On tangent cone to systems of inequalities and equations in Banach spaces under relaxed constant rank condition

¹ Warsaw University of Technology, 00-662 Warszawa, Koszykowa 75, Systems Research Institute of PAS, PAS, 01-447 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: k.rutkowski@uksw.edu.pl

Received: 10 October 2019
Accepted: 5 January 2021

Abstract

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.