CONTRACTION-MAPPING ALGORITHM FOR THE EQUILIBRIUM PROBLEM OVER THE FIXED POINT SET OF A NONEXPANSIVE SEMIGROUP

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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Veröffentlicht in:Mathematical modelling and analysis 2019-01, Vol.24 (1), p.43-61
Hauptverfasser: Hai, Trinh Ngoc, Thuy, Le Qung
Format: Artikel
Sprache:eng
Schlagworte:
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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Beschreibung
Zusammenfassung: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.
ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2019.004