A gradient-based methodology for the analysis of stochastic variational inequalities

We propose to develop a new methodology to analyze Stochastic Variational Inequalities. Our goal is to reduce the computational effort associated with “brute force” simulation techniques that generate a large sample, size N, of solutions for the parametric form of these stochastic problems. Our methodology generates a sample of N solutions without solving all N parametric problems by using the gradient information at actual solutions to estimate some of the N solutions. We present and illustrate methodologies for problems with single and multiple parameters. To demonstrate our method's efficacy we include the analysis of an application of our methodology to a spatial price equilibrium model of the United States interstate natural gas pipeline. We use quasi-Monte Carlo sampling techniques and discuss how other sampling techniques may be employed. Our results are very encouraging. We obtain results using our method that are similar to those attained using a simulation technique while significantly reducing burdensome computation. We hope that our results will encourage systems engineering analysts to abandon the current practice of using point estimates in place of uncertain parameters when analyzing Stochastic Variational Inequalities.