On the Convergence Rate of an Inexact Proximal Point Algorithm for Quasiconvex Minimization on Hadamard Manifolds

Nancy Baygorrea; Erik Alex Papa Quiroz; Nelson Maculan

doi:10.1007/s40305-016-0129-z

On the Convergence Rate of an Inexact Proximal Point Algorithm for Quasiconvex Minimization on Hadamard Manifolds

Nancy Baygorrea, Erik Alex Papa Quiroz, Nelson Maculan

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

6 Citas (Scopus)

Resumen

In this paper, we present an analysis about the rate of convergence of an inexact proximal point algorithm to solve minimization problems for quasiconvex objective functions on Hadamard manifolds. We prove that under natural assumptions the sequence generated by the algorithm converges linearly or superlinearly to a critical point of the problem.

Idioma original	Inglés
Páginas (desde-hasta)	457-467
Número de páginas	11
Publicación	Journal of the Operations Research Society of China
Volumen	5
N.º	4
DOI	https://doi.org/10.1007/s40305-016-0129-z
Estado	Publicada - 1 dic. 2017
Publicado de forma externa	Sí

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Publisher Copyright:
© 2016, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag Berlin Heidelberg.

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abstract = "In this paper, we present an analysis about the rate of convergence of an inexact proximal point algorithm to solve minimization problems for quasiconvex objective functions on Hadamard manifolds. We prove that under natural assumptions the sequence generated by the algorithm converges linearly or superlinearly to a critical point of the problem.",

keywords = "Abstract subdifferential, Convergence rate, Hadamard manifolds, Nonsmooth optimization, Proximal point method, Quasiconvex function",

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AU - Baygorrea, Nancy

AU - Papa Quiroz, Erik Alex

AU - Maculan, Nelson

PY - 2017/12/1

Y1 - 2017/12/1

N2 - In this paper, we present an analysis about the rate of convergence of an inexact proximal point algorithm to solve minimization problems for quasiconvex objective functions on Hadamard manifolds. We prove that under natural assumptions the sequence generated by the algorithm converges linearly or superlinearly to a critical point of the problem.

AB - In this paper, we present an analysis about the rate of convergence of an inexact proximal point algorithm to solve minimization problems for quasiconvex objective functions on Hadamard manifolds. We prove that under natural assumptions the sequence generated by the algorithm converges linearly or superlinearly to a critical point of the problem.

KW - Abstract subdifferential

KW - Convergence rate

KW - Hadamard manifolds

KW - Nonsmooth optimization

KW - Proximal point method

KW - Quasiconvex function

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ER -

On the Convergence Rate of an Inexact Proximal Point Algorithm for Quasiconvex Minimization on Hadamard Manifolds

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