* Corresponding author. Tel.: #86-551-3601340; fax: #86-551-3631-1760. E-mail address: ytan@ustc.edu.cn (Y. Tan) Neurocomputing 30 (2000) 117}128 Solving for a quadratic programming with a quadratic constraint based on a neural network frame Ying Tan*, Chao Deng Department of Electronic Engineering and Information Science, University of Science and Technology of China, P.O. Box 4, Hefei 230027, China Received 2 June 1997; accepted 22 March 1999 Abstract In many applications, a class of optimization problems called quadratic programming with a special quadratic constraint (QPQC) often occurs, such as in the "elds of maximum entropy spectral estimation, FIR "lter design with time}frequency constraint and design of an FIR "lter 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 e!ectiveness 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.  2000 Elsevier Science B.V. All rights reserved. Keywords: Arti"cial neural network; Quadratic programming; Generalized eigen-decomposi- tion; QPQC; Analog-circuit neural network; Real-time optimization; Minimum eigenvector and eigenvalue 1. Introduction In the last 40 years, various dynamic solvers have been proposed for solving constrained optimization problems. The dynamical systems approach for solving 0925-2312/00/$ } see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 2 3 1 2 ( 9 9 ) 0 0 1 2 0 - 4