Goldstein, Levitin-Polyak投影法中的一个可行步长准则  

AN IMPLEMENTABLE STEP SIZE RULE FOR GOLDSTEIN, LEVITIN-POLYAK PROJECTION METHOD

作　　者：韩德仁[1] 何炳生[1] 

机构地区：[1]南京大学数学系,南京210093

出　　处：《高等学校计算数学学报》2001年第1期56-62,共7页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金项目!19971040

摘　　要：The projection methods proposed by Goldstein, Levitin and Polyak are the simplest iterative methods for solving monotone variational inequality problems. However, it is difficult to estimate the value of Lipschitz constant L and the strongly monotone modules α, which is necessary for the determination of the step-size in the method. In this paper, we propose an implementable step-size rule, which doesn’t need the estimates of the value of L and a, and is almost as simple as the original one. Finally, we also present some numerical examples by using the proposed step size rule.The projection methods proposed by Goldstein, Levitin and Polyak are the simplest iterative methods for solving monotone variational inequality problems. However, it is difficult to estimate the value of Lipschitz constant L and the strongly monotone modules α, which is necessary for the determination of the step-size in the method. In this paper, we propose an implementable step-size rule, which doesn't need the estimates of the value of L and a, and is almost as simple as the original one. Finally, we also present some numerical examples by using the proposed step size rule.

关 键 词：Levitin-Polyak投影法 Goldstein投影法 变分不等式 投影迭代法 强单调算子 步长准则 LIPSCHITZ连续 

分 类 号：O221.2[理学—运筹学与控制论]