Riemannian Optimization for Normal Matrix Completion

Determine whether the Riemannian manifold optimization techniques developed for the Normal Procrustes Problem can be modified to solve the Normal Matrix Completion Problem.

Background

The Normal Matrix Completion Problem prescribes selected entries or a pattern and seeks a completion that is normal. The paper notes that Guglielmi and Scalone’s method can accommodate this setting, whereas the proposed unitary-manifold formulation is developed for the Procrustes and closest-normal-matrix objectives. Extending the Riemannian framework to completion constraints is therefore left as an explicit unresolved methodological question.

References

Whether our Riemannian manifold optimization techniques could be modified to similarly work over this problem, we leave to future work.

— The Normal Procrustes Problem: A Riemannian Optimization Approach  (2608.19513 - Bierly, 20 Aug 2026) in Section 5.3, subsection “Comparison with Established Algorithms over the CNP”