Department of Mathematics
This paper considers a class of vector variational inequalities. First, we present an equivalent formulation, which is a scalar variational inequality, for the deterministic vector variational inequality. Then we concentrate on the stochastic circumstance. By noting that the stochastic vector variational inequality may not have a solution feasible for all realizations of the random variable in general, for tractability, we employ the expected residual minimization approach, which aims at minimizing the expected residual of the so-called regularized gap function. We investigate the properties of the expected residual minimization problem, and furthermore, we propose a sample average approximation method for solving the expected residual minimization problem. Comprehensive convergence analysis for the approximation approach is established as well.
Stochastic vector variational inequalities, Expected residual minimization formulation, Sample average approximation
Source Publication Title
Journal of Optimization Theory and Applications
The final publication is available at link.springer.com via http://dx.doi.org/10.1007/s10957-016-0939-5
Link to Publisher's Edition
Zhao, Y., Zhang, J., Yang, X., & Lin, G. (2016). Expected residual minimization formulation for a class of stochastic vector variational inequalities. Journal of Optimization Theory and Applications, 175 (2), 545-566. https://doi.org/10.1007/s10957-016-0939-5