解变分不等式的三步松弛混合最速下降法  

Three-Step Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities

作　　者：丁协平[1] 林炎诚 姚任之[3] 

机构地区：[1]四川师范大学数学与软件科学学院,成都610066 [2]中国医药大学公共教育中心 [3]国立中山大学应用数学系

出　　处：《应用数学和力学》2007年第8期921-928,共8页Applied Mathematics and Mechanics

基　　金：四川省教育厅重点科研基金资助项目(2003A081);四川重点学科基金资助项目(0406)

摘　　要：在Hilbert空间的非空闭凸子集上研究了具有Lipschitz和强单调算子的经典变分不等式.为求解此变分不等式引入了一类新的三步松弛混合最速下降法.在算法参数的适当假设下,证明了此算法的强收敛性.The classical variational inequality problem with a Lipschitzian and strongly monotone operator on a nonempty dosed convex subset in a real Hilbert space was studied. A new three-step relaxed hybrid steepest-descent method for this class of variational inequalities was introduced. Strong convergence of this method was established under suitable assumptions imposed on the algorithm parameters.

关 键 词：变分不等式 松弛混合最速下降法 强收敛 非扩张映射 Hillbert空间 

分 类 号：O177.92[理学—数学]