A projected gradient method with nonmonotonic backtracking technique for solving convex constrained monotone variational inequality problem  

作　　者：WANG Yun-juan ZHU De-tong 

机构地区：[1]School of Arts and Sci., Shanghai Dianji Univ., Shanghai 200240, China [2]Dept. of Math., Shanghai Normal Univ., Shanghai 200234, China [3]College of Business, Shanghai Normal Univ., Shanghai 200234, China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2008年第4期463-474,共12页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China (10871130);the Ph.D.Foundation of China Education Ministry (0527003);Shanghai Educational Development Foundation;the Science Foundation of Shanghai Education Committee(06A110)

摘　　要：Based on a differentiable merit function proposed by Taji, et al in “Mathematical Programming, 1993, 58： 369-383”, a projected gradient trust region method for the monotone variational inequality problem with convex constraints is presented. Theoretical analysis is given which proves that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.Based on a differentiable merit function proposed by Taji, et al in “Mathematical Programming, 1993, 58： 369-383”, a projected gradient trust region method for the monotone variational inequality problem with convex constraints is presented. Theoretical analysis is given which proves that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.

关 键 词：trust region line search projected gradient variational inequality 

分 类 号：O17[理学—数学]