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Quantitative Stability Analysis in Distributionally Robust Optimization

Banff International Research Station for Mathematical Innovation and Discovery

Ambiguity set is a key element in distributionally robust optimization models. Here we investigate the impact of perturbation of ambiguity set on the optimal value and the optimal solutions. We consider the case where the ambiguity set is defined through generalized prior moment conditions and the perturbation is caused by (a) increasing sample data to be used in the moment system and (b) discretization of the moment system. We quantify the perturbation against change of sample data or refinement of discretization and its impact on the underlying optimization problem. We also consider the case where the ambiguity set is constructed through zeta-ball and extend the analysis to a two-stage distributionally robust risk minimization problem and a distributionally robust chance constrained optimization problem.

Mathematics; Operations research, mathematical programming; Probability theory and stochastic processes; Operation research

video/mp4

Author affiliation: University of Southampton

2018-09-02

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/67062

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/