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<p>In the presence of time-varying variables and constraints, nonconvex properties, and noise disturbances, it is difficult to solve time-varying constrained nonconvex optimization (TVCNO) problems. In this paper, we propose an attention-subspace-assisted collaborative neurodynamic optimization (AS-CNO) approach for the TVCNO problems. AS-CNO employs adaptive integral gradient neurodynamics (AIGND) to reduce lagging errors and handle noise disturbances, coordinates multiple AIGND-based neural agents to collaboratively search for the global optimum, and uses attention-subspace-assisted initialization to improve the quality of initial neural-agent states and enhance the efficiency of subsequent collaborative search. Theoretical analysis establishes the exponential convergence of the AIGND residual error in the noise-free case, the boundedness of its residual error under bounded noise, and shows that the proposed AS-CNO can converge to a global optimum with probability one. The effectiveness of AS-CNO is numerically demonstrated by comparison with existing neurodynamic and heuristic optimization methods.</p>

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An Attention-Subspace-Assisted Collaborative Neurodynamic Optimization Approach for Time-Varying Constrained Nonconvex Optimization

  • 期刊论文

  • 发表日期：

    2026年7月17日

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  • Zhaohong Wu,
  • Peng Luo,
  • Haoen Huang,
  • Lei Guo,
  • Limei Shi

摘要

In the presence of time-varying variables and constraints, nonconvex properties, and noise disturbances, it is difficult to solve time-varying constrained nonconvex optimization (TVCNO) problems. In this paper, we propose an attention-subspace-assisted collaborative neurodynamic optimization (AS-CNO) approach for the TVCNO problems. AS-CNO employs adaptive integral gradient neurodynamics (AIGND) to reduce lagging errors and handle noise disturbances, coordinates multiple AIGND-based neural agents to collaboratively search for the global optimum, and uses attention-subspace-assisted initialization to improve the quality of initial neural-agent states and enhance the efficiency of subsequent collaborative search. Theoretical analysis establishes the exponential convergence of the AIGND residual error in the noise-free case, the boundedness of its residual error under bounded noise, and shows that the proposed AS-CNO can converge to a global optimum with probability one. The effectiveness of AS-CNO is numerically demonstrated by comparison with existing neurodynamic and heuristic optimization methods.