Solving for a quadratic programming with a quadratic constraint based on a neural network frame

Abstract

In many applications, a class of optimization problems called quadratic programming with a special quadratic constraint (QPQC) often occurs, such as in the fields of maximum entropy spectral estimation, FIR filter design with time–frequency constraint and design of an FIR filter bank with perfect reconstruction property. In order to deal with this kind of optimization problems and be inspired by the computational virtue of analog or dynamic neural networks, a feedback neural network is proposed for solving for this class of QPQC computation problems in real time in this paper. The stability, convergence and computational performance of the proposed neural network have also been analyzed and proved in detail so as to theoretically guarantee the computational effectiveness and capability of the network. From the theoretical analyses it turns out that the solution of a QPQC problem is just the generalized minimum eigenvector of the objective matrix with respect to the constrained matrix. A number of simulation experiments have been given to further support our theoretical analysis and illustrate the computational performance of the proposed network.