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<p>In this paper, we study Fréchet basic constraint qualification (Fréchet BCQ) and error bounds for a system of finitely many inequalities defined by lower semicontinuous functions. The Fréchet BCQ is given in terms of Fréchet subdifferentials and normal cones, and this Fréchet BCQ is proved to closely relates with strong Fréchet CHIP for a collection of the inequality’s solution sets. Then we consider error bounds of such inequalities system and derive sufficient dual conditions for the error bound via Fréchet subdifferentials and singular subdifferentials.</p>

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Fréchet BCQ and Error Bounds for A System of Finitely Many Inequalities

  • 期刊论文

  • 发表日期：

    2025年7月14日

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  • Jie Peng,
  • Liang Chen,
  • Zhou Wei

摘要

In this paper, we study Fréchet basic constraint qualification (Fréchet BCQ) and error bounds for a system of finitely many inequalities defined by lower semicontinuous functions. The Fréchet BCQ is given in terms of Fréchet subdifferentials and normal cones, and this Fréchet BCQ is proved to closely relates with strong Fréchet CHIP for a collection of the inequality’s solution sets. Then we consider error bounds of such inequalities system and derive sufficient dual conditions for the error bound via Fréchet subdifferentials and singular subdifferentials.