Improved minimax optimisation algorithms and their application in the design of recursive digital filters

A technique that can improve the performance of available optimisation algorithms, in applications where the objective function involves the sampling of a function with respect to an independent variable, is proposed. The technique is then applied in conjunction with two well known minimax algorithms for the design of recursive digital filters. Extensive experimental results show that the new technique reduces the approximation errors significantly and eliminates the problem of spikes in the error function. Although the amount of computation needed to carry out a design for a fixed density of grid points is increased somewhat, improved robustness is achieved, which allows a reduced density of grid points and eliminates waste of computational effort in unsuccessful designs