Variational Inequality And Algorithm In Hilbert Space

This thesis is concerned with algorithms for solving variational inequalities in Hilbert space. In Chapter one, a system of generalized-Quasi-Variational-Like inequalities is introduced, a new iterative algorithm is suggested and analyzed, strong convergence of this method is proved. In Chapter two, an extra-gradient projection method for general variational inequalities on R~n is proposed, which has a better performance in computational experience than some known in the literature. Under some mild assumptions, global convergence is proved and convergence rate is analyzed. In Chapter three, a general framework of expansive-extra-gradient projection method for classic variational inequalities is proposed. A new efficient algorithm is put forward by computational experience.