  Complex-variable matrix optimization problems (CMOPs) in Frobenius norm
emerge in many areas of applied mathematics and engineering applications. In
this letter, we focus on solving CMOPs by iterative methods. For unconstrained
CMOPs, we prove that the gradient descent (GD) method is feasible in the
complex domain. Further, in view of reducing the computation complexity,
constrained CMOPs are solved by a projection gradient descent (PGD) method. The
theoretical analysis shows that the PGD method maintains a good convergence in
the complex domain. Experiment results well support the theoretical analysis.
