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<p>This paper addresses time-varying constrained optimization problems (TVCOP), characterized by dynamically evolving objective functions and constraints over time. Leveraging a novel yet well-established smoothing technique from static optimization, we derive a time-varying smooth system of equations corresponding to the Karush-Kuhn-Tucker (KKT) conditions of TVCOP. By integrating a proportional-integral (PI) controller with the regularized time-varying smooth system, we propose a proportional-integral-derivative (PID)-controlled continuous-time smoothing Newton dynamics framework, termed PID-SND, for solving TVCOP. Theoretical analyses, including convergence properties of PID-SND, are rigorously established. Computational experiments demonstrate that the proposed method performs competitively when compared to existing approaches and the CVX toolbox.</p>

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Regularized continuous-time smoothing Newton dynamics and feedback control for time-varying constrained optimization

  • 期刊论文

  • 发表日期：

    2026年4月22日

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  • Tie Ni

摘要

This paper addresses time-varying constrained optimization problems (TVCOP), characterized by dynamically evolving objective functions and constraints over time. Leveraging a novel yet well-established smoothing technique from static optimization, we derive a time-varying smooth system of equations corresponding to the Karush-Kuhn-Tucker (KKT) conditions of TVCOP. By integrating a proportional-integral (PI) controller with the regularized time-varying smooth system, we propose a proportional-integral-derivative (PID)-controlled continuous-time smoothing Newton dynamics framework, termed PID-SND, for solving TVCOP. Theoretical analyses, including convergence properties of PID-SND, are rigorously established. Computational experiments demonstrate that the proposed method performs competitively when compared to existing approaches and the CVX toolbox.