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 Hilbert spaces.
Dedicated to Michel Théra on the occasion of his 70 th birthday.
AbstractWe investigate the existence of directional derivatives for strongly cone-paraconvex mappings. Our result is an extension of the classical Valadier result on the existence of the directional derivative for cone convex mappings with values in weakly sequentially Banach space.
We prove that a strongly cone paraconvex mapping defined on a normed space X and taking values in a reflexive separable Banach space Y is Gâteaux differentiable on a dense G δ subset of X. Our results are generalizations of Rolewicz's theorems (Theorem 3.1) from Rolewicz (2011).
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.
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