TY - JOUR
T1 - A new class of hybrid extragradient algorithms for solving quasi-equilibrium problems
AU - Strodiot, Jean-Jacques
AU - Nguyen, Thi Thu Van
AU - Nguyen, Van Hien
PY - 2013/6/1
Y1 - 2013/6/1
N2 - Generalized Nash equilibrium problems are important examples of quasi-equilibrium problems. The aim of this paper is to study a general class of algorithms for solving such problems. The method is a hybrid extragradient method whose second step consists in finding a descent direction for the distance function to the solution set. This is done thanks to a linesearch. Two descent directions are studied and for each one several steplengths are proposed to obtain the next iterate. A general convergence theorem applicable to each algorithm of the class is presented. It is obtained under weak assumptions: the pseudomonotonicity of the equilibrium function and the continuity of the multivalued mapping defining the constraint set of the quasi-equilibrium problem. Finally some preliminary numerical results are displayed to show the behavior of each algorithm of the class on generalized Nash equilibrium problems.
AB - Generalized Nash equilibrium problems are important examples of quasi-equilibrium problems. The aim of this paper is to study a general class of algorithms for solving such problems. The method is a hybrid extragradient method whose second step consists in finding a descent direction for the distance function to the solution set. This is done thanks to a linesearch. Two descent directions are studied and for each one several steplengths are proposed to obtain the next iterate. A general convergence theorem applicable to each algorithm of the class is presented. It is obtained under weak assumptions: the pseudomonotonicity of the equilibrium function and the continuity of the multivalued mapping defining the constraint set of the quasi-equilibrium problem. Finally some preliminary numerical results are displayed to show the behavior of each algorithm of the class on generalized Nash equilibrium problems.
KW - Generalized Nash equilibrium problems
KW - Hybrid extragradient methods
KW - Quasi-equilibrium problems
KW - Quasi-variational inequalities
UR - http://www.scopus.com/inward/record.url?scp=84879012406&partnerID=8YFLogxK
U2 - 10.1007/s10898-011-9814-y
DO - 10.1007/s10898-011-9814-y
M3 - Article
AN - SCOPUS:84879012406
SN - 0925-5001
VL - 56
SP - 373
EP - 397
JO - Journal of Global Optimization
JF - Journal of Global Optimization
IS - 2
ER -