Conditioning for optimization problems under general perturbations - Bianchi, M.; Kassay, G.; Pini, R. (Nonlinear analysis, 2012)
Given a function f ∈ C 1 , 1 ( B ( 0 , r ) ) , where B ( 0 , r ) denotes a ball of radius r in a real Banach space E , we provide the definition of a positive extended real number c ˆ ( f ) defined through the function, that plays a role in the study of the sensitivity of the Argmin map of the perturbed function F g ( p , u ) = f ( u ) − g ( p , u ) . This number coincides with the number c 2 ( f ) introduced by Zolezzi (2003) if linear perturbations g ( p , u ) = 〈 p , u 〉 are considered.