Contraction-mapping algorithm for the equilibrium problem over the fixed point set of a nonexpansive semigroup

In this paper, we consider the proximal mapping of a bifunction. Under the Lipschitz-type and the strong monotonicity conditions, we prove that the proximal mapping is contractive. Based on this result, we construct an iterative process for solving the equilibrium problem over the fixed point sets o...

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Published inMathematical modelling and analysis Vol. 24; no. 1; pp. 43 - 61
Main Authors Hai, Trinh Ngoc, Thuy, Le Qung
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 01.01.2019
Subjects
Algorithms
bilevel optimization
Boundary value problems
contractive mapping
equilibrium problem
Fixed point theory
Fixed points (mathematics)
Functions (Mathematics)
Groups (Mathematics)
Iterative methods
Mapping
Maps (Mathematics)
Mathematical research
nonexpansive semigroup
strong monotonicity
contractive mapping
strong monotonicity
bilevel optimization
nonexpansive semigroup
equilibrium problem
Online AccessGet full text
ISSN1392-6292
1648-3510
DOI10.3846/mma.2019.004

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Abstract In this paper, we consider the proximal mapping of a bifunction. Under the Lipschitz-type and the strong monotonicity conditions, we prove that the proximal mapping is contractive. Based on this result, we construct an iterative process for solving the equilibrium problem over the fixed point sets of a nonexpansive semigroup and prove a weak convergence theorem for this algorithm. Also, some preliminary numerical experiments and comparisons are presented. First Published Online: 21 Nov 2018
AbstractList In this paper, we consider the proximal mapping of a bifunction. Under the Lipschitz-type and the strong monotonicity conditions, we prove that the proximal mapping is contractive. Based on this result, we construct an iterative process for solving the equilibrium problem over the fixed point sets of a nonexpansive semigroup and prove a weak convergence theorem for this algorithm. Also, some preliminary numerical experiments and comparisons are presented. First Published Online: 21 Nov 2018
In this paper, we consider the proximal mapping of a bifunction. Under the Lipschitz-type and the strong monotonicity conditions, we prove that the proximal mapping is contractive. Based on this result, we construct an iterative process for solving the equilibrium problem over the fixed point sets of a nonexpansive semigroup and prove a weak convergence theorem for this algorithm. Also, some preliminary numerical experiments and comparisons are presented.
In this paper, we consider the proximal mapping of a bifunction. Under the Lipschitz-type and the strong monotonicity conditions, we prove that the proximal mapping is contractive. Based on this result, we construct an iterative process for solving the equilibrium problem over the fixed point sets of a nonexpansive semigroup and prove a weak convergence theorem for this algorithm. Also, some preliminary numerical experiments and comparisons are presented.Keywords: bilevel optimization, contractive mapping, nonexpansive semigroup, equilibrium problem, strong monotonicity.AMS Subject Classification: 47H05; 47H09; 47J25; 65K10; 90C25.
In this paper, we consider the proximal mapping of a bifunction. Under the Lipschitz-type and the strong monotonicity conditions, we prove that the proximal mapping is contractive. Based on this result, we construct an iterative process for solving the equilibrium problem over the fixed point sets of a nonexpansive semigroup and prove a weak convergence theorem for this algorithm. Also, some preliminary numerical experiments and comparisons are presented. First Published Online: 21 Nov 2018
Audience Academic
Author Thuy, Le Qung
Hai, Trinh Ngoc
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Keywords contractive mapping
strong monotonicity
bilevel optimization
nonexpansive semigroup
equilibrium problem
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SubjectTerms Algorithms
bilevel optimization
Boundary value problems
contractive mapping
equilibrium problem
Fixed point theory
Fixed points (mathematics)
Functions (Mathematics)
Groups (Mathematics)
Iterative methods
Mapping
Maps (Mathematics)
Mathematical research
nonexpansive semigroup
strong monotonicity
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Title Contraction-mapping algorithm for the equilibrium problem over the fixed point set of a nonexpansive semigroup
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