TY - JOUR
T1 - A class of shrinking projection extragradient methods for solving non-monotone equilibrium problems in Hilbert spaces
AU - Strodiot, Jean Jacques
AU - Vuong, Phan Tu
AU - Nguyen, Thi Thu Van
PY - 2016/1/1
Y1 - 2016/1/1
N2 - A new class of extragradient-type methods is introduced for solving an equilibrium problem in a real Hilbert space without any monotonicity assumption on the equilibrium function. The strategy is to replace the second projection step in the classical extragradient method by a projection onto shrinking convex subsets of the feasible set. Furthermore, to ensure a sufficient decrease on the equilibrium function, a general Armijo-type condition is imposed. This condition is shown to be satisfied for four different linesearches used in the literature. Then, the weak and strong convergence of the resulting algorithms is obtained under non-monotonicity assumptions. Finally, some numerical experiments are reported.
AB - A new class of extragradient-type methods is introduced for solving an equilibrium problem in a real Hilbert space without any monotonicity assumption on the equilibrium function. The strategy is to replace the second projection step in the classical extragradient method by a projection onto shrinking convex subsets of the feasible set. Furthermore, to ensure a sufficient decrease on the equilibrium function, a general Armijo-type condition is imposed. This condition is shown to be satisfied for four different linesearches used in the literature. Then, the weak and strong convergence of the resulting algorithms is obtained under non-monotonicity assumptions. Finally, some numerical experiments are reported.
KW - Extragradient methods
KW - Non-monotone equilibrium problems
KW - Shrinking projection methods
KW - Strong convergence
KW - Weak convergence
UR - http://www.scopus.com/inward/record.url?scp=84952717987&partnerID=8YFLogxK
U2 - 10.1007/s10898-015-0365-5
DO - 10.1007/s10898-015-0365-5
M3 - Article
AN - SCOPUS:84952717987
SN - 0925-5001
VL - 64
SP - 159
EP - 178
JO - Journal of Global Optimization
JF - Journal of Global Optimization
IS - 1
ER -