8
IRUS Total
Downloads

On linear optimization over Wasserstein balls

File Description SizeFormat 
wasserstein.pdfAccepted version285.53 kBAdobe PDFView/Open
Title: On linear optimization over Wasserstein balls
Authors: Yue, M-C
Kuhn, D
Wiesemann, W
Item 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.
Issue Date: 1-Sep-2022
Date of Acceptance: 7-Jun-2021
URI: http://hdl.handle.net/10044/1/90115
DOI: 10.1007/s10107-021-01673-8
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/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/R045518/1
Keywords: Science & Technology
Technology
Physical Sciences
Computer Science, Software Engineering
Operations Research & Management Science
Mathematics, Applied
Computer Science
Mathematics
90C25
90C05
90C17
Science & Technology
Technology
Physical Sciences
Computer Science, Software Engineering
Operations Research & Management Science
Mathematics, Applied
Computer Science
Mathematics
90C25
90C05
90C17
Operations Research
0102 Applied Mathematics
0103 Numerical and Computational Mathematics
0802 Computation Theory and Mathematics
Publication Status: Published
Online Publication Date: 2021-06-17
Appears in Collections:Imperial College Business School