{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T01:11:56Z","timestamp":1778548316292,"version":"3.51.4"},"reference-count":44,"publisher":"Elsevier BV","issue":"2","license":[{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2027,3,18]],"date-time":"2027-03-18T00:00:00Z","timestamp":1805328000000},"content-version":"am","delay-in-days":260,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS2318519"],"award-info":[{"award-number":["DMS2318519"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CMMI2533372"],"award-info":[{"award-number":["CMMI2533372"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["European Journal of Operational Research"],"published-print":{"date-parts":[[2026,7]]},"DOI":"10.1016\/j.ejor.2026.02.036","type":"journal-article","created":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T15:42:35Z","timestamp":1772984555000},"page":"542-561","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"title":["Distributionally robust optimal uncertainty quantification under Phi-divergence ambiguity"],"prefix":"10.1016","volume":"332","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7743-0779","authenticated-orcid":false,"given":"H.N.","family":"Nguyen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6952-7212","authenticated-orcid":false,"given":"M.A.","family":"Lejeune","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.ejor.2026.02.036_bib0001","series-title":"Uncertainty analyses in environmental sciences and hydrogeology","author":"Ababou","year":"2023"},{"issue":"2","key":"10.1016\/j.ejor.2026.02.036_bib0002","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1287\/moor.8.2.273","article-title":"Jointly constrained biconvex programming","volume":"8","author":"Al-Khayyal","year":"1983","journal-title":"Mathematics of Operations Research"},{"issue":"5","key":"10.1016\/j.ejor.2026.02.036_bib0003","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1504\/EJIE.2016.078804","article-title":"One-sided run rules control charts for monitoring the coefficient of variation in short production runs","volume":"10","author":"Amdouni","year":"2016","journal-title":"European Journal of Industrial Engineering"},{"key":"10.1016\/j.ejor.2026.02.036_bib0004","series-title":"The operations research revolution","first-page":"1","article-title":"Data-driven stochastic programming using Phi-divergences","author":"Bayraksan","year":"2015"},{"issue":"2","key":"10.1016\/j.ejor.2026.02.036_bib0005","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1287\/mnsc.1120.1641","article-title":"Robust solutions of optimization problems affected by uncertain probabilities","volume":"59","author":"Ben-Tal","year":"2013","journal-title":"Management Science"},{"key":"10.1016\/j.ejor.2026.02.036_bib0006","series-title":"Uncertainty modeling for engineering applications","author":"Canavero","year":"2019"},{"issue":"3\u20134","key":"10.1016\/j.ejor.2026.02.036_bib0007","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1002\/nav.3800090303","article-title":"Programming with linear fractional functionals","volume":"9","author":"Charnes","year":"1962","journal-title":"Naval Research Logistics Quarterly"},{"key":"10.1016\/j.ejor.2026.02.036_bib0008","article-title":"The 101 ways to measure portfolio performance","author":"Cogneau","year":"2009","journal-title":"Available at SSRN 1326076"},{"issue":"5","key":"10.1016\/j.ejor.2026.02.036_bib0009","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1057\/jam.2013.21","article-title":"Robust portfolio optimization with value-at-risk-adjusted Sharpe ratios","volume":"14","author":"Deng","year":"2013","journal-title":"Journal of Asset Management"},{"issue":"7","key":"10.1016\/j.ejor.2026.02.036_bib0010","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1287\/mnsc.13.7.492","article-title":"On nonlinear fractional programming","volume":"13","author":"Dinkelbach","year":"1967","journal-title":"Management Science"},{"issue":"3","key":"10.1016\/j.ejor.2026.02.036_bib0011","doi-asserted-by":"crossref","first-page":"1378","DOI":"10.1214\/20-AOS2004","article-title":"Learning models with uniform performance via distributionally robust optimization","volume":"49","author":"Duchi","year":"2021","journal-title":"The Annals of Statistics"},{"key":"10.1016\/j.ejor.2026.02.036_bib0012","series-title":"Operations research forum","first-page":"6","article-title":"Block coordinate Dinkelbach algorithms for solving block-structured constrained fractional optimization problems","author":"Ennouri","year":"2026"},{"issue":"1","key":"10.1016\/j.ejor.2026.02.036_bib0013","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/s10107-017-1172-1","article-title":"Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations","volume":"171","author":"Esfahani","year":"2018","journal-title":"Mathematical Programming"},{"issue":"3","key":"10.1016\/j.ejor.2026.02.036_bib0014","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/s00186-007-0161-1","article-title":"Biconvex sets and optimization with biconvex functions: A survey and extensions","volume":"66","author":"Gorski","year":"2007","journal-title":"Mathematical Methods of Operations Research"},{"issue":"3","key":"10.1016\/j.ejor.2026.02.036_bib0015","doi-asserted-by":"crossref","first-page":"1368","DOI":"10.1137\/13094712X","article-title":"Convex optimal uncertainty quantification","volume":"25","author":"Han","year":"2015","journal-title":"SIAM Journal on Optimization"},{"key":"10.1016\/j.ejor.2026.02.036_bib0016","doi-asserted-by":"crossref","DOI":"10.1016\/j.cie.2021.107600","article-title":"Monitoring the coefficient of variation: A literature review","volume":"161","author":"Jalilibal","year":"2021","journal-title":"Computers & Industrial Engineering"},{"issue":"4","key":"10.1016\/j.ejor.2026.02.036_bib0017","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1007\/s10898-020-00966-0","article-title":"Data-driven distributionally robust chance-constrained optimization with Wasserstein metric","volume":"79","author":"Ji","year":"2021","journal-title":"Journal of Global Optimization"},{"issue":"3","key":"10.1016\/j.ejor.2026.02.036_bib0018","doi-asserted-by":"crossref","first-page":"1120","DOI":"10.1287\/ijoc.2020.1002","article-title":"Data-driven optimization of reward-risk ratio measures","volume":"33","author":"Ji","year":"2021","journal-title":"INFORMS Journal on Computing"},{"issue":"1","key":"10.1016\/j.ejor.2026.02.036_bib0019","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/s10107-015-0929-7","article-title":"Data-driven chance constrained stochastic program","volume":"158","author":"Jiang","year":"2016","journal-title":"Mathematical Programming"},{"issue":"3","key":"10.1016\/j.ejor.2026.02.036_bib0020","doi-asserted-by":"crossref","first-page":"1571","DOI":"10.1007\/s11081-023-09856-2","article-title":"Distributionally robust optimization using optimal transport for Gaussian mixture models","volume":"25","author":"Kammammettu","year":"2024","journal-title":"Optimization and Engineering"},{"issue":"4","key":"10.1016\/j.ejor.2026.02.036_bib0021","doi-asserted-by":"crossref","first-page":"1539","DOI":"10.1109\/TSP.2007.911498","article-title":"Robust beamforming via worst-case SINR maximization","volume":"56","author":"Kim","year":"2008","journal-title":"IEEE Transactions on Signal Processing"},{"key":"10.1016\/j.ejor.2026.02.036_bib0022","first-page":"1","article-title":"Maximizing the Sharpe ratio and information ratio in the Barra optimizer","author":"Kopman","year":"2009","journal-title":"MSCI Barra Research"},{"key":"10.1016\/j.ejor.2026.02.036_bib0023","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1017\/S0962492924000084","article-title":"Distributionally robust optimization","volume":"34","author":"Kuhn","year":"2025","journal-title":"Acta Numerica"},{"issue":"1","key":"10.1016\/j.ejor.2026.02.036_bib0024","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10898-025-01582-6","article-title":"Distributionally robust fractional optimization of probability of exceedance","volume":"94","author":"Lejeune","year":"2026","journal-title":"Journal of Global Optimization"},{"issue":"23","key":"10.1016\/j.ejor.2026.02.036_bib0025","doi-asserted-by":"crossref","first-page":"3785","DOI":"10.3390\/math12233785","article-title":"Adaptive Douglas\u2013Rachford algorithms for biconvex optimization problem in the finite dimensional real Hilbert spaces","volume":"12","author":"Lin","year":"2024","journal-title":"Mathematics"},{"issue":"3","key":"10.1016\/j.ejor.2026.02.036_bib0026","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1007\/s10898-021-01064-5","article-title":"An objective penalty function method for biconvex programming","volume":"81","author":"Meng","year":"2021","journal-title":"Journal of Global Optimization"},{"issue":"1","key":"10.1016\/j.ejor.2026.02.036_bib0027","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s10957-022-02077-0","article-title":"Random games under elliptically distributed dependent joint chance constraints","volume":"195","author":"Nguyen","year":"2022","journal-title":"Journal of Optimization Theory and Applications"},{"key":"10.1016\/j.ejor.2026.02.036_bib0028","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.patrec.2025.04.026","article-title":"Maximizing generalized mean of trace ratios for discriminative feature learning","volume":"194","author":"Oh","year":"2025","journal-title":"Pattern Recognition Letters"},{"issue":"2","key":"10.1016\/j.ejor.2026.02.036_bib0029","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1137\/10080782X","article-title":"Optimal uncertainty quantification","volume":"55","author":"Owhadi","year":"2013","journal-title":"SIAM Review"},{"key":"10.1016\/j.ejor.2026.02.036_bib0030","doi-asserted-by":"crossref","first-page":"3036","DOI":"10.1109\/LCSYS.2023.3290362","article-title":"Distributionally robust uncertainty quantification via data-driven stochastic optimal control","volume":"7","author":"Pan","year":"2023","journal-title":"IEEE Control Systems Letters"},{"issue":"2","key":"10.1016\/j.ejor.2026.02.036_bib0031","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1007\/s11590-024-02123-y","article-title":"Approximating optimal solutions to biconvex parametric programs","volume":"19","author":"Pangia","year":"2025","journal-title":"Optimization Letters"},{"key":"10.1016\/j.ejor.2026.02.036_bib0032","doi-asserted-by":"crossref","DOI":"10.1016\/j.compositesb.2019.107681","article-title":"Stiffness-based optimization framework for the topology and fiber paths of continuous fiber composites","volume":"183","author":"Papapetrou","year":"2020","journal-title":"Composites Part B: Engineering"},{"key":"10.1016\/j.ejor.2026.02.036_bib0033","series-title":"IEEE\/ASME International conference on advanced intelligent mechatronics","first-page":"407","article-title":"Topology optimization of leaf flexures for stiffness ratio maximization in compliant mechanisms","author":"Pinskier","year":"2018"},{"issue":"1","key":"10.1016\/j.ejor.2026.02.036_bib0034","first-page":"3","article-title":"Uncertainty quantification: Artificial intelligence and machine learning in military systems","volume":"2","author":"Reed","year":"2023","journal-title":"Air & Space Operations Review"},{"key":"10.1016\/j.ejor.2026.02.036_bib0035","doi-asserted-by":"crossref","DOI":"10.1016\/j.compbiomed.2023.107441","article-title":"Application of uncertainty quantification to artificial intelligence in healthcare: A review of last decade (2013\u20132023)","volume":"165","author":"Seoni","year":"2023","journal-title":"Computers in Biology and Medicine"},{"issue":"2","key":"10.1016\/j.ejor.2026.02.036_bib0036","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1007\/s00291-016-0462-y","article-title":"Omega-CVar portfolio optimization and its worst case analysis","volume":"39","author":"Sharma","year":"2017","journal-title":"OR Spectrum"},{"issue":"10","key":"10.1016\/j.ejor.2026.02.036_bib0037","doi-asserted-by":"crossref","first-page":"2616","DOI":"10.1109\/TSP.2018.2812733","article-title":"Fractional programming for communication systems\u2013part i: Power control and beamforming","volume":"66","author":"Shen","year":"2018","journal-title":"IEEE Transactions on Signal Processing"},{"key":"10.1016\/j.ejor.2026.02.036_bib0038","series-title":"Uncertainty quantification: Theory, implementation, and applications","author":"Smith","year":"2024"},{"issue":"3","key":"10.1016\/j.ejor.2026.02.036_bib0039","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1109\/TR.2011.2161029","article-title":"System reliability optimization considering uncertainty: Minimization of the coefficient of variation for series-parallel systems","volume":"60","author":"Tekiner-Mogulkoc","year":"2011","journal-title":"IEEE Transactions on Reliability"},{"issue":"5","key":"10.1016\/j.ejor.2026.02.036_bib0040","doi-asserted-by":"crossref","first-page":"236","DOI":"10.3847\/1538-3881\/abee7d","article-title":"Improved contrast in images of exoplanets using direct signal-to-noise ratio optimization","volume":"161","author":"Thompson","year":"2021","journal-title":"The Astronomical Journal"},{"issue":"3","key":"10.1016\/j.ejor.2026.02.036_bib0041","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.orl.2023.03.015","article-title":"Distributionally robust chance constrained games under Wasserstein ball","volume":"51","author":"Xia","year":"2023","journal-title":"Operations Research Letters"},{"key":"10.1016\/j.ejor.2026.02.036_bib0042","series-title":"International conference on machine learning","first-page":"40488","article-title":"Coordinate descent methods for fractional minimization","author":"Yuan","year":"2023"},{"issue":"1","key":"10.1016\/j.ejor.2026.02.036_bib0043","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/s10589-012-9479-6","article-title":"On optimizing the sum of the Rayleigh quotient and the generalized Rayleigh quotient on the unit sphere","volume":"54","author":"Zhang","year":"2013","journal-title":"Computational Optimization and Applications"},{"key":"10.1016\/j.ejor.2026.02.036_bib0044","doi-asserted-by":"crossref","DOI":"10.1016\/j.cor.2025.106974","article-title":"Integer programming approaches for distributionally robust chance constraints with adjustable risks","volume":"177","author":"Zhang","year":"2025","journal-title":"Computers & Operations Research"}],"container-title":["European Journal of Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377221726002080?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377221726002080?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T00:31:29Z","timestamp":1778545889000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377221726002080"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7]]},"references-count":44,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,7]]}},"alternative-id":["S0377221726002080"],"URL":"https:\/\/doi.org\/10.1016\/j.ejor.2026.02.036","relation":{},"ISSN":["0377-2217"],"issn-type":[{"value":"0377-2217","type":"print"}],"subject":[],"published":{"date-parts":[[2026,7]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Distributionally robust optimal uncertainty quantification under Phi-divergence ambiguity","name":"articletitle","label":"Article Title"},{"value":"European Journal of Operational Research","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.ejor.2026.02.036","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}]}}