Low-Complexity Iterative Methods for Complex-Variable Matrix Optimization Problems in Frobenius Norm

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.