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Quantitative Stability of Two-stage Stochastic Linear Programs with Full Random Recourse

Jie Jiang(majiejiang***at***gmail.com)
Zhiping Chen(zchen***at***mail.xjtu.edu.cn)

Abstract: In this paper, we use the parametric programming technique and pseudo metrics to study the quantitative stability of the two-stage stochastic linear programming problem with full random recourse. Under the simultaneous perturbation of the cost vector, coefficient matrix and right-hand side vector, we first establish the locally Lipschitz continuity of the optimal value function and the boundedness of optimal solutions of parametric linear programs. On the basis of these results, we deduce the locally Lipschitz continuity and the upper bound estimation of the objective function of the two-stage stochastic linear programming problem with full random recourse. Then under moderate assumptions and different pseudo metrics, we obtain the quantitative stability results of two-stage stochastic linear programs with full random recourse, which improve the current results in terms of tractability and the necessary assumptions. Finally, we consider the empirical approximation of the two-stage stochastic programming model and derive the rate of convergence of the corresponding SAA method.

Keywords: stochastic programming; full random recourse; parametric programming; pseudo metrics; quantitative stability; empirical approximation

Category 1: Stochastic Programming

Citation:

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Entry Submitted: 04/25/2018
Entry Accepted: 05/01/2018
Entry Last Modified: 04/25/2018

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