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Quantitative stability of mixed-integer two-stage quadratic stochastic programs

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  • Zhiping Chen
  • Youpan Han

Abstract

For our introduced mixed-integer quadratic stochastic program with fixed recourse matrices, random recourse costs, technology matrix and right-hand sides, we study quantitative stability properties of its optimal value function and optimal solution set when the underlying probability distribution is perturbed with respect to an appropriate probability metric. To this end, we first establish various Lipschitz continuity results about the value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of linear constraints. The obtained results extend earlier results about quantitative stability properties of stochastic integer programming and stability results for mixed-integer parametric quadratic programs. Copyright Springer-Verlag 2012

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  • Zhiping Chen & Youpan Han, 2012. "Quantitative stability of mixed-integer two-stage quadratic stochastic programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(2), pages 149-163, April.
    • Handle: RePEc:spr:mathme:v:75:y:2012:i:2:p:149-163
    DOI: 10.1007/s00186-010-0326-1
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    References listed on IDEAS

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    1. Svetlozar T. Rachev & Werner Römisch, 2002. "Quantitative Stability in Stochastic Programming: The Method of Probability Metrics," Mathematics of Operations Research, INFORMS, vol. 27(4), pages 792-818, November.
    2. B. Curtis Eaves, 1971. "On Quadratic Programming," Management Science, INFORMS, vol. 17(11), pages 698-711, July.
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