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Quantitative stability analysis for distributionally robust optimization with moment constraints

Quantitative stability analysis for distributionally robust optimization with moment constraints
Quantitative stability analysis for distributionally robust optimization with moment constraints
In this paper we consider a broad class of distributionally robust optimization (DRO) problems where the probability of the underlying random variables depends on the decision variables and the ambiguity set is defined through parametric moment conditions with generic cone constraints. Under some moderate conditions, including Slater-type conditions of a cone constrained moment system and Hölder continuity of the underlying random functions in the objective and moment conditions, we show local Hölder continuity of the optimal value function of the inner maximization problem with respect to (w.r.t.) the decision vector and other parameters in moment conditions, and local Hölder continuity of the optimal value of the whole minimax DRO w.r.t. the parameter. Moreover, under the second order growth condition of the Lagrange dual of the inner maximization problem, we demonstrate and quantify the outer semicontinuity of the set of optimal solutions of the minimax DRO w.r.t. variation of the parameter. Finally, we apply the established stability results to two particular classes of DRO problems.
1052-6234
1855-1882
Zhang, Jie
21de2303-4727-4097-9b0f-ae43d95d052a
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Zhang, Liwei
10fce21c-16d9-4096-b07a-cf2cab1591c0
Zhang, Jie
21de2303-4727-4097-9b0f-ae43d95d052a
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Zhang, Liwei
10fce21c-16d9-4096-b07a-cf2cab1591c0

Zhang, Jie, Xu, Huifu and Zhang, Liwei (2016) Quantitative stability analysis for distributionally robust optimization with moment constraints. SIAM Journal on Optimization, 26 (3), 1855-1882.

Record type: Article

Abstract

In this paper we consider a broad class of distributionally robust optimization (DRO) problems where the probability of the underlying random variables depends on the decision variables and the ambiguity set is defined through parametric moment conditions with generic cone constraints. Under some moderate conditions, including Slater-type conditions of a cone constrained moment system and Hölder continuity of the underlying random functions in the objective and moment conditions, we show local Hölder continuity of the optimal value function of the inner maximization problem with respect to (w.r.t.) the decision vector and other parameters in moment conditions, and local Hölder continuity of the optimal value of the whole minimax DRO w.r.t. the parameter. Moreover, under the second order growth condition of the Lagrange dual of the inner maximization problem, we demonstrate and quantify the outer semicontinuity of the set of optimal solutions of the minimax DRO w.r.t. variation of the parameter. Finally, we apply the established stability results to two particular classes of DRO problems.

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More information

Accepted/In Press date: 13 June 2016
e-pub ahead of print date: 8 September 2016
Organisations: Operational Research

Identifiers

Local EPrints ID: 407318
URI: http://eprints.soton.ac.uk/id/eprint/407318
ISSN: 1052-6234
PURE UUID: b21c3463-9c01-441e-8350-1e21b49bd313
ORCID for Huifu Xu: ORCID iD orcid.org/0000-0001-8307-2920

Catalogue record

Date deposited: 01 Apr 2017 01:15
Last modified: 28 Apr 2022 01:51

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Contributors

Author: Jie Zhang
Author: Huifu Xu ORCID iD
Author: Liwei Zhang

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