Volume 27, 2021
|Number of page(s)||22|
|Published online||03 March 2021|
On tangent cone to systems of inequalities and equations in Banach spaces under relaxed constant rank condition
Warsaw University of Technology, 00-662 Warszawa, Koszykowa 75, Systems Research Institute of PAS, PAS,
Warsaw, Newelska 6.
2 Systems Research Institute, PAS, 01-447 Warsaw, Newelska 6.
3 Cardinal Stefan Wyszyński University, 01-815 Warsaw, Dewajtis 5.
* Corresponding author: email@example.com
Accepted: 5 January 2021
Under the relaxed constant rank condition, introduced by Minchenko and Stakhovski, we prove that the linearized cone is contained in the tangent cone (Abadie condition) for sets represented as solution sets to systems of finite numbers of inequalities and equations given by continuously differentiable functions defined on Banach spaces.
Mathematics Subject Classification: 47J07 / 47J30 / 49J27 / 49K27 / 90C46
Key words: Tangent cone / relaxed constant rank condition / Abadie condition / rank theorem / Ljusternik theorem / Lagrange multipliers
© EDP Sciences, SMAI 2021
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