A new hybrid descent method with application to the optimal design of finite precision FIR filters

Abstract

In this paper, the problem of the optimal design of discrete coefficient FIR filters is considered. A novel hybrid descent method, consisting of a simulated annealing algorithm and a gradient-based method, is proposed. The simulated annealing algorithm operates on the space of orthogonal matrices and is used to locate descent points for previously converged local minima. The gradient-based method is derived from converting the discrete problem to a continuous problem via the Stiefel manifold, where convergence can be guaranteed. To demonstrate the effectiveness of the proposed hybrid descent method, several numerical examples show that better discrete filter designs can be sought via this hybrid descent method.

Differential optimization in finite-dimensional spaces

“…a unified gradient flow approach to nonlinear constrained optimization problems was presented in [24]. A novel hybrid descent method, consisting of a simulated annealing algorithm and a gradient-based method, was proposed to consider the optimal design of finite precision FIR filters in [26]. Gradient descent methods can be applied to solve integer programming problems in [6].…”