A randomized progressive hedging algorithm for stochastic variational inequality

Recently, stochastic variational inequality (SVI) has been extended from single stage to multistage by Rockafellar and Wets (Math. Program., 165:331-360, 2017) progressive hedging algorithm (PHA) also programming linear complementarity SVI Sun 174:453-471, 2019). However, the per-iteration cost of PHA can be prohibitively high when scenario set is large, despite decomposition parallelizable nature algorithm. To address this issue, we propose a randomized that allows us control randomly selecting small subset scenarios updating only corresponding variable components while freezing variables unselected at current iteration. By measuring quality an approximate solution using restricted merit function, demonstrate significant reduction in cost, converges expectation ergodic sense same sublinear rate as original PHA.