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Journal of Industrial and Management Optimization

2026, Volume 22, Issue 10: 5106-5124. doi: 10.3934/jimo.2026176
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Research article

Global error bounds for TCP and VTCP

  • School of Big Data, Zunyi Normal College, Zunyi, Guizhou, 563006, P.R. China
  • Published: 17 September 2026

  • 90C33, 90C26

  • This paper investigated conditionally computable global error bounds for tensor complementarity problems (TCP) and vertical tensor complementarity problems (VTCP). Existing global error bounds for TCP and VTCP rely on an unknown exact solution vector, which cannot be numerically evaluated in practice and thus limits their applicability. To address this limitation, we established conditionally computable global error bounds under structured tensor assumptions. The derived bounds only require an arbitrary feasible test vector and are independent of the unknown true solution. Moreover, our theoretical results generalized several classic error bound theorems for linear complementarity problems (LCP), such as the Mathias–Pang and Chen–Xiang estimates. Numerical examples were presented to verify the tightness and computational efficiency of our proposed bounds.

    Citation: Xiaowei Shen, Jun He, Yanmin Liu. Global error bounds for TCP and VTCP[J]. Journal of Industrial and Management Optimization, 2026, 22(10): 5106-5124. doi: 10.3934/jimo.2026176

    Related Papers:

  • This paper investigated conditionally computable global error bounds for tensor complementarity problems (TCP) and vertical tensor complementarity problems (VTCP). Existing global error bounds for TCP and VTCP rely on an unknown exact solution vector, which cannot be numerically evaluated in practice and thus limits their applicability. To address this limitation, we established conditionally computable global error bounds under structured tensor assumptions. The derived bounds only require an arbitrary feasible test vector and are independent of the unknown true solution. Moreover, our theoretical results generalized several classic error bound theorems for linear complementarity problems (LCP), such as the Mathias–Pang and Chen–Xiang estimates. Numerical examples were presented to verify the tightness and computational efficiency of our proposed bounds.



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