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

Bednarczuk, E. M.; Leśniewski, K. W.; Rutkowski, K. E.

ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 9

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.

Classification : 47J07, 47J30, 49J27, 49K27, 90C46
Keywords: Tangent cone, relaxed constant rank condition, Abadie condition, rank theorem, Ljusternik theorem, Lagrange multipliers

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