广义变分不等式的一个投影型算法及收敛速度

提出一个修改的投影类型方法来求解广义变分不等式.该方法保证了校正步长的一致有正下界性.在所含函数g-单调的条件下,证明了方法的全局收敛性.在所含函数Lipschitz连续和g-强单调的条件下讨论了广义变分不等式的全局误差界,并证明了预估步长的一致有正下界性.借助于全局误差界的分析,证明了所提方法具有R-线性收敛速度.

A Projection-type Method of the General Variational Inequalities and Its Convergence Rate

In this paper,we propose a modified projection-type method of the general variational inequalities.The method ensures that the corrector stepsizes have a uniformly positive bound from below.Under the g- monotone of the underlying mapping,we prove its global convergence.Under the Lipschitz continuity and g- strong monotonicity of the underlying mapping,we give the global error bound of the general variational inequalities,and prove that the predictor stepsizes have a uniformly positive bound from below.By means of analysing the global error bound,we prove that the method has a R-linear convergence rate.