TY - JOUR
AU - Wets, Roger
AB - We propose a two-stage stochastic variational inequality model to deal with random variables in variational inequalities, and formulate this model as a two-stage stochastic programming with recourse by using an expected residual minimization solution procedure. The solvability, differentiability and convexity of the two-stage stochastic programming and the convergence of its sample average approximation are established. Examples of this model are given, including the optimality conditions for stochastic programs, a Walras equilibrium problem and Wardrop flow equilibrium. We also formulate stochastic traffic assignments on arcs flow as a two-stage stochastic variational inequality based on Wardrop flow equilibrium and present numerical results of the Douglas–Rachford splitting method for the corresponding two-stage stochastic programming with recourse.
TI - Two-stage stochastic variational inequalities: an ERM-solution procedure
JO - Mathematical Programming
DO - 10.1007/s10107-017-1132-9
DA - 2017-03-14
UR - https://www.deepdyve.com/lp/springer-journals/two-stage-stochastic-variational-inequalities-an-erm-solution-k1rV50TbQv
SP - 71
EP - 111
VL - 165
IS - 1
DP - DeepDyve
ER -