Quasi-Monte Carlo Method For The Structured Stochastic Variational Inequalities

Variational inequalities problems are an important branch of operational research. Variational inequalities are widely used in natural science, engineering calculations, economic equilibrium, and many other disciplines. There are often many uncertain factors for practical problems, which makes the deterministic problem into a number of random problems.This paper discusses a class of special variational inequalitie—structured stochastic variational inequality, which have widely applications for supply chain network. It has great significance for research in the theory and practical applications.Firstly, a lagrange multiplier for linear constraints is introduced in the structure stochastic variational inequality, which makes the structure of random variational inequality into a relatively compact form. In the compact form, the two sub-variational inequality problems are studied.Second, variational inequality problem is changed into optimization problem through the merit function, and the equivalence between the two issues is proved.Finally, a specific algorithm is given to the structured stochastic variational inequalities, and two examples are solve by the algorithm. Numerical results show that this method is effective.