Data-Driven Chance Constrained Programs over Wasserstein Balls

被引：60

作者：

Chen, Zhi ^{[1
]}

Kuhn, Daniel ^{[2
]}

Wiesemann, Wolfram ^{[3
]}

机构：

[1] City Univ Hong Kong, Coll Business, Dept Management Sci, Kowloon Tong, Hong Kong, Peoples R China

[2] Ecole Polytech Fed Lausann, Risk Analyt & Optimizat Chair, CH-1015 Lausanne, Switzerland

[3] Imperial Coll London, Imperial Coll Business Sch, South Kensington Campus, London SW7 2AZ, England

来源：

OPERATIONS RESEARCH | 2024年 / 72卷 / 01期

基金：

瑞士国家科学基金会; 英国工程与自然科学研究理事会;

关键词：

distributionally robust optimization; ambiguous chance constraints; Wasserstein distance; DISTRIBUTIONALLY ROBUST OPTIMIZATION;

D O I：

10.1287/opre.2022.2330

中图分类号：

C93 [管理学];

学科分类号：

12 ; 1201 ; 1202 ; 120202 ;

摘要：

We provide an exact deterministic reformulation for data-driven, chanceconstrained programs over Wasserstein balls. For individual chance constraints as well as joint chance constraints with right-hand-side uncertainty, our reformulation amounts to a mixed-integer conic program. In the special case of a Wasserstein ball with the 1-norm or the ???-norm, the cone is the nonnegative orthant, and the chance-constrained program can be reformulated as a mixed-integer linear program. Our reformulation compares favorably to several state-of-the-art data-driven optimization schemes in our numerical experiments.

引用

页码：410 / 424

页数：16

共 38 条

[1] Wasserstein distributionally robust chance-constrained optimization for energy and reserve dispatch: An exact and physically-bounded formulation [J].

Arrigo, Adriano ;

Ordoudis, Christos ;

Kazempour, Jalal ;

De Greve, Zacharie ;

Toubeau, Jean-Francois ;

Vallee, Francois .

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2022, 296 (01) :304-322

[2]

Ben-Tal A., 2001, LECT MODERN CONVEX O

[3] A branch and bound method for stochastic integer problems under probabilistic constraints [J].

Beraldi, P ;

Ruszczynski, A .

OPTIMIZATION METHODS & SOFTWARE, 2002, 17 (03) :359-382

[4] ROBUST WASSERSTEIN PROFILE INFERENCE AND APPLICATIONS TO MACHINE LEARNING [J].

Blanchet, Jose ;

Kang, Yang ;

Murthy, Karthyek .

JOURNAL OF APPLIED PROBABILITY, 2019, 56 (03) :830-857

[5] Quantifying Distributional Model Risk via Optimal Transport [J].

Blanchet, Jose ;

Murthy, Karthyek .

MATHEMATICS OF OPERATIONS RESEARCH, 2019, 44 (02) :565-600

[6] Wasserstein Distance and the Distributionally Robust TSP [J].

Carlsson, John Gunnar ;

Behroozi, Mehdi ;

Mihic, Kresimir .

OPERATIONS RESEARCH, 2018, 66 (06) :1603-1624

[7] Sharing the value-at-risk under distributional ambiguity [J].

Chen, Zhi ;

Xie, Weijun .

MATHEMATICAL FINANCE, 2021, 31 (01) :531-559

[8] Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems [J].

Delage, Erick ;

Ye, Yinyu .

OPERATIONS RESEARCH, 2010, 58 (03) :595-612

[9] Optimal guaranteed return portfolios and the casino effect [J].

Dert, C ;

Oldenkamp, B .

OPERATIONS RESEARCH, 2000, 48 (05) :768-775

[10] Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations [J].

Esfahani, Peyman Mohajerin ;

Kuhn, Daniel .

MATHEMATICAL PROGRAMMING, 2018, 171 (1-2) :115-166

← 1 2 3 4 →