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<p>This paper examines various questions related to approximate minimality and approximate criticality in constrained scalar optimization. We establish necessary optimality conditions for the approximate minimality of a lower semicontinuous (and therefore non-Lipschitz) function under a set constraint. Additionally, we explore the relationship between approximate criticality and genuine minimality of perturbed functions. A key tool in deriving these results is the use of well-known penalization functions.</p>

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Revisiting approximate minimality and approximate criticality in scalar optimization with constraints

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月28日

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  • Marius Durea,
  • Elena-Andreea Florea,
  • Radu Strugariu

摘要

This paper examines various questions related to approximate minimality and approximate criticality in constrained scalar optimization. We establish necessary optimality conditions for the approximate minimality of a lower semicontinuous (and therefore non-Lipschitz) function under a set constraint. Additionally, we explore the relationship between approximate criticality and genuine minimality of perturbed functions. A key tool in deriving these results is the use of well-known penalization functions.