Semi-infinite optimization technique for the design of matrix filters

We propose the design of a matrix filter by a semi-infinite programming technique. The basic idea is to formulate the design problem into a semi-infinite optimization model where the mean square error between the desired response and the designed filter in the passband is minimized subject to a set of nonlinear functional inequalities. These inequality constraints are used to ensure that the stopband attenuation satisfies the prescribed performance specifications. Three design examples are given to show the feasibility of the proposed method.