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Quantitative stability of fully random two-stage stochastic programs with mixed-integer recourse

  • Zhiping ChenEmail author
  • Jie Jiang
Original Paper
  • 16 Downloads

Abstract

The quantitative stability and empirical approximation of two-stage stochastic programs with mixed-integer recourse are investigated. We first study the boundedness of optimal solutions to the second stage problem by utilizing relevant results for parametric (mixed-integer) linear programs. After that, we reestablish existing quantitative stability results with fixed recourse matrices by adopting different probability metrics. This helps us to extend our stability results to the fully random case under the boundedness assumption of integer variables. Finally, we consider the issue of empirical approximation, and the exponential rates of convergence of the optimal value function and the optimal solution set are derived when the support set is countable but may be unbounded.

Keywords

Stochastic programming Mixed-integer recourse Quantitative stability Fully random Probability metric Exponential convergence 

Notes

Acknowledgements

The authors are grateful to the relevant editors and two anonymous reviewers for their detailed and insightful comments and suggestions, which have led to a substantial improvement of the paper in both content and style.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anChina

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