TY - JOUR
T1 - A family of extragradient methods for solving equilibrium problems
AU - Nguyen, Thi Phuong Dong
AU - Strodiot, Jean-Jacques
AU - Van Nguyen, Thi Thu
AU - Nguyen, Van Hien
PY - 2015
Y1 - 2015
N2 - In this paper we introduce a class of numerical methods for solving an equilibrium problem. This class depends on a parameter and contains the classical extragradient method and a generalization of the two-step extragradient method proposed recently by Zykina and Melen'chuk for solving variational inequality problems. Convergence of each algorithm of this class to a solution of the equilibrium problem is obtained under the condition that the equilibrium function associated with the problem is pseudomonotone and Lipschitz continuous. Some preliminary numerical results are given to compare the numerical behavior of the two-step extragradient method with respect to the other methods of the class and in particular to the extragradient method.
AB - In this paper we introduce a class of numerical methods for solving an equilibrium problem. This class depends on a parameter and contains the classical extragradient method and a generalization of the two-step extragradient method proposed recently by Zykina and Melen'chuk for solving variational inequality problems. Convergence of each algorithm of this class to a solution of the equilibrium problem is obtained under the condition that the equilibrium function associated with the problem is pseudomonotone and Lipschitz continuous. Some preliminary numerical results are given to compare the numerical behavior of the two-step extragradient method with respect to the other methods of the class and in particular to the extragradient method.
KW - Equilibrium problems
KW - Extragradient method
KW - Two-step extragradient method
KW - Variational inequalities
UR - http://www.scopus.com/inward/record.url?scp=84907164422&partnerID=8YFLogxK
U2 - 10.3934/jimo.2015.11.619
DO - 10.3934/jimo.2015.11.619
M3 - Article
AN - SCOPUS:84907164422
SN - 1547-5816
VL - 11
SP - 619
EP - 630
JO - Journal of Industrial and Management Optimization
JF - Journal of Industrial and Management Optimization
IS - 2
ER -