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<p>Based on the minimum and maximum nuclear norm of all mode matrices of a tensor, a bilevel optimization model with an inequality constraint is proposed for tensor completion with noise. By using a special penalty function, a separable unconstrained optimization and the corresponding proximal gradient method are proposed. Furthermore, the objective function is proved to be a Kurdyka-Lojasiewicz (K L) function with an exponent of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\tfrac{1}{2}\)</EquationSource> </InlineEquation>, which guarantees that the sequence produced by the proposed algorithm globally converges to a stationary point. Moreover, numerical experiments on random tensor completion and real image recovery show that the proposed model and algorithm are superior to some traditional nuclear models and algorithms in terms of CPU time or precision.</p>

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Bilevel optimization for tensor completion with noise

  • 期刊论文

  • 发表日期：

    2026年2月9日

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  • Chuanlong Wang,
  • Rongrong Xue,
  • Yaru Fu

摘要

Based on the minimum and maximum nuclear norm of all mode matrices of a tensor, a bilevel optimization model with an inequality constraint is proposed for tensor completion with noise. By using a special penalty function, a separable unconstrained optimization and the corresponding proximal gradient method are proposed. Furthermore, the objective function is proved to be a Kurdyka-Lojasiewicz (K L) function with an exponent of \(\tfrac{1}{2}\) , which guarantees that the sequence produced by the proposed algorithm globally converges to a stationary point. Moreover, numerical experiments on random tensor completion and real image recovery show that the proposed model and algorithm are superior to some traditional nuclear models and algorithms in terms of CPU time or precision.