Regularization of proximal point algorithms in Hadamard manifolds

Qamrul Hasan Ansari; Feeroz Babu; Jen Chih Yao

doi:10.1007/s11784-019-0658-2

Regularization of proximal point algorithms in Hadamard manifolds

Qamrul Hasan Ansari^*, Feeroz Babu, Jen Chih Yao

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

109 Scopus citations

Abstract

In this paper, we consider the regularization method for exact as well as for inexact proximal point algorithms for finding the singularities of maximal monotone set-valued vector fields. We prove that the sequences generated by these algorithms converge to an element of the set of singularities of a maximal monotone set-valued vector field. A numerical example is provided to illustrate the inexact proximal point algorithm with regularization. Applications of our results to minimization problems and saddle point problems are given in the setting of Hadamard manifolds.

Original language	English
Article number	25
Journal	Journal of Fixed Point Theory and Applications
Volume	21
Issue number	1
DOIs	https://doi.org/10.1007/s11784-019-0658-2
State	Published - 1 Mar 2019

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

Keywords

Hadamard manifolds
Inclusion problems
maximal monotone vector fields
minimization problems
proximal point algorithms
regularization method
saddle point problems

ASJC Scopus subject areas

Modeling and Simulation
Geometry and Topology
Applied Mathematics

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title = "Regularization of proximal point algorithms in Hadamard manifolds",

abstract = "In this paper, we consider the regularization method for exact as well as for inexact proximal point algorithms for finding the singularities of maximal monotone set-valued vector fields. We prove that the sequences generated by these algorithms converge to an element of the set of singularities of a maximal monotone set-valued vector field. A numerical example is provided to illustrate the inexact proximal point algorithm with regularization. Applications of our results to minimization problems and saddle point problems are given in the setting of Hadamard manifolds.",

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T1 - Regularization of proximal point algorithms in Hadamard manifolds

AU - Ansari, Qamrul Hasan

AU - Babu, Feeroz

AU - Yao, Jen Chih

PY - 2019/3/1

Y1 - 2019/3/1

N2 - In this paper, we consider the regularization method for exact as well as for inexact proximal point algorithms for finding the singularities of maximal monotone set-valued vector fields. We prove that the sequences generated by these algorithms converge to an element of the set of singularities of a maximal monotone set-valued vector field. A numerical example is provided to illustrate the inexact proximal point algorithm with regularization. Applications of our results to minimization problems and saddle point problems are given in the setting of Hadamard manifolds.

AB - In this paper, we consider the regularization method for exact as well as for inexact proximal point algorithms for finding the singularities of maximal monotone set-valued vector fields. We prove that the sequences generated by these algorithms converge to an element of the set of singularities of a maximal monotone set-valued vector field. A numerical example is provided to illustrate the inexact proximal point algorithm with regularization. Applications of our results to minimization problems and saddle point problems are given in the setting of Hadamard manifolds.

KW - Hadamard manifolds

KW - Inclusion problems

KW - maximal monotone vector fields

KW - minimization problems

KW - proximal point algorithms

KW - regularization method

KW - saddle point problems

UR - https://www.scopus.com/pages/publications/85060912242

U2 - 10.1007/s11784-019-0658-2

DO - 10.1007/s11784-019-0658-2

M3 - Article

AN - SCOPUS:85060912242

SN - 1661-7738

VL - 21

JO - Journal of Fixed Point Theory and Applications

JF - Journal of Fixed Point Theory and Applications

IS - 1

M1 - 25

ER -

Regularization of proximal point algorithms in Hadamard manifolds

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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