Reference : A Lyusternik - Graves theorem for the proximal point method
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
A Lyusternik - Graves theorem for the proximal point method
Aragón Artacho, Francisco Javier mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
Gaydu, M. [> >]
Computational Optimization and Applications
[en] proximal point algorithm ; generalized equations ; metric regularity
[en] We consider a generalized version of the proximal point algorithm for solving the perturbed inclusion y∈T(x), where y is a perturbation element near 0 and T is a set-valued mapping acting from a Banach space X to a Banach space Y which is metrically regular around some point (x̅,0) in its graph. We study the behavior of the convergent iterates generated by the algorithm and we prove that they inherit the regularity properties of T, and vice versa. We analyze the cases when the mapping T is metrically regular and strongly regular.
Luxembourg Centre for Systems Biomedicine (LCSB): Systems Biochemistry (Fleming Group)

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