Generalized conditioning based approaches to computing confidence intervals for solutions to stochastic variational inequalities
| Autor: | Shu Lu, Michael Lamm |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
021103 operations research
General Mathematics Computation Numerical analysis 0211 other engineering and technologies Asymptotic distribution 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Confidence interval Nonlinear programming Piecewise linear function Convergence (routing) Variational inequality Applied mathematics 0101 mathematics Software Mathematics |
| Zdroj: | Mathematical Programming. 174:99-127 |
| ISSN: | 1436-4646 0025-5610 |
| Popis: | Stochastic variational inequalities (SVI) provide a unified framework for the study of a general class of nonlinear optimization and Nash-type equilibrium problems with uncertain model data. Often the true solution to an SVI cannot be found directly and must be approximated. This paper considers the use of a sample average approximation (SAA), and proposes a new method to compute confidence intervals for individual components of the true SVI solution based on the asymptotic distribution of SAA solutions. We estimate the asymptotic distribution based on one SAA solution instead of generating multiple SAA solutions, and can handle inequality constraints without requiring the strict complementarity condition in the standard nonlinear programming setting. The method in this paper uses the confidence regions to guide the selection of a single piece of a piecewise linear function that governs the asymptotic distribution of SAA solutions, and does not rely on convergence rates of the SAA solutions in probability. It also provides options to control the computation procedure and investigate effects of certain key estimates on the intervals. |
| Databáze: | OpenAIRE |
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