where is any unitarily invariant norm, , and or . Then, we characterize the optimal solutions and also give sufficient conditions for the uniqueness and the rank-one property of optimal solutions for the following optimization problem: (Section.Display) where, is the inner product of matrices;, , , and 's, are different arbitrary norms.