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Sun Min(ziyouxiaodou163.com) Abstract: As a special kind of recurrent neural networks, Zhang neural network (ZNN) has been successfully applied to various timevariant problems solving. In this paper, we first propose a special twostep Zhang et al. discretization (ZeaD) formula and a general twostep ZeaD formula, whose truncation errors are ${O}(\tau^3)$ and ${O}(\tau^2)$, respectively, and $\tau>0$ denotes the sampling gap. We also propose a general fivestep ZeaD formula with truncation error ${O}(\tau^5)$, and prove that the special and general twostep ZdaD formulas is convergent but the general fivestep ZeaD formula is not zerostable, thus is not convergent. Then, to solve the timevarying nonlinear optimization (TVNO) in real time, based on the Taylor series expansion and the above two convergent twostep ZeaD formulas, we discrete the continuoustime ZNN (CTZNN) model of TVNO proposed in the literature, and thus get a special twostep discretetime ZNN (DTZNN) model and a general twostep DTZNN model, which contains a free parameter $a_1\in(1/2,+\infty)$. Theoretical analyses indicate that the sequence generated by the first DTZNN model is not convergent, and for any $a_1\in(1/2,+\infty)$ and the stepsize $h\in(0,(2+4a_1)/(1+a_1))$, the sequence generated by the second DTZNN model converges to zero in an $\mathcal{O}(\tau^2)$ manner, where $\mathcal{O}(\tau^2)$ denotes a vector with every entries being $O(\tau^2)$. Furthermore, we prove that for any fixed $a_1\in(1/2,+\infty)$, the constant $(2+4a_1)/(1+a_1)$ is the tight upper bound of the stepsize $h$ and the constant $(1+2a_1)/(1+a_1)$ is the optimal stepsize. Finally, some numerical results and comparisons are provided and analyzed to substantiate the efficacy of the proposed DTZNN models. Keywords: Timevarying nonlinear optimization; Zhang et al. discretization; discretetime Zhang neural network. Category 1: Applications  OR and Management Sciences Citation: Download: [PDF] Entry Submitted: 11/30/2018 Modify/Update this entry  
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