Warmstarting strategies for convex optimization based multi-channel constrained active noise control filter design

In real-world applications of active noise control (ANC) systems, various constraints are supposed to be satisfied in the controller design process. The optimal control filter coefficients can be obtained by solving a constrained optimization problem, which usually requires a significant computational effort. Recently, a convex formulation in conic form was proposed for ANC filter design. The proposed formulation was shown to result in a computational time reduction by several orders of magnitude. It is of great interest to further improve its efficiency by using a priori information of the optimal filter coefficients. One potential way of achieving this goal is to introduce a warmstart technique so that the filter solution of a similar system or environment can be referred to for selecting the starting point of the optimization algorithm. However, the conic formulation should be solved by the interior-point method, which, in general, is challenging for applying warmstart techniques. In the current work, relaxation methods are proposed to the constraints of original ANC filter design formulation so that the warmstart techniques can be applied. Then, a warmstarting technique proposed in previous study is used to solve a series of perturbed problems, and the performance of the warmstarting technique is investigated. Results show that with the proposed modifications applied, the warmstarting strategy can significantly reduce the number of iterations needed for solving the conic formulation of the ANC filter design problem without much tuning efforts, and the method is effective and robust in various environmental setups.