We propose a method that allows the computation of the continuous adjoint network system based on the discretized direct equations. This hybrid approach exploits the self-adjoint character of the duct element, which allows all jump conditions to be derived from the direct scattering matrix. We, thus, eliminate the need to derive the adjoint equations for every element of the network model. This methodology combines the advantages of the discrete and continuous adjoint, as the accuracy of the continuous adjoint is achieved whilst maintaining the flexibility of the discrete adjoint. We show how the obtained adjoint system may be utilized to optimize the thermoacoustic model by determining the optimal damper setting for an annular combustor.