Institut für Mathematik
We introduce three projection type methods for stochastic variational inequalities. The first one considers stochastic variational inequalities with monotone operators defined as the expected value of a random operator. We assume the feasible set is the intersection of a large family of convex sets. We propose a method that combines stochastic approximation with incremental constraint projections meaning that at each iteration, a step similar to some variant of a deterministic projection method is taken after the random operator is sampled and a component of the intersection defining the feasible set is chosen at random. Such sequential scheme is well suited for applications involving large data sets, online opti- mization and distributed learning. In the second one we propose an extragradient method with stepsizes bounded away from zero for stochastic variational inequalities requiring only pseudo-monotonicity. We provide convergence and complexity analysis, allowing for an un- bounded feasible set, unbounded operator, non-uniform variance of the oracle and, also, we do not require any regularization. In the third one we propose an stochastic extragradient method for stochastic variational inequalities with a linear search, requiring only pseudo- monotonicity of the operator and no knowledge of the Lipschitz constant L. We provide convergence and complexity analysis, allowing for an unbounded feasible set, unbounded operator, non-uniform variance of the oracle and we do not require any regularization.
Prof. Alfredo N. Iusem (IMPA, Rio de Janeiro, Brazil)
Senka Omerhodzic (senka.omerhodzic [at] aau.at)