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

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English
Pages (from-to)	457-467
Number of pages	11
Journal	Journal of the Operations Research Society of China
Volume	5
Issue number	4
DOIs	https://doi.org/10.1007/s40305-016-0129-z
State	Published - 1 Dec 2017

Bibliographical note

Funding Information:
This work was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior of the Federal University of Rio de Janeiro (UFRJ), Brazil.

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

Keywords

Abstract subdifferential
Convergence rate
Hadamard manifolds
Nonsmooth optimization
Proximal point method
Quasiconvex function

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10.1007/s40305-016-0129-z

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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.",

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AU - Maculan, Nelson

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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.

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KW - Convergence rate

KW - Hadamard manifolds

KW - Nonsmooth optimization

KW - Proximal point method

KW - Quasiconvex function

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

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Keywords

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