Abstract
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.
Original language | English |
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Pages (from-to) | 545-566 |
Number of pages | 22 |
Journal | Journal of Optimization Theory and Applications |
Volume | 175 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Nov 2017 |
Scopus Subject Areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics
User-Defined Keywords
- Expected residual minimization formulation
- Sample average approximation
- Stochastic vector variational inequalities