In this paper we study general complex eigenvalue problems in engineering fields. The eigenvalue problems can be transformed into the associated problems for solving large systems of nonlinear ordinary differential equations (dynamic equations) by optimization techniques. The known waveform relaxation method in circuit simulation can then be successfully applied to compute the resulting dynamic equations. The approach reported here, which is implemented on a message passing multi-processor system, can determine all eigenvalues and their eigenvectors for general complex matrices without any restriction on the matrices. The numerical results are provided to confirm the theoretical analysis.