An LQP-Based Two-Step Method for Structured Variational Inequalities  

作　　者：Hong-Jin He Kai Wang Xing-Ju Cai De-Ren Han 

机构地区：[1]Department of Mathematics,School of Science,Hangzhou Dianzi University,Hangzhou 310018,China [2]School of Mechanical and Aerospace Engineering,Nanyang Technological University,Singapore 639798,Singapore [3]School of Mathematical Sciences,Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems,Nanjing Normal University,Nanjing 210023,China

出　　处：《Journal of the Operations Research Society of China》2017年第3期301-317,共17页中国运筹学会会刊（英文）

基　　金：the National Natural Science Foundation of China(Nos.11571087 and 71471051);the National Natural Science Foundation of Zhejiang Province(No.LY17A010028);The third author is supported by the National Natural Science Foundation of China(Nos.11431002 and 11401315);Jiangsu Provincial National Natural Science Foundation of China(No.BK20140914).

摘　　要：t The logarithmic quadratic proximal(LQP)regularization is a popular and powerful proximal regularization technique for solving monotone variational inequalities with nonnegative constraints.In this paper,we propose an implementable two-step method for solving structured variational inequality problems by combining LQP regularization and projection method.The proposed algorithm consists of two parts.The first step generates a pair of predictors via inexactly solving a system of nonlinear equations.Then,the second step updates the iterate via a simple correction step.We establish the global convergence of the new method under mild assumptions.To improve the numerical performance of our new method,we further present a self-adaptive version and implement it to solve a traffic equilibrium problem.The numerical results further demonstrate the efficiency of the proposed method.

关 键 词：Logarithmic quadratic proximal Projection method Variational inequality problem Traffic equilibrium problem 

分 类 号：O17[理学—数学]