TY - JOUR
T1 - Expected Residual Minimization Formulation for a Class of Stochastic Vector Variational Inequalities
AU - Zhao, Yong
AU - Zhang, Jin
AU - Yang, Xinmin
AU - Lin, Gui-Hua
N1 - Publisher Copyright:
© 2016, Springer Science+Business Media New York.
PY - 2017/11/1
Y1 - 2017/11/1
N2 - 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.
AB - 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.
KW - Expected residual minimization formulation
KW - Sample average approximation
KW - Stochastic vector variational inequalities
UR - http://www.scopus.com/inward/record.url?scp=84964453016&partnerID=8YFLogxK
U2 - 10.1007/s10957-016-0939-5
DO - 10.1007/s10957-016-0939-5
M3 - Journal article
AN - SCOPUS:84964453016
SN - 0022-3239
VL - 175
SP - 545
EP - 566
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 2
ER -