A Recurrent Neural Network for Nonlinear Fractional Programming

• Published in: Mathematical Problems in Engineering Vol. 2012; no. 2012; pp. 1104 - 1121-565
• Main Authors: Zhang, Quan-Ju, Lu, Xiao Qing
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Limiteds 01.01.2012; Hindawi Publishing Corporation; John Wiley & Sons, Inc
• Subjects: Algorithms; Computer simulation; Constraints; Continuity (mathematics); Engineering; Intervals; Linear programming; Mathematical analysis; Mathematical models; Mathematical programming; Neural networks; Nonlinearity; Optimization; Programming; Recurrent neural networks; Studies; Trajectory optimization
• ISSN: 1024-123X; 1563-5147
• DOI: 10.1155/2012/807656

This paper presents a novel recurrent time continuous neural network model which performs nonlinear fractional optimization subject to interval constraints on each of the optimization variables. The network is proved to be complete in the sense that the set of optima of the objective function to be minimized with interval constraints coincides with the set of equilibria of the neural network. It is also shown that the network is primal and globally convergent in the sense that its trajectory cannot escape from the feasible region and will converge to an exact optimal solution for any initial point being chosen in the feasible interval region. Simulation results are given to demonstrate further the global convergence and good performance of the proposing neural network for nonlinear fractional programming problems with interval constraints.