Primal–dual hybrid gradient method for distributionally robust optimization problems

Yongchao Liu; Xiaoming Yuan; Shangzhi Zeng; Jin Zhang

doi:10.1016/j.orl.2017.10.001

Primal–dual hybrid gradient method for distributionally robust optimization problems

Yongchao Liu, Xiaoming Yuan, Shangzhi Zeng, Jin Zhang^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

10 Citations (Scopus)

Abstract

We focus on the discretization approach to distributionally robust optimization (DRO) problems and propose a numerical scheme originated from the primal–dual hybrid gradient (PDHG) method that recently has been well studied in convex optimization area. Specifically, we consider the cases where the ambiguity set of the discretized DRO model is defined through the moment condition and Wasserstein metric, respectively. Moreover, we apply the PDHG to a portfolio selection problem modelled by DRO and verify its efficiency.

Original language	English
Pages (from-to)	625-630
Number of pages	6
Journal	Operations Research Letters
Volume	45
Issue number	6
DOIs	https://doi.org/10.1016/j.orl.2017.10.001
Publication status	Published - Nov 2017

User-Defined Keywords

Discretization method
Distributionally robust optimization
Moment conditions
Primal–dual hybrid gradient
Wasserstein metric

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10.1016/j.orl.2017.10.001

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@article{e0d63a3d0a0541248a3fbd8e01a07b6c,

title = "Primal–dual hybrid gradient method for distributionally robust optimization problems",

abstract = "We focus on the discretization approach to distributionally robust optimization (DRO) problems and propose a numerical scheme originated from the primal–dual hybrid gradient (PDHG) method that recently has been well studied in convex optimization area. Specifically, we consider the cases where the ambiguity set of the discretized DRO model is defined through the moment condition and Wasserstein metric, respectively. Moreover, we apply the PDHG to a portfolio selection problem modelled by DRO and verify its efficiency.",

keywords = "Discretization method, Distributionally robust optimization, Moment conditions, Primal–dual hybrid gradient, Wasserstein metric",

author = "Yongchao Liu and Xiaoming Yuan and Shangzhi Zeng and Jin Zhang",

note = "Funding Information: We would like to thank the editor for organizing an effective review and two anonymous referees for insightful comments and constructive suggestions which help us significantly consolidate the paper. The research is supported by the NSFC grants # 11571056 , # 11771255 and # 11601458 ; and the General Research Fund from Hong Kong Research Grants Council : HKBU12300515 . ",

year = "2017",

month = nov,

doi = "10.1016/j.orl.2017.10.001",

language = "English",

volume = "45",

pages = "625--630",

journal = "Operations Research Letters",

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TY - JOUR

T1 - Primal–dual hybrid gradient method for distributionally robust optimization problems

AU - Liu, Yongchao

AU - Yuan, Xiaoming

AU - Zeng, Shangzhi

AU - Zhang, Jin

N1 - Funding Information: We would like to thank the editor for organizing an effective review and two anonymous referees for insightful comments and constructive suggestions which help us significantly consolidate the paper. The research is supported by the NSFC grants # 11571056 , # 11771255 and # 11601458 ; and the General Research Fund from Hong Kong Research Grants Council : HKBU12300515 .

PY - 2017/11

Y1 - 2017/11

N2 - We focus on the discretization approach to distributionally robust optimization (DRO) problems and propose a numerical scheme originated from the primal–dual hybrid gradient (PDHG) method that recently has been well studied in convex optimization area. Specifically, we consider the cases where the ambiguity set of the discretized DRO model is defined through the moment condition and Wasserstein metric, respectively. Moreover, we apply the PDHG to a portfolio selection problem modelled by DRO and verify its efficiency.

AB - We focus on the discretization approach to distributionally robust optimization (DRO) problems and propose a numerical scheme originated from the primal–dual hybrid gradient (PDHG) method that recently has been well studied in convex optimization area. Specifically, we consider the cases where the ambiguity set of the discretized DRO model is defined through the moment condition and Wasserstein metric, respectively. Moreover, we apply the PDHG to a portfolio selection problem modelled by DRO and verify its efficiency.

KW - Discretization method

KW - Distributionally robust optimization

KW - Moment conditions

KW - Primal–dual hybrid gradient

KW - Wasserstein metric

UR - http://www.scopus.com/inward/record.url?scp=85032192162&partnerID=8YFLogxK

U2 - 10.1016/j.orl.2017.10.001

DO - 10.1016/j.orl.2017.10.001

M3 - Journal article

AN - SCOPUS:85032192162

SN - 0167-6377

VL - 45

SP - 625

EP - 630

JO - Operations Research Letters

JF - Operations Research Letters

IS - 6

ER -

Primal–dual hybrid gradient method for distributionally robust optimization problems

Abstract

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