ALTERNATING PROJECTION BASED PREDICTION-CORRECTION METHODS FOR STRUCTURED VARIATIONAL INEQUALITIES  

作　　者：Bing-sheng He Li-zhi Liao Mai-jian Qian 

机构地区：[1]Department of Mathematics, Nanjing University, Nanjing 210093, China [2]Department of Mathematics, Hong Kong Baptist University, Hong Kong, China [3]Department of Mathematics, California State University, FuUerton CA 92834, USA

出　　处：《Journal of Computational Mathematics》2006年第6期693-710,共18页计算数学（英文）

摘　　要：The monotone variational inequalities VI（Ω, F） have vast applications, including optimal controls and convex programming. In this paper we focus on the VI problems that have a particular splitting structure and in which the mapping F does not have an explicit form, therefore only its function values can be employed in the numerical methods for solving such problems. We study a set of numerical methods that are easily implementable. Each iteration of the proposed methods consists of two procedures. The first （prediction） procedure utilizes alternating projections to produce a predictor. The second （correction） procedure generates the new iterate via some minor computations. Convergence of the proposed methods is proved under mild conditions. Preliminary numerical experiments for some traffic equilibrium problems illustrate the effectiveness of the proposed methods.The monotone variational inequalities VI（Ω, F） have vast applications, including optimal controls and convex programming. In this paper we focus on the VI problems that have a particular splitting structure and in which the mapping F does not have an explicit form, therefore only its function values can be employed in the numerical methods for solving such problems. We study a set of numerical methods that are easily implementable. Each iteration of the proposed methods consists of two procedures. The first （prediction） procedure utilizes alternating projections to produce a predictor. The second （correction） procedure generates the new iterate via some minor computations. Convergence of the proposed methods is proved under mild conditions. Preliminary numerical experiments for some traffic equilibrium problems illustrate the effectiveness of the proposed methods.

关 键 词：Structured variational inequality MONOTONICITY Prediction-correction method. 

分 类 号：O221[理学—运筹学与控制论]