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<p>Conditions allowing the interchange between the supremum and biconjugation in the bidual space are provided. We establish alternative characterizations which involve both approximate and exact subdifferential calculus rules for the supremum. The so-called concave-like setting, which covers the particular case of finite families, gives rise to simpler criteria. We give an application to the regularization problem in convex optimization.</p>

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On the Regularization of the Supremum Function in the Bidual Space

  • 期刊论文

  • 发表日期：

    2025年12月24日

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  • Rafael Correa,
  • Abderrahim Hantoute,
  • Marco A. López

摘要

Conditions allowing the interchange between the supremum and biconjugation in the bidual space are provided. We establish alternative characterizations which involve both approximate and exact subdifferential calculus rules for the supremum. The so-called concave-like setting, which covers the particular case of finite families, gives rise to simpler criteria. We give an application to the regularization problem in convex optimization.