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Indexed by:Journal Papers

Date of Publication:2019-08-03

Journal:OPTIMIZATION

Included Journals:SCIE

Volume:68

Issue:8

Page Number:1551-1576

ISSN No.:0233-1934

Key Words:Stochastic programming; quadratic programming; Fortet-Mourier metric; asymptotic behaviour

Abstract:In this paper, we discuss quantitative stability of two-stage stochastic programs with quadratic recourse where all parameters in the second-stage problem are random. By establishing the Lipschitz continuity of the feasible set mapping of the restricted Wolfe dual of the second-stage quadratic programming in terms of the Hausdorff distance, we prove the local Lipschitz continuity of the integrand of the objective function of the two-stage stochastic programming problem and then establish quantitative stability results of the optimal values and the optimal solution sets when the underlying probability distribution varies under the Fortet-Mourier metric. Finally, the obtained results are applied to study the asymptotic behaviour of the empirical approximation of the model.