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Quantitative Stability of Two-Stage Linear Second-Order Conic Stochastic Programs with Full Random Recourse

Author

Listed:
  • Qingsong Duan

    (School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China)

  • Mengwei Xu

    (School of Mathematics, Tianjin University, Tianjin 300072, P. R. China)

  • Shaoyan Guo

    (School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China)

  • Liwei Zhang

    (School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China)

Abstract

In this paper, we consider quantitative stability for full random two-stage linear stochastic program with second-order conic constraints when the underlying probability distribution is subjected to perturbation. We first investigate locally Lipschitz continuity of feasible set mappings of the primal and dual problems in the sense of Hausdorff distance which derives the Lipschitz continuity of the objective function, and then establish the quantitative stability results of the optimal value function and the optimal solution mapping for the perturbation problem. Finally, the obtained results are applied to the convergence analysis of optimal values and solution sets for empirical approximations of the stochastic problems.

Suggested Citation

  • Qingsong Duan & Mengwei Xu & Shaoyan Guo & Liwei Zhang, 2018. "Quantitative Stability of Two-Stage Linear Second-Order Conic Stochastic Programs with Full Random Recourse," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(05), pages 1-24, October.
    • Handle: RePEc:wsi:apjorx:v:35:y:2018:i:05:n:s0217595918500318
    DOI: 10.1142/S0217595918500318
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    References listed on IDEAS

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    1. Hailin Sun & Huifu Xu, 2016. "Convergence Analysis for Distributionally Robust Optimization and Equilibrium Problems," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 377-401, May.
    2. 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.
    3. F. Maggioni & F. A. Potra & M. I. Bertocchi & E. Allevi, 2009. "Stochastic Second-Order Cone Programming in Mobile Ad Hoc Networks," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 309-328, November.
    4. Sainan Zhang & Liwei Zhang & Hongwei Zhang & Qingsong Duan, 2018. "Hadamard Directional Differentiability of the Optimal Value Function of a Quadratic Programming Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(03), pages 1-22, June.
    5. Rüdiger Schultz, 2000. "Some Aspects of Stability in Stochastic Programming," Annals of Operations Research, Springer, vol. 100(1), pages 55-84, December.
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