{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T06:06:10Z","timestamp":1760853970748},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Manag Sci"],"published-print":{"date-parts":[[2018,1]]},"DOI":"10.1007\/s10287-018-0298-9","type":"journal-article","created":{"date-parts":[[2018,1,17]],"date-time":"2018-01-17T04:46:24Z","timestamp":1516164384000},"page":"111-134","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["A data-driven distributionally robust bound on the expected optimal value of uncertain mixed 0-1 linear programming"],"prefix":"10.1007","volume":"15","author":[{"given":"Guanglin","family":"Xu","sequence":"first","affiliation":[]},{"given":"Samuel","family":"Burer","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,1,17]]},"reference":[{"issue":"4","key":"298_CR1","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1002\/rsa.1015","volume":"18","author":"DJ Aldous","year":"2001","unstructured":"Aldous DJ (2001) The $$\\zeta $$ \u03b6 (2) limit in the random assignment problem. Random Struct Algorithms 18(4):381\u2013418","journal-title":"Random Struct Algorithms"},{"issue":"2\u20133","key":"298_CR2","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1007\/s10898-008-9372-0","volume":"43","author":"KM Anstreicher","year":"2009","unstructured":"Anstreicher KM (2009) Semidefinite programming versus the reformulation-linearization technique for nonconvex quadratically constrained quadratic programming. J Glob Optim 43(2\u20133):471\u2013484","journal-title":"J Glob Optim"},{"issue":"2","key":"298_CR3","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1287\/mnsc.1120.1641","volume":"59","author":"A Ben-Tal","year":"2013","unstructured":"Ben-Tal A, Den Hertog D, De Waegenaere A, Melenberg B, Rennen G (2013) Robust solutions of optimization problems affected by uncertain probabilities. Manag Sci 59(2):341\u2013357","journal-title":"Manag Sci"},{"issue":"3","key":"298_CR4","doi-asserted-by":"publisher","first-page":"780","DOI":"10.1137\/S1052623401399903","volume":"15","author":"D Bertsimas","year":"2005","unstructured":"Bertsimas D, Popescu I (2005) Optimal inequalities in probability theory: a convex optimization approach. SIAM J Optim 15(3):780\u2013804","journal-title":"SIAM J Optim"},{"issue":"1","key":"298_CR5","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1137\/S1052623403430610","volume":"15","author":"D Bertsimas","year":"2004","unstructured":"Bertsimas D, Natarajan K, Teo C-P (2004) Probabilistic combinatorial optimization: moments, semidefinite programming, and asymptotic bounds. SIAM J Optim 15(1):185\u2013209","journal-title":"SIAM J Optim"},{"issue":"2","key":"298_CR6","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1007\/s10107-006-0710-z","volume":"108","author":"D Bertsimas","year":"2006","unstructured":"Bertsimas D, Natarajan K, Teo C-P (2006) Persistence in discrete optimization under data uncertainty. Math Program 108(2):251\u2013274","journal-title":"Math Program"},{"key":"298_CR7","unstructured":"Bertsimas D, Gupta V, Kallus N (2013) Data-driven robust optimization. arXiv preprint arXiv:1401.0212"},{"key":"298_CR8","unstructured":"Bertsimas D, Gupta V, Kallus N (2014) Robust SAA. arXiv preprint arXiv:1408.4445"},{"issue":"1","key":"298_CR9","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1287\/mnsc.41.1.58","volume":"41","author":"RA Bowman","year":"1995","unstructured":"Bowman RA (1995) Efficient estimation of arc criticalities in stochastic activity networks. Manag Sci 41(1):58\u201367","journal-title":"Manag Sci"},{"issue":"2","key":"298_CR10","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1007\/s10107-008-0223-z","volume":"120","author":"S Burer","year":"2009","unstructured":"Burer S (2009) On the copositive representation of binary and continuous nonconvex quadratic programs. Math Program 120(2):479\u2013495","journal-title":"Math Program"},{"key":"298_CR11","doi-asserted-by":"crossref","unstructured":"Burer S (2012) Copositive programming. In: Handbook on semidefinite, conic and polynomial optimization, Springer, pp 201\u2013218","DOI":"10.1007\/978-1-4614-0769-0_8"},{"issue":"1","key":"298_CR12","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/s10107-015-0888-z","volume":"151","author":"S Burer","year":"2015","unstructured":"Burer S (2015) A gentle, geometric introduction to copositive optimization. Math Program 151(1):89\u2013116","journal-title":"Math Program"},{"key":"298_CR13","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/j.orl.2012.02.001","volume":"40","author":"S Burer","year":"2012","unstructured":"Burer S, Dong H (2012) Representing quadratically constrained quadratic programs as generalized copositive programs. Oper Res Lett 40:203\u2013206","journal-title":"Oper Res Lett"},{"issue":"1","key":"298_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10957-006-9084-x","volume":"130","author":"GC Calafiore","year":"2006","unstructured":"Calafiore GC, Ghaoui LEl (2006) On distributionally robust chance-constrained linear programs. J Optim Theory Appl 130(1):1\u201322","journal-title":"J Optim Theory Appl"},{"key":"298_CR15","unstructured":"Chen Z, Sim M, Xu H (2016) Distributionally robust optimization with infinitely constrained ambiguity sets. Working Paper"},{"issue":"3","key":"298_CR16","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1287\/opre.1090.0741","volume":"58","author":"E Delage","year":"2010","unstructured":"Delage E, Ye Y (2010) Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper Res 58(3):595\u2013612","journal-title":"Oper Res"},{"issue":"4","key":"298_CR17","doi-asserted-by":"publisher","first-page":"862","DOI":"10.1287\/opre.33.4.862","volume":"33","author":"B Dodin","year":"1985","unstructured":"Dodin B (1985) Bounding the project completion time distribution in pert networks. Oper Res 33(4):862\u2013881","journal-title":"Oper Res"},{"key":"298_CR18","unstructured":"Duchi J, Glynn P, Namkoong H (2016) Statistics of robust optimization: a generalized empirical likelihood approach. arXiv preprint arXiv:1610.03425"},{"issue":"1","key":"298_CR19","first-page":"73","volume":"20","author":"J Dupa\u010dov\u00e1","year":"1987","unstructured":"Dupa\u010dov\u00e1 J (1987) The minimax approach to stochastic programming and an illustrative application. Stoch Int J Probab Stoch Process 20(1):73\u201388","journal-title":"Stoch Int J Probab Stoch Process"},{"key":"298_CR20","first-page":"767","volume":"15","author":"G Eichfelder","year":"2008","unstructured":"Eichfelder G, Jahn J (2008) Set-semidefinite optimization. J Convex Anal 15:767\u2013801","journal-title":"J Convex Anal"},{"issue":"4","key":"298_CR21","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1287\/opre.51.4.543.16101","volume":"51","author":"L Ghaoui El","year":"2003","unstructured":"El Ghaoui L, Oks M, Oustry F (2003) Worst-case value-at-risk and robust portfolio optimization: a conic programming approach. Oper Res 51(4):543\u2013556","journal-title":"Oper Res"},{"issue":"1\u20132","key":"298_CR22","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/s10107-005-0678-0","volume":"107","author":"E Erdo\u011fan","year":"2006","unstructured":"Erdo\u011fan E, Iyengar G (2006) Ambiguous chance constrained problems and robust optimization. Math Program 107(1\u20132):37\u201361","journal-title":"Math Program"},{"key":"298_CR23","unstructured":"Esfahani PM, Kuhn D (2015) Data-driven distributionally robust optimization using the wasserstein metric: performance guarantees and tractable reformulations. arXiv preprint arXiv:1505.05116"},{"issue":"2","key":"298_CR24","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1007\/BF02579273","volume":"1","author":"M Gr\u00f6tschel","year":"1981","unstructured":"Gr\u00f6tschel M, Lov\u00e1sz L, Schrijver A (1981) The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1(2):169\u2013197","journal-title":"Combinatorica"},{"issue":"2","key":"298_CR25","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1002\/net.3230180206","volume":"18","author":"JN Hagstrom","year":"1988","unstructured":"Hagstrom JN (1988) Computational complexity of pert problems. Networks 18(2):139\u2013147","journal-title":"Networks"},{"key":"298_CR26","unstructured":"Halliwell LJ (2015) The lognormal random multivariate. In: Casualty actuarial society E-Forum, Spring"},{"key":"298_CR27","unstructured":"Hanasusanto GA, Kuhn D (2016) Conic programming reformulations of two-stage distributionally robust linear programs over wasserstein balls. arXiv preprint arXiv:1609.07505"},{"issue":"1","key":"298_CR28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10107-014-0776-y","volume":"152","author":"GA Hanasusanto","year":"2015","unstructured":"Hanasusanto GA, Kuhn D, Wallace SW, Zymler S (2015) Distributionally robust multi-item newsvendor problems with multimodal demand distributions. Math Program 152(1):1\u201332","journal-title":"Math Program"},{"issue":"3","key":"298_CR29","doi-asserted-by":"publisher","first-page":"751","DOI":"10.1287\/opre.2016.1583","volume":"65","author":"GA Hanasusanto","year":"2017","unstructured":"Hanasusanto GA, Roitch V, Kuhn D, Wiesemann W (2017) Ambiguous joint chance constraints under mean and dispersion information. Oper Res 65(3):751\u2013767","journal-title":"Oper Res"},{"key":"298_CR30","unstructured":"Hu Z, Hong LJ (2013) Kullback-leibler divergence constrained distributionally robust optimization. Available at Optimization Online"},{"key":"298_CR31","doi-asserted-by":"crossref","unstructured":"Jiang R, Guan Y (2016) Data-driven chance constrained stochastic program. Math Program 158(1\u20132):291\u2013327","DOI":"10.1007\/s10107-015-0929-7"},{"issue":"3","key":"298_CR32","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1111\/j.1937-5956.2012.01420.x","volume":"22","author":"D Klabjan","year":"2013","unstructured":"Klabjan D, Simchi-Levi D, Song M (2013) Robust stochastic lot-sizing by means of histograms. Prod Oper Manag 22(3):691\u2013710","journal-title":"Prod Oper Manag"},{"key":"298_CR33","unstructured":"Lam H (2016) Recovering best statistical guarantees via the empirical divergence-based distributionally robust optimization. arXiv preprint arXiv:1605.09349"},{"key":"298_CR34","doi-asserted-by":"crossref","unstructured":"Lofberg J (2004) Yalmip: a toolbox for modeling and optimization in matlab. In: 2004 IEEE international symposium on computer aided control systems design, pp 284\u2013289","DOI":"10.1109\/CACSD.2004.1393890"},{"key":"298_CR35","volume-title":"Knapsack problems: algorithms and computer implementations","author":"S Martello","year":"1990","unstructured":"Martello S, Toth P (1990) Knapsack problems: algorithms and computer implementations. Wiley, New York"},{"key":"298_CR36","doi-asserted-by":"crossref","unstructured":"M\u00f6hring RH (2001) Scheduling under uncertainty: bounding the makespan distribution. In: Computational discrete mathematics, Springer, pp 79\u201397","DOI":"10.1007\/3-540-45506-X_7"},{"key":"298_CR37","unstructured":"MOSEK ApS. The MOSEK optimization toolbox for MATLAB manual. Version 8.0., 2016"},{"issue":"1","key":"298_CR38","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1007\/s10107-016-1019-1","volume":"161","author":"K Natarajan","year":"2017","unstructured":"Natarajan K, Teo CP (2017) On reduced semidefinite programs for second order moment bounds with applications. Math Program 161(1):487\u2013518","journal-title":"Math Program"},{"issue":"3","key":"298_CR39","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1287\/mnsc.1080.0951","volume":"55","author":"K Natarajan","year":"2009","unstructured":"Natarajan K, Song M, Teo C-P (2009) Persistency model and its applications in choice modeling. Manag Sci 55(3):453\u2013469","journal-title":"Manag Sci"},{"issue":"3","key":"298_CR40","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1287\/opre.1110.0918","volume":"59","author":"K Natarajan","year":"2011","unstructured":"Natarajan K, Teo CP, Zheng Z (2011) Mixed 0\u20131 linear programs under objective uncertainty: a completely positive representation. Oper Res 59(3):713\u2013728","journal-title":"Oper Res"},{"issue":"4","key":"298_CR41","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1080\/14697680701455410","volume":"7","author":"G Pflug","year":"2007","unstructured":"Pflug G, Wozabal D (2007) Ambiguity in portfolio selection. Quant Finance 7(4):435\u2013442","journal-title":"Quant Finance"},{"issue":"2","key":"298_CR42","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1023\/A:1026543900054","volume":"40","author":"Y Rubner","year":"2000","unstructured":"Rubner Y, Tomasi C, Guibas LJ (2000) The earth mover\u2019s distance as a metric for image retrieval. Int J Comput Vis 40(2):99\u2013121","journal-title":"Int J Comput Vis"},{"key":"298_CR43","doi-asserted-by":"crossref","unstructured":"Shapiro A (2001) On duality theory of conic linear problems. In: Semi-infinite programming. Springer, pp 135\u2013165","DOI":"10.1007\/978-1-4757-3403-4_7"},{"key":"298_CR44","volume-title":"A reformulation-linearization technique for solving discrete and continuous nonconvex problems","author":"HD Sherali","year":"2013","unstructured":"Sherali HD, Adams WP (2013) A reformulation-linearization technique for solving discrete and continuous nonconvex problems, vol 31. Springer, Berlin"},{"issue":"2","key":"298_CR45","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1287\/moor.28.2.246.14485","volume":"28","author":"JF Sturm","year":"2003","unstructured":"Sturm JF, Zhang S (2003) On cones of nonnegative quadratic functions. Math Oper Res 28(2):246\u2013267","journal-title":"Math Oper Res"},{"issue":"1","key":"298_CR46","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1137\/S0036144504440543","volume":"49","author":"L Vandenberghe","year":"2007","unstructured":"Vandenberghe L, Boyd S, Comanor K (2007) Generalized chebyshev bounds via semidefinite programming. SIAM Rev 49(1):52\u201364","journal-title":"SIAM Rev"},{"issue":"6","key":"298_CR47","doi-asserted-by":"publisher","first-page":"1358","DOI":"10.1287\/opre.2014.1314","volume":"62","author":"W Wiesemann","year":"2014","unstructured":"Wiesemann W, Kuhn D, Sim M (2014) Distributionally robust convex optimization. Oper Res 62(6):1358\u20131376","journal-title":"Oper Res"},{"key":"298_CR48","volume-title":"Integer programming","author":"LA Wolsey","year":"1998","unstructured":"Wolsey LA (1998) Integer programming, vol 42. Wiley, New York"},{"issue":"1\u20132","key":"298_CR49","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/s10107-011-0494-7","volume":"137","author":"S Zymler","year":"2013","unstructured":"Zymler S, Kuhn D, Rustem B (2013a) Distributionally robust joint chance constraints with second-order moment information. Math Program 137(1\u20132):167\u2013198","journal-title":"Math Program"},{"issue":"1","key":"298_CR50","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1287\/mnsc.1120.1615","volume":"59","author":"S Zymler","year":"2013","unstructured":"Zymler S, Kuhn D, Rustem B (2013b) Worst-case value at risk of nonlinear portfolios. Manag Sci 59(1):172\u2013188","journal-title":"Manag Sci"}],"container-title":["Computational Management Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10287-018-0298-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10287-018-0298-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10287-018-0298-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,9]],"date-time":"2019-10-09T12:29:06Z","timestamp":1570624146000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10287-018-0298-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":50,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["298"],"URL":"https:\/\/doi.org\/10.1007\/s10287-018-0298-9","relation":{},"ISSN":["1619-697X","1619-6988"],"issn-type":[{"value":"1619-697X","type":"print"},{"value":"1619-6988","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]},"assertion":[{"value":"13 September 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 January 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 January 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}