A new nonlinear optimization algorithm is presented for designing lowpass asymmetric FIR digital filters. The new algorithm is based on the iterative use of the generalized multiple exchange (GME) algorithm. The new algorithm can design optimal filters that simultaneously meet specifications on the group delay and the magnitude of the frequency response. The algorithm is based on nonlinear optimization because the frequency response magnitude and group delay are nonlinear functions of the filter coefficients. This ISCAS-94 paper includes a filter design example with specifications on the maximum permissible errors in the group delay and the frequency response magnitude. In spite of the nonlinearities in this design problem, the new algorithm determines a unique optimal solution. A mathematical proof of optimality is included. >