Finite-Time Convergent Recurrent Neural Network With a Hard-Limiting Activation Function for Constrained Optimization With Piecewise-Linear Objective Functions

• Published in: IEEE transactions on neural networks Vol. 22; no. 4; pp. 601 - 613
• Main Authors: Liu, Qingshan, Wang, Jun
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2011; Institute of Electrical and Electronics Engineers
• Subjects: Algorithms; Applied sciences; Artificial intelligence; Artificial neural networks; Complexity theory; Computer science; control theory; systems; Computer Simulation; Connectionism. Neural networks; Constrained optimization; Constraints; Convergence; convergence in finite time; Deviation; Exact sciences and technology; global Lyapunov method; Humans; Linear programming; Mathematical models; Neural networks; Neural Networks (Computer); Nonlinear Dynamics; Optimization; Programming; Programming, Linear; Recurrent neural networks; Time Factors; Lower bound; Recurrent neural nets; convergence in finite time; L1 approximation; Lyapunov method; Shortest path; Linear programming; Routing; Regression analysis; Network management; Neural network; Modeling; Constrained optimization; Minimum time; recurrent neural networks; Activation function; Optimal solution; piecewise function; Objective function; global Lyapunov method; Piecewise linearization; Mathematical programming
• ISSN: 1045-9227; 1941-0093; 1941-0093
• DOI: 10.1109/TNN.2011.2104979

This paper presents a one-layer recurrent neural network for solving a class of constrained nonsmooth optimization problems with piecewise-linear objective functions. The proposed neural network is guaranteed to be globally convergent in finite time to the optimal solutions under a mild condition on a derived lower bound of a single gain parameter in the model. The number of neurons in the neural network is the same as the number of decision variables of the optimization problem. Compared with existing neural networks for optimization, the proposed neural network has a couple of salient features such as finite-time convergence and a low model complexity. Specific models for two important special cases, namely, linear programming and nonsmooth optimization, are also presented. In addition, applications to the shortest path problem and constrained least absolute deviation problem are discussed with simulation results to demonstrate the effectiveness and characteristics of the proposed neural network.