IMPLICIT AND EXPLICIT VISCOSITY METHODS FOR HIERARCHICAL VARIATIONAL INEQUALITIES ON HADAMARD MANIFOLDS

Qamrul Hasan Ansari; Feeroz Babu; Mohd Zeeshan

doi:10.24193/fpt-ro.2023.1.02

IMPLICIT AND EXPLICIT VISCOSITY METHODS FOR HIERARCHICAL VARIATIONAL INEQUALITIES ON HADAMARD MANIFOLDS

Qamrul Hasan Ansari, Feeroz Babu, Mohd Zeeshan

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

Abstract

In this paper, we consider a hierarchical variational inequality problem defined over the set of zeros of a set-valued monotone vector field in the setting of Hadamard manifolds. We also consider bilevel variational inequality problems and bilevel optimization problems as special cases of our variational inequality problem. We develop implicit and explicit viscosity methods for solving our problem for weak contraction mappings. An inexact version of the explicit viscosity method is also studied. At the end, we provide two examples and computational experiments to illustrate implicit and explicit viscosity methods.

Original language	English
Pages (from-to)	23-48
Number of pages	26
Journal	Fixed Point Theory
Volume	24
Issue number	1
DOIs	https://doi.org/10.24193/fpt-ro.2023.1.02
State	Published - 1 Feb 2023
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2023, House of the Book of Science. All rights reserved.

Keywords

Hadamard manifolds
Hierarchical variational inequality problems
bilevel optimization problems
bilevel variational inequality problems
monotone vector fields
nonexpansive mappings
weak contraction map-pings

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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abstract = "In this paper, we consider a hierarchical variational inequality problem defined over the set of zeros of a set-valued monotone vector field in the setting of Hadamard manifolds. We also consider bilevel variational inequality problems and bilevel optimization problems as special cases of our variational inequality problem. We develop implicit and explicit viscosity methods for solving our problem for weak contraction mappings. An inexact version of the explicit viscosity method is also studied. At the end, we provide two examples and computational experiments to illustrate implicit and explicit viscosity methods.",

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AU - Ansari, Qamrul Hasan

AU - Babu, Feeroz

AU - Zeeshan, Mohd

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N2 - In this paper, we consider a hierarchical variational inequality problem defined over the set of zeros of a set-valued monotone vector field in the setting of Hadamard manifolds. We also consider bilevel variational inequality problems and bilevel optimization problems as special cases of our variational inequality problem. We develop implicit and explicit viscosity methods for solving our problem for weak contraction mappings. An inexact version of the explicit viscosity method is also studied. At the end, we provide two examples and computational experiments to illustrate implicit and explicit viscosity methods.

AB - In this paper, we consider a hierarchical variational inequality problem defined over the set of zeros of a set-valued monotone vector field in the setting of Hadamard manifolds. We also consider bilevel variational inequality problems and bilevel optimization problems as special cases of our variational inequality problem. We develop implicit and explicit viscosity methods for solving our problem for weak contraction mappings. An inexact version of the explicit viscosity method is also studied. At the end, we provide two examples and computational experiments to illustrate implicit and explicit viscosity methods.

KW - Hadamard manifolds

KW - Hierarchical variational inequality problems

KW - bilevel optimization problems

KW - bilevel variational inequality problems

KW - monotone vector fields

KW - nonexpansive mappings

KW - weak contraction map-pings

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SN - 1583-5022

VL - 24

SP - 23

EP - 48

JO - Fixed Point Theory

JF - Fixed Point Theory

IS - 1

ER -

IMPLICIT AND EXPLICIT VISCOSITY METHODS FOR HIERARCHICAL VARIATIONAL INEQUALITIES ON HADAMARD MANIFOLDS

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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