Abstract
Online solution of time-varying nonlinear optimization problems is considered an important issue in the fields of scientific and engineering research. In this study, the continuous-time derivative (CTD) model and two gradient dynamics (GD) models are developed for real-time varying nonlinear optimization (RTVNO). A continuous-time Zhang dynamics (CTZD) model is then generalized and investigated for RTVNO to remedy the weaknesses of CTD and GD models. For possible digital hardware realization, a discrete-time Zhang dynamics (DTZD) model, which can be further reduced to Newton-Raphson iteration (NRI), is also proposed and developed. Theoretical analyses indicate that the residual error of the CTZD model has an exponential convergence, and that the maximum steady-state residual error (MSSRE) of the DTZD model has an O(τ 2) pattern with τ denoting the sampling gap. Simulation and numerical results further illustrate the efficacy and advantages of the proposed CTZD and DTZD models for RTVNO.
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This work is supported by the National Natural Science Foundation of China (with numbers 61473323), by the Foundation of Key Laboratory of Autonomous Systems and Networked Control, Ministry of Education, China (with number 2013A07), and also by the Science and Technology Program of Guangzhou, China (with number 2014J4100057). Besides, kindly note that both authors of the paper are jointly of the first authorship.
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Jin, L., Zhang, Y. Continuous and discrete Zhang dynamics for real-time varying nonlinear optimization. Numer Algor 73, 115–140 (2016). https://doi.org/10.1007/s11075-015-0088-1
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DOI: https://doi.org/10.1007/s11075-015-0088-1