Deterministic Bicriteria Model for Stochastic Variational Inequalities  

作　　者：Xin-Min Yang Yong Zhao Gui-Hua Lin 

机构地区：[1]Department of Mathematics,Chongqing Normal University,Chongqing 400047,China [2]College of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,China [3]School of Management,Shanghai University,Shanghai 200444,China

出　　处：《Journal of the Operations Research Society of China》2018年第4期507-527,共21页中国运筹学会会刊（英文）

基　　金：This work was supported in part by the National Natural Science Foundation of China(Nos.11431004,11671250);the Humanity and Social Science Foundation of Ministry of Education of China(No.15YJA630034);the Innovation Program of Shanghai Municipal Education Commission(No.14ZS086).

摘　　要：We propose a deterministic bicriteria model for stochastic variational inequalities based on some existing deterministic models.We reformulate the bicriteria model into a single objective problem involving a conditional value-at-risk(CVaR)term and introduce two approximation methods for solving the single objective problem,which are based on the primal and dual formulations of CVaR,respectively.In particular,for the primal problem,we introduce a smooth approximation of CVaR and establish some properties for this approximation problem.Then,we use sample average approximation methods to deal with the single objective problem and investigate the limiting behaviors of optimal solutions and stationary points.For the dual problem,we regularize the inner maximization problem and demonstrate the convergence of the approximation.

关 键 词：Stochastic variational inequalities Bicriteria model Expected residual minimization REGULARIZATION 

分 类 号：O22[理学—运筹学与控制论]