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Design and analysis of two discrete-time ZD algorithms for time-varying nonlinear minimization

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Abstract

Nonlinear minimization, as a subcase of nonlinear optimization, is an important issue in the research of various intelligent systems. Recently, Zhang et al. developed the continuous-time and discrete-time forms of Zhang dynamics (ZD) for time-varying nonlinear minimization. Based on this previous work, another two discrete-time ZD (DTZD) algorithms are proposed and investigated in this paper. Specifically, the resultant DTZD algorithms are developed for time-varying nonlinear minimization by utilizing two different types of Taylor-type difference rules. Theoretically, each steady-state residual error in the DTZD algorithm changes in an O(τ 3) manner with τ being the sampling gap. Comparative numerical results are presented to further substantiate the efficacy and superiority of the proposed DTZD algorithms for time-varying nonlinear minimization.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (with number 61603143), the Natural Science Foundation of Fujian Province (with number 2016J01307), the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (with number ZQN-YX402), the Scientific Research Funds of Huaqiao University (with number 15BS410), and also the National Innovation Training Program for University Students (with number 201610385032). Besides, the authors would like to thank the editors and anonymous reviewers for their time and effort in handling this paper, as well as for providing constructive comments that enabled us to improve the presentation and quality of this paper.

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Authors and Affiliations

  1. College of Information Science and Engineering, Huaqiao University, Xiamen, 361021, China

    Dongsheng Guo, Xinjie Lin, Zhaozhu Su, Sibo Sun & Zhijing Huang

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  1. Dongsheng Guo
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  2. Xinjie Lin
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  3. Zhaozhu Su
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  4. Sibo Sun
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  5. Zhijing Huang
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Correspondence to Dongsheng Guo.

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Guo, D., Lin, X., Su, Z. et al. Design and analysis of two discrete-time ZD algorithms for time-varying nonlinear minimization. Numer Algor 77, 23–36 (2018). https://doi.org/10.1007/s11075-017-0302-4

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