Confidence regions of stochastic variational inequalities: error bound approach

Liu，Yongchao1; Zhang，Jin2

2020

10.1080/02331934.2020.1857755

OPTIMIZATION   影响因子和分区

0233-1934

1029-4945

In this paper, we aim to build confidence regions of the true solution to the stochastic variational inequalities problem (SVIP) when the sample average approximation (SAA) scheme is implemented. A new approach based on error bound conditions admitted by the SVIP is proposed. This so-called error bound approach provides an upper bound of the distance between SAA solutions and the true solution set through the distance between the SAA function and the true counterpart at the SAA solutions. Certain statistical tools such as central limit theorem and Owen's empirical likelihood theorem are then employed to construct the asymptotic confidence regions of the solutions to SVIP. In particular, if the SVIP admits a global error bound condition, the non-asymptotic (uniform) confidence regions of the solutions are also approachable. Different from the conventional normal map approach, our error bound approach does not require any information regarding the derivative of the solution mapping with respect to perturbations of involved functions in SVIP. For constructing component-wise confidence regions, the validity of the error bound approach is guaranteed for those cases where the functions own separable structures.

(non-)asymptotic confidence regions empirical likelihood method Stochastic programming stochastic variational inequalities

SCI

英语

其他

National Natural Science Foundation of China[11971090,1971220]

Operations Research & Management Science ; Mathematics

Operations Research & Management Science ; Mathematics, Applied

WOS:000597806100001

TAYLOR & FRANCIS LTD

MATHEMATICS

2-s2.0-85097439187

Scopus

1.School of Mathematical Sciences,Dalian University of Technology,Dalian,China
2.Department of Mathematics,SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,China

Liu，Yongchao,Zhang，Jin. Confidence regions of stochastic variational inequalities: error bound approach[J]. OPTIMIZATION,2020.

Liu，Yongchao,&Zhang，Jin.(2020).Confidence regions of stochastic variational inequalities: error bound approach.OPTIMIZATION.

Liu，Yongchao,et al."Confidence regions of stochastic variational inequalities: error bound approach".OPTIMIZATION (2020).