New Noise-Tolerant Neural Algorithms for Future Dynamic Nonlinear Optimization With Estimation on Hessian Matrix Inversion

Nonlinear optimization problems with dynamical parameters are widely arising in many practical scientific and engineering applications, and various computational models are presented for solving them under the hypothesis of short-time invariance. To eliminate the large lagging error in the solution of the inherently dynamic nonlinear optimization problem, the only way is to estimate the future unknown information by using the present and previous data during the solving process, which is termed the future dynamic nonlinear optimization (FDNO) problem. In this paper, to suppress noises and improve the accuracy in solving FDNO problems, a novel noise-tolerant neural (NTN) algorithm based on zeroing neural dynamics is proposed and investigated. In addition, for reducing algorithm complexity, the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is employed to eliminate the intensively computational burden for matrix inversion, termed NTN-BFGS algorithm. Moreover, theoretical analyses are conducted, which show that the proposed algorithms are able to globally converge to a tiny error bound with or without the pollution of noises. Finally, numerical experiments are conducted to validate the superiority of the proposed NTN and NTN-BFGS algorithms for the online solution of FDNO problems.