A One-Layer Recurrent Neural Network With a Discontinuous Hard-Limiting Activation Function for Quadratic Programming

• Published in: IEEE transactions on neural networks Vol. 19; no. 4; pp. 558 - 570
• Main Authors: Liu, Q, Wang, J
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2008; Institute of Electrical and Electronics Engineers
• Subjects: Activation; Applied sciences; Artificial intelligence; Computer science; control theory; systems; Computer Simulation; Connectionism. Neural networks; Convergence; Data processing. List processing. Character string processing; Differential inclusion; Exact sciences and technology; global convergence; hard-limiting activation function; Lagrangian functions; Linear programming; Lyapunov stability; Machine learning; Mathematical analysis; Mathematical models; Memory organisation. Data processing; Nerve Net; Neural network hardware; Neural networks; Nonlinear Dynamics; nonlinear programming; Numerical simulation; Programming, Linear; Quadratic programming; recurrent neural network; Recurrent neural networks; Signal Processing, Computer-Assisted; Software; Support vector machines; Time Factors; Recurrent neural nets; Statistical analysis; recurrent neural network; nonlinear programming; global convergence; Lyapunov method; Non linear programming; Neural network; Quadratic programming; hard-limiting activation function; Activation function; Sequential method; Optimal solution; Equality constraint; Vector support machine; Lyapunov stability; Convex function; Objective function; Differential inclusion; Lyapunov function; Quadratic function
• ISSN: 1045-9227; 1941-0093
• DOI: 10.1109/TNN.2007.910736

In this paper, a one-layer recurrent neural network with a discontinuous hard-limiting activation function is proposed for quadratic programming. This neural network is capable of solving a large class of quadratic programming problems. The state variables of the neural network are proven to be globally stable and the output variables are proven to be convergent to optimal solutions as long as the objective function is strictly convex on a set defined by the equality constraints. In addition, a sequential quadratic programming approach based on the proposed recurrent neural network is developed for general nonlinear programming. Simulation results on numerical examples and support vector machine (SVM) learning show the effectiveness and performance of the neural network.