Confidence Regions for Stochastic Variational Inequalities

Symmetric Confidence Regions and Confidence Intervals for Normal Map Formulations of Stochastic Variational Inequalities

Stochastic variational inequalities (SVI) model a large class of equilibrium problems subject to data uncertainty, and are closely related to stochastic optimization problems. The SVI solution is usually estimated by a solution to a sample average approximation (SAA) problem. This paper considers the normal map formulation of an SVI, and proposes a method to build asymptotically exact confidenc...

Individual confidence intervals for true solutions to stochastic variational inequalities

Stochastic variational inequalities (SVI) provide a means for modeling various optimization and equilibrium problems where data are subject to uncertainty. Often it is necessary to estimate the true SVI solution by the solution of a sample average approximation (SAA) problem. This paper proposes three methods for building confidence intervals for components of the true solution, and those inter...

Hadamard Well-posedness for a Family of Mixed Variational Inequalities and Inclusion Problems‎

In this paper, the concepts of well-posednesses and Hadamard well-posedness for a family of mixed variational inequalities are studied. Also, some metric characterizations of them are presented and some relations between well-posedness and Hadamard well-posedness of a family of mixed variational inequalities is studied. Finally, a relation between well-posedness for the family of mixed variatio...

A probabilistic approach to second order variational inequalities with bilateral constraints

We study a class of second order nonlinear variational inequalities with bilateral constraints. This type of inequalities arises in zero sum stochastic differential games of mixed type where each player uses both continuous control and stopping times. Under a nondegeneracy assumption Bensoussan and Friedman [1,4] have studied this type of problems. They proved the existence of a unique solution...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points