Sample average approximation method for a class of stochastic variational inequality problems

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...

Stochastic Variational Inequalities: Residual Minimization Smoothing Sample Average Approximations

Abstract. The stochastic variational inequality (SVI) has been used widely, in engineering and economics, as an effective mathematical model for a number of equilibrium problems involving uncertain data. This paper presents a new expected residual minimization (ERM) formulation for a class of SVI. The objective of the ERM-formulation is Lipschitz continuous and semismooth which helps us guarant...

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems

Strong convergence theorem for a class of multiple-sets split variational inequality problems in Hilbert spaces

In this paper, we introduce a new iterative algorithm for approximating a common solution of certain class of multiple-sets split variational inequality problems. The sequence of the proposed iterative algorithm is proved to converge strongly in Hilbert spaces. As application, we obtain some strong convergence results for some classes of multiple-sets split convex minimization problems.

Cvar–based Formulation and Approximation Method for a Class of Stochastic Variational Inequality Problems

In this paper, we consider CVaR-based formulation and approximation method proposed by Chen and Lin [5] for a class of stochastic variational inequality problems (for short, SVIP). Different from the work mentioned above, we regard the regularized gap function for SVIP as a loss function for SVIPs and obtain a restrained deterministic minimization reformulation for SVIPs. We show that the refor...