Contraction of the proximal mapping and applications to the equilibrium problem

Optimization ◽  
2017 ◽  
Vol 66 (3) ◽  
pp. 381-396 ◽  
Author(s):  
Ngoc Hai Trinh
Keyword(s):  
Equilibrium Problem ◽  
Proximal Mapping

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

2018 ◽  
Vol 24 (1) ◽  
pp. 43-61
Author(s):  
Trinh Ngoc Hai ◽  
Le Qung Thuy
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Nonexpansive Semigroup ◽  
Strong Monotonicity ◽  
Fixed Point Set ◽  
Proximal Mapping ◽  
Mapping Algorithm ◽  
Point Set ◽  
Monotonicity Conditions ◽  
Weak Convergence Theorem

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.

Existence of the Solution for Equilibrium Problem

2010 ◽  
Vol 12 (1) ◽  
pp. 51-59
Author(s):  
Yanhong HU ◽  
Wen SONG
Keyword(s):  
Equilibrium Problem

Iterative algorithm for a split equilibrium problem and fixed problem for finite asymptotically nonexpansive mappings in Hlbert space

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1423-1434 ◽  
Author(s):  
Sheng Wang ◽  
Min Chen
Keyword(s):  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Fixed Point Set ◽  
Split Equilibrium Problem ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Point Set ◽  
The Common

In this paper, we propose an iterative algorithm for finding the common element of solution set of a split equilibrium problem and common fixed point set of a finite family of asymptotically nonexpansive mappings in Hilbert space. The strong convergence of this algorithm is proved.

scholarly journals Iterative Computation for Solving the Variational Inequality and the Generalized Equilibrium Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Xiujuan Pan ◽  
Shin Min Kang ◽  
Young Chel Kwun
Keyword(s):  
Variational Inequality ◽  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Convergence Result ◽  
Generalized Equilibrium Problem ◽  
Iterative Computation ◽  
Generalized Equilibrium

An iterative algorithm for solving the variational inequality and the generalized equilibrium problem has been introduced. Convergence result is given.

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