Individual confidence intervals for solutions to expected value formulations of stochastic variational inequalities

• 成果类型: Article
• 署名作者: Lamm, Michael; Lu, Shu; Budhiraja, Amarjit
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-016-1046-y
• 发表日期: 2017
• 页码: 151-196
• 关键词: linear complementarity-problems; residual minimization method; optimization problems; normal manifolds; approximation; regions; sets

摘要

Stochastic variational inequalities (SVIs) provide a means for modeling various optimization and equilibrium problems where data are subject to uncertainty. Often the SVI cannot be solved directly and requires a numerical approximation. This paper considers the use of a sample average approximation and proposes three methods for computing confidence intervals for components of the true solution. The first two methods use an indirect approach that requires initially computing asymptotically exact confidence intervals for the solution to the normal map formulation of the SVI. The third method directly constructs confidence intervals for the true SVI solution; intervals produced with this method meet a minimum specified level of confidence in the same situations for which the first two methods are applicable. We justify the three methods theoretically with weak convergence results, discuss how to implement these methods, and test their performance using three numerical examples.