Comparison of optimization techniques for coupling matrix synthesis using eigenvalue based approach

This paper presents a comparison of the optimization techniques used for coupling matrix synthesis problem involving cost function constructed from eigenvalues of coupling matrix as well as eigenvalues of principal sub-matrices. Minimization of cost function is performed via three different optimization techniques: linear least-square problem (LL-S), Nelder - Mead (N-M) and quasi - Newton (q-N). The efficiency of linear least-squares method for various starting points is tested. Convergence of the optimization routines are improved through analytically obtained derivatives and trust region (TR) which limits the search area at each iteration step. Examples of the synthesis of cross-coupled filters with symmetric and asymmetric responses are presented.