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July 16, 2026Computational Optimization and ApplicationsOpen Access

An inexact alternating projection method with application to matrix completion

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Authors

SBStefania BellaviaIstituto Nazionale di Alta Matematica Francesco SeveriSRSimone RebegoldiUniversity of Modena and Reggio EmiliaMSMattia SileiIstituto Nazionale di Alta Matematica Francesco Severi

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Implication

Randomized trial demonstrates the effectiveness of a novel method in matrix completion, suggesting improved feasibility processes.

Key Points

  • This research focuses on developing a regularized alternating projection method for solving nonconvex feasibility problems, specifically targeting matrix completion.
  • Analyzed inexact regularized alternating projection method.
  • Specialized in affine rank minimization, employing a Krylov solver for truncating Singular Value Decomposition.
  • Developed stopping criteria that leverage by-products of the Krylov method.
  • The algorithm exhibited global convergence under specified conditions related to a merit function.
  • Numerical tests showed effective matrix completion without requiring excessive computational resources.
  • Proved that the stopping criteria help prevent oversolving phenomena.

Cite This Study

Bellavia et al. (2026) studied this question.

synapsesocial.com/papers/6a5873ed2b46c88ba9ad040fhttps://doi.org/10.1007/s10589-026-00806-z
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