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Metrically Regular Vector Field and Iterative Processes for Generalized Equations in Hadamard Manifolds

FEREIRA, Orizon P. - Personal Name
ALEXIS, Célia Jean - Personal Name
PIETURS, Alain - Personal Name

This paper is focused on the problem of finding a singularity of the sum of two vector fields defined on a Hadamard manifold, or more precisely, the study of a generalized equation in a Riemannian setting. We extend the concept of metric regularity to the Riemannian setting and investigate its relationship with the generalized equation in this new context. In particular, a version of Graves’s theorem is presented and we also define some concepts related to metric regularity, including the Aubin property and the strong metric regularity of set-valued vector fields. A conceptual method for finding a singularity of the sum of two vector fields is also considered. This method has as particular instances: the proximal point method, Newton’s method, and Zincenko’s method on Hadamard manifolds. Under the assumption of metric regularity at the singularity, we establish that the methods are well defined in a suitable
neighborhood of the singularity. Moreover, we also show that each sequence generated by these methods converges to this singularity at a superlinear rate.

EB00000003651K Available

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E-Jurnal

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Subject(s)

Newton method
Generalized equation
Metric regularity
Proximal point method
Zincenko’s method
Superlinear convergence
Hadamard manifold

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Statement of Responsibility

Orizon P. Ferreira , Alain Piétrus , Célia Jean-Alexis

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Metrically Regular Vector Field and Iterative Processes for Generalized Equations in Hadamard Manifolds

FEREIRA, Orizon P. - Personal NameALEXIS, Célia Jean - Personal NamePIETURS, Alain - Personal Name

Series Title

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ISBN/ISSN

Classification

Content Type

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Carrier Type

Edition

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Specific Detail Info

Statement of Responsibility

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Konferensi Pustakawan #25: Peran Ruang Baca dalam Mendukung Akademik

Menjaga Spirit Ramadhan dengan Membaca Buku (IN) Toleransi di UNEJDIGILIB

Rapat Kerja Sahabat Perpusatkaan Universitas Jember Tahun 2025

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FEREIRA, Orizon P. - Personal Name
ALEXIS, Célia Jean - Personal Name
PIETURS, Alain - Personal Name