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.
Acknowledgements
The author would like to thank the referees for careful reading of the paper and for very helpful comments and suggestions.
Notes
No potential conflict of interest was reported by the author.