The convergence of the hierarchical identification algorithm and variable elimination algorithm

doi:10.1016/j.automatica.2025.112683

The convergence of the hierarchical identification algorithm and variable elimination algorithm

2025-11-10

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DOI：10.1016/j.automatica.2025.112683

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The hierarchical identification algorithm (HIE) is particularly suitable for large-scale system identification where the cost function decomposes into separable sub-functions, offering structural simplicity and reduced computational complexity. However, convergence guarantees remain less established due to HIE’s neglect of cross-sub-vector couplings. To address this limitation, we propose a variable elimination algorithm (VE) that simultaneously achieves: (1) dimensionality reduction through system decomposition, and (2) explicitly models the relationships between sub-systems/sub-vectors. Furthermore, we introduce an accelerated optimization framework for both HIE and VE to enhance convergence rates. Rigorous analysis demonstrates that VE achieves a smaller convergence factor than HIE, implying provably faster convergence. Two numerical examples demonstrate the effectiveness of the proposed method.

Keywords:

Parameter estimation

Hierarchical identification algorithm

Variable elimination algorithm

Convergence factor

Convergence rate

The convergence of the hierarchical identification algorithm and variable elimination algorithm

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