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

Jie Peng (), Liang Chen () and Zhou Wei ()
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Jie Peng: Hebei University
Liang Chen: Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Zhou Wei: Hebei University

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 1, No 13, 17 pages

Abstract: Abstract 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.

Keywords: Fréchet BCQ; Error bound; Fréchet subdifferential; Inequalities system; Strong Fréchet CHIP; 90C31; 90C25; 49J52; 46B20 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02742-0

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