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A flexible block coordinate descent method utilizing quadratic regularization guarantees convergence to stationary points for unconstrained optimization problems under Hölder continuity assumptions, achieving worst-case complexity comparable to single-block methods. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

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. AmaralUniversidade Federal do Piauí RAR. AndreaniUniversidade Estadual de Campinas (UNICAMP)LSLeonardo D. SecchinUniversidade Federal do Espírito Santo

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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/6a97e318c562ede874ec7bbb https://doi.org/10.1007/s10589-026-00827-8

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September 2, 2026Computational Optimization and ApplicationsOpen Access

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

View Full Paper

Ask AI

Bookmark

Authors

VAV. S. AmaralUniversidade Federal do Piauí RAR. AndreaniUniversidade Estadual de Campinas (UNICAMP)LSLeonardo D. SecchinUniversidade Federal do Espírito Santo

Discussion

Member takes

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/6a97e318c562ede874ec7bbb https://doi.org/10.1007/s10589-026-00827-8

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