On Robust Solutions To Uncertain Variational Inequality Problems

The variational inequality problems has been rapied development for a long time,and has been widely used to solve the practical problems of economic,transportation,management and so on in the past few decades.However,it is inevitably that there are some uncertain variables in practice,and how to deal with the uncertain variables has been receiving widely attention.A popular approach for addressing uncertainty in variational inequality problems is by minimizing the expected residual function of the problem,to obtain a solution in the sense of minimized expect,but,one premise condition of using this approach is that we need to know the probability distributed information of the uncertain variable,while which is not easy to get in the actual problems.Further moer,for someone with a lower risk tolerance,minimizing the expected residual is not a good choice.This paper consider the uncertain variational inequality(UVI)problems with a view of robust optimization,we propose the robust counterpart of the UVI by minimizing the worst-case of the gap function of the UVI,and the conception of robust solution of the problem was proposed,some optimality conditions of the robust solution of some special UVI problems are obtained,and,we extend this approach to deal with the uncertain vector variational(UVVI)problems,we defined the robust solution of UVVI in a similar way,and also,we derived some optimality conditions of the robust solution of a class of special UVVI problems.