Minimax IIR digital filter design using SOCP

An iterative second-order cone programming (SOCP) approach is proposed in this paper. The original nonconvex design problem is first relaxed into an SOCP problem, which can provide a lower bound on the optimal value of the original problem. For reducing the gap between the original and the convex problem, an iterative procedure is developed. The initial point of the iterative procedure can be chosen as the solution obtained from the relaxed SOCP problem. Unlike other iterative approaches, the convergence of the proposed iterative procedure is definitely guaranteed. Design examples demonstrate the effectiveness of the proposed method.