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September 2, 2026Computational Optimization and ApplicationsOpen Access

A flexible block coordinate descent method for unconstrained optimization under Hölder continuity

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Authors

VAV. S. AmaralRAR. AndreaniLSLeonardo D. Secchin

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Overview

Theoretical analysis demonstrates stationary point convergence for flexible block coordinate descent in unconstrained optimization, highlighting complexity matching traditional single-block methods.

Key Points

  • To develop and analyze a flexible block coordinate descent method for unconstrained optimization under Hölder continuity assumptions.
  • Constructed an optimization algorithm combining quadratic models with quadratic regularization alongside flexible block selection strategies.
  • Unified distinct sufficient descent criteria into a single framework and incorporated a practical stationarity certificate as a termination condition.
  • Conducted illustrative numerical experiments using a freely available implementation to validate theoretical results.
  • Established well-definiteness and convergence to stationary points under Hölder continuity of the objective function gradient.
  • Achieved worst-case complexity bounds qualitatively comparable to those established for standard single-block methods under Lipschitz or Hölder continuity.

Cite This Study

Amaral et al. (2026) studied this question.

synapsesocial.com/papers/6a97e318c562ede874ec7bbbhttps://doi.org/10.1007/s10589-026-00827-8
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