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

Universidade Federal do Rio de Janeiro

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

6 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
Externally published	Yes

Keywords

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

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10.1007/s40305-016-0129-z

Cite this

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

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",

author = "Nancy Baygorrea and \{Papa Quiroz\}, \{Erik Alex\} and Nelson Maculan",

note = "Publisher Copyright: {\textcopyright} 2016, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag Berlin Heidelberg.",

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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

UR - https://www.scopus.com/pages/publications/85037606159

U2 - 10.1007/s40305-016-0129-z

DO - 10.1007/s40305-016-0129-z

M3 - Article

AN - SCOPUS:85037606159

SN - 2194-668X

VL - 5

SP - 457

EP - 467

JO - Journal of the Operations Research Society of China

JF - Journal of the Operations Research Society of China

IS - 4

ER -

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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