TY - JOUR
T1 - Hybrid Methods for Solving Simultaneously an Equilibrium Problem and Countably Many Fixed Point Problems in a Hilbert Space
AU - Nguyen, Thi Thu Van
AU - Strodiot, Jean-Jacques
AU - Nguyen, Van Hien
PY - 2013/12/11
Y1 - 2013/12/11
N2 - This paper presents a framework of iterative methods for finding a common solution to an equilibrium problem and a countable number of fixed point problems defined in a Hilbert space. A general strong convergence theorem is established under mild conditions. Two hybrid methods are derived from the proposed framework in coupling the fixed point iterations with the iterations of the proximal point method or the extragradient method, which are well-known methods for solving equilibrium problems. The strategy is to obtain the strong convergence from the weak convergence of the iterates without additional assumptions on the problem data. To achieve this aim, the solution set of the problem is outer approximated by a sequence of polyhedral subsets.
AB - This paper presents a framework of iterative methods for finding a common solution to an equilibrium problem and a countable number of fixed point problems defined in a Hilbert space. A general strong convergence theorem is established under mild conditions. Two hybrid methods are derived from the proposed framework in coupling the fixed point iterations with the iterations of the proximal point method or the extragradient method, which are well-known methods for solving equilibrium problems. The strategy is to obtain the strong convergence from the weak convergence of the iterates without additional assumptions on the problem data. To achieve this aim, the solution set of the problem is outer approximated by a sequence of polyhedral subsets.
KW - Armijo backtracking linesearch
KW - Equilibrium problems
KW - Fixed-point problems
KW - Hybrid extragradient methods
KW - Proximal point method
KW - Variational inequalities
UR - http://www.scopus.com/inward/record.url?scp=84889248004&partnerID=8YFLogxK
U2 - 10.1007/s10957-013-0400-y
DO - 10.1007/s10957-013-0400-y
M3 - Article
SN - 0022-3239
SP - 1
EP - 23
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
ER -