Release Time:2019-11-04  Hits:

Indexed by: Journal Papers

Date of Publication: 2019-08-03

Journal: OPTIMIZATION

Included Journals: SCIE

Volume: 68

Issue: 8

Page Number: 1551-1576

ISSN: 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.