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On linear optimization over Wasserstein balls
File(s)
wasserstein.pdf (285.53 KB)
Accepted version
Author(s)
Yue, Man-Chung
Kuhn, Daniel
Wiesemann, Wolfram
Type
Journal Article
Abstract
Wasserstein balls, which contain all probability measures within a pre-specified Wasserstein distance to a reference measure, have recently enjoyed wide popularity in the distributionally robust optimization and machine learning communities to formulate and solve data-driven optimization problems with rigorous statistical guarantees. In this technical note we prove that the Wasserstein ball is weakly compact under mild conditions, and we offer necessary and sufficient conditions for the existence of optimal solutions. We also characterize the sparsity of solutions if the Wasserstein ball is centred at a discrete reference measure. In comparison with the existing literature, which has proved similar results under different conditions, our proofs are self-contained and shorter, yet mathematically rigorous, and our necessary and sufficient conditions for the existence of optimal solutions are easily verifiable in practice.
Date Issued
2022-09-01
Date Acceptance
2021-06-07
Citation
Mathematical Programming, 2022, 195, pp.1107-1122
URI
URL
DOI
ISSN
0025-5610
Publisher
Springer
Start Page
1107
End Page
1122
Journal / Book Title
Mathematical Programming
Volume
195
Copyright Statement
© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2021. The final publication is available at Springer via https://doi.org/10.1007/s10107-021-01673-8
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000662825900001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
EP/R045518/1
Subjects
Science & Technology
Technology
Physical Sciences
Computer Science, Software Engineering
Operations Research & Management Science
Mathematics, Applied
Computer Science
Mathematics
90C25
90C05
90C17
Publication Status
Published
Date Publish Online
2021-06-17