SOLVING TWO-STAGE STOCHASTIC VARIATIONAL INEQUALITIES BY A HYBRID PROJECTION SEMISMOOTH NEWTON ALGORITHM

A hybrid projection semismooth Newton algorithm (PSNA) is developed for solving two-stage stochastic variational inequalities; the algorithm is globally and superlinearly convergent under suitable assumptions. PSNA is a hybrid algorithm of the semismooth Newton algorithm and extragradient algorithm. At each step of PSNA, the second stage problem is split into a number of small variational inequality problems and solved in parallel for a fixed first stage decision iterate. The projection algorithm and semismooth Newton algorithm are used to find a new first stage decision iterate. Numerical results for large-scale nonmonotone two-stage stochastic variational inequalities and applications in traffic assignments show the efficiency of PSNA.