广义变分不等式的一个投影型算法及收敛速度  

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

作　　者：孙洪春[1] 孙敏[1] 李国成[2] 

机构地区：[1]曲阜师范大学运筹与管理学院,山东日照276826 [2]临沂师范学院蒙山学院,山东费县273400

出　　处：《重庆师范大学学报（自然科学版）》2005年第3期53-57,共5页Journal of Chongqing Normal University:Natural Science

摘　　要：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L ipsch itz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。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.

关 键 词：广义变分不等式 投影收缩方法 全局收敛性 全局误差界 R-线性收敛 

分 类 号：O221.2[理学—运筹学与控制论]