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

Qingsong Duan (), Mengwei Xu, Shaoyan Guo () and Liwei Zhang ()
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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

Asia-Pacific Journal of Operational Research (APJOR), 2018, vol. 35, issue 05, 1-24

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.

Keywords: Stochastic program; second-order conic optimization; optimal value function; solution mapping; quantitative stability (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S0217595918500318

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