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 - Article
AN - SCOPUS:85032192162
VL - 45
SP - 625
EP - 630
JO - Operations Research Letters
JF - Operations Research Letters
SN - 0167-6377
IS - 6
ER -