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Quantitative stability of full random two-stage stochastic programs with recourse

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Abstract

In this paper, we consider quantitative stability analysis for two-stage stochastic linear programs when recourse costs, the technology matrix, the recourse matrix and the right-hand side vector are all random. For this purpose, we first investigate continuity properties of parametric linear programs. After deriving an explicit expression for the upper bound of its feasible solutions, we establish locally Lipschitz continuity of the feasible solution sets of parametric linear programs. These results are then applied to prove continuity of the generalized objective function derived from the full random second-stage recourse problem, from which we derive new forms of quantitative stability results of the optimal value function and the optimal solution set with respect to the Fortet–Mourier probability metric. The obtained results are finally applied to establish asymptotic behavior of an empirical approximation algorithm for full random two-stage stochastic programs.

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Acknowledgments

This research was supported by the National Natural Science Foundation of China (Grant Numbers 70971109, 71371152). and the first author was also supported by the Talents Fund of Xi’an Polytechnic University (Grant Number BS1320)

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Authors and Affiliations

  1. Department of Computing Science, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, People’s Republic of China

    Youpan Han & Zhiping Chen

  2. School of Science, Xi’an Polytechnic University, Xi’an, 710048, Shaanxi, People’s Republic of China

    Youpan Han

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  1. Youpan Han
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  2. Zhiping Chen
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Correspondence to Zhiping Chen.

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Han, Y., Chen, Z. Quantitative stability of full random two-stage stochastic programs with recourse. Optim Lett 9, 1075–1090 (2015). https://doi.org/10.1007/s11590-014-0827-6

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  • DOI: https://doi.org/10.1007/s11590-014-0827-6

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