A Projection Neural Network for Constrained Quadratic Minimax Optimization

• Published in: IEEE transaction on neural networks and learning systems Vol. 26; no. 11; pp. 2891 - 2900
• Main Authors: Liu, Qingshan, Wang, Jun
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.11.2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Biological neural networks; Computer Simulation; Constraints; Convergence; Dynamical systems; Dynamics; Global convergence; Humans; Linear Models; Linear programming; Lyapunov methods; Lyapunov stability; Mathematical model; Mathematical models; Minimax technique; Neural networks; Neural Networks (Computer); Optimization; Pattern Recognition, Automated - methods; projection neural network; quadratic minimax optimization; projection neural network; Lyapunov stability; Global convergence; quadratic minimax optimization
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2015.2425301

This paper presents a projection neural network described by a dynamic system for solving constrained quadratic minimax programming problems. Sufficient conditions based on a linear matrix inequality are provided for global convergence of the proposed neural network. Compared with some of the existing neural networks for quadratic minimax optimization, the proposed neural network in this paper is capable of solving more general constrained quadratic minimax optimization problems, and the designed neural network does not include any parameter. Moreover, the neural network has lower model complexities, the number of state variables of which is equal to that of the dimension of the optimization problems. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network.