Computational Neural Dynamics Model for Time-Variant Constrained Nonlinear Optimization Applied to Winner-Take-All Operation

Abstract

Although time-variant nonlinear optimization with equality and inequality constraints (TVNOEIC) is a widespread problem in real life, the research on this issue is much less than the time-invariant one. Large lagging errors may not be inevitable if the traditional models designed for time-invariant optimizations are exploited to time-variant ones. To eliminate the lagging errors, models for handling time-variant optimization problems are urgently required. Recently, neural networks and the related neural dynamics approaches have witnessed rapid developments and made significant contributions to the online solution of various problems. On this basis, a noise-suppressing discrete-time neural dynamics (NSDTND) model is proposed in this article for solving the TVNOEIC problem. Theoretical analysis is presented to prove that the residual error of the proposed model is tiny enough to estimate the actual solution even in the presence of noise perturbation. In addition, numerical simulations, including an application on winner-take-all operation, are provided to further demonstrate the effectiveness and robustness of the proposed NSDTND model.