Convergence of Quasi-Newton Method for Fully Complex-Valued Neural Networks

In this paper, based on Wirtinger calculus, we introduce a quasi-Newton method for training complex-valued neural networks with analytic activation functions. Using the duality between Wirtinger calculus and multivariate real calculus, we prove a convergence theorem of the proposed method for the minimization of real-valued complex functions. This lays the theoretical foundation for the complex quasi-Newton method and generalizes Powell’s well-known result for the real-valued case. The simulation results are given to show the effectiveness of the method.