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 chapter, to suppress noises and improve the accuracy in solving FDNO problems, a noise-tolerant neural dynamics (NTND) model is presented and investigated. In addition, in reducing model complexity, the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is employed to eliminate the intensively computational burden for matrix inversion, termed the NTND-BFGS model. Moreover, theoretical analyses are conducted, which show that the constructed models 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 designed NTND and NTND-BFGS models for the online solution of FDNO problems.