Distributionally robust optimization with marginals : theory and applications

In this thesis, we consider distributionally robust optimization (DRO) problems in which the ambiguity sets are designed from marginal distribution information - more specifically, when the ambiguity set includes any distribution whose marginals are consistent with given prescribed distributions that have been estimated from data. In the first chapter, we study the class of linear and discrete optimization problems in which the objective coefficients are chosen randomly from a distribution, and the goal is to evaluate robust bounds on the expected optimal value as well as the marginal distribution of the optimal solution. The set of joint distributions is assumed to be specified up to only the marginal distributions. We generalize the primal-dual formulations for this problem from the set of joint distributions with absolutely continuous marginal distributions to arbitrary marginal distributions using techniques from optimal transport theory.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Operations Research Center

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2019

Author dc:creator

• Chen, Louis Lester.

Advisor dc:contributor.advisor

• David Simchi-Levi.

• Operations Research Center.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/123731

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/123731