Proximal point method for minimizing quasiconvex locally Lipschitz functions on Hadamard manifolds

E. A. Papa Quiroz; P. R. Oliveira

doi:10.1016/j.na.2012.06.005

Proximal point method for minimizing quasiconvex locally Lipschitz functions on Hadamard manifolds

E. A. Papa Quiroz, P. R. Oliveira

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

24 Scopus citations

Abstract

In this paper we propose an extension of the proximal point method to solve minimization problems with quasiconvex locally Lipschitz objective functions on Hadamard manifolds. To reach this goal, we use the concept of Clarke subdifferential on Hadamard manifolds and assuming that the function is bounded from below, we prove the global convergence of the sequence generated by the method to a critical point of the function.

Original language	English
Pages (from-to)	5924-5932
Number of pages	9
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	75
Issue number	15
DOIs	https://doi.org/10.1016/j.na.2012.06.005
State	Published - Oct 2012
Externally published	Yes

Keywords

Global convergence
Hadamard manifolds
Locally Lipschitz functions
Proximal point method
Quasiconvex functions

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10.1016/j.na.2012.06.005

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title = "Proximal point method for minimizing quasiconvex locally Lipschitz functions on Hadamard manifolds",

abstract = "In this paper we propose an extension of the proximal point method to solve minimization problems with quasiconvex locally Lipschitz objective functions on Hadamard manifolds. To reach this goal, we use the concept of Clarke subdifferential on Hadamard manifolds and assuming that the function is bounded from below, we prove the global convergence of the sequence generated by the method to a critical point of the function.",

keywords = "Global convergence, Hadamard manifolds, Locally Lipschitz functions, Proximal point method, Quasiconvex functions",

author = "{Papa Quiroz}, {E. A.} and Oliveira, {P. R.}",

year = "2012",

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doi = "10.1016/j.na.2012.06.005",

language = "English",

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T1 - Proximal point method for minimizing quasiconvex locally Lipschitz functions on Hadamard manifolds

AU - Papa Quiroz, E. A.

AU - Oliveira, P. R.

PY - 2012/10

Y1 - 2012/10

N2 - In this paper we propose an extension of the proximal point method to solve minimization problems with quasiconvex locally Lipschitz objective functions on Hadamard manifolds. To reach this goal, we use the concept of Clarke subdifferential on Hadamard manifolds and assuming that the function is bounded from below, we prove the global convergence of the sequence generated by the method to a critical point of the function.

AB - In this paper we propose an extension of the proximal point method to solve minimization problems with quasiconvex locally Lipschitz objective functions on Hadamard manifolds. To reach this goal, we use the concept of Clarke subdifferential on Hadamard manifolds and assuming that the function is bounded from below, we prove the global convergence of the sequence generated by the method to a critical point of the function.

KW - Global convergence

KW - Hadamard manifolds

KW - Locally Lipschitz functions

KW - Proximal point method

KW - Quasiconvex functions

UR - http://www.scopus.com/inward/record.url?scp=84871331691&partnerID=8YFLogxK

U2 - 10.1016/j.na.2012.06.005

DO - 10.1016/j.na.2012.06.005

M3 - Article

AN - SCOPUS:84871331691

SN - 0362-546X

VL - 75

SP - 5924

EP - 5932

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 15

ER -

Proximal point method for minimizing quasiconvex locally Lipschitz functions on Hadamard manifolds

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Keywords

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